FACULTE UNIVERSITG QUEBEC
166
MATHIEU NGOUAJIO DÉVELOPPEMENT D'UN MODÈLE DE PRÉDICTION DES PERTES DUES AUX MAUVAISES HERBES BASÉ SUR L'ANALYSE D'IMAGES NUMÉRIQUES Thèse présentée à la Faculté des études supérieures de I'Universit6 Laval pour l'obtention du grade de Philosophiae Doctor (Ph.D.) Département de phytologie FACULTE DES SCIENCES DE L'AGRICULTURE ET DE L'ALIMENTATION UNIVERSITG LAVAL QUEBEC AVRIL 1999 O Mathieu Ngouajio, 1999
Transcript of FACULTE UNIVERSITG QUEBEC
MATHIEU NGOUAJIO
DÉVELOPPEMENT D'UN MODÈLE DE PRÉDICTION DES PERTES DUES AUX
MAUVAISES HERBES BASÉ SUR L'ANALYSE D'IMAGES NUMÉRIQUES
Thèse
présentée
à la Faculté des études supérieures
de I'Universit6 Laval
pour l'obtention
du grade de Philosophiae Doctor (Ph.D.)
Département de phytologie
FACULTE DES SCIENCES DE L'AGRICULTURE ET DE L'ALIMENTATION
UNIVERSITG LAVAL
QUEBEC
AVRIL 1999
O Mathieu Ngouajio, 1999
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Canada
Du fond du cœur, je dédie cette thése à :
- mon 6pouse : Ndongrno Babette Rita
En temoignage de mon amour ;
- mes enfants : Ngouajio Erica
Ngouajio Tankeu Boris Duvalier
Ngouajio Sokeng Amanda Laurette
Ngouajio Téguiafa Lynne Lionnelle
En reconnaissance de leur excellente tenue et comme exemple A dépasser ;
- mes parents : Sokeng David
TsaguéJeanne
Pour tout ce qu'ils ont fait pour mon éducation ;
- mon feu oncle : Tankeu Pierre Loti
Qui a guidé mes premiers pas vers l'école.
RÉSUMÉ LONG
Au cours de la demiére decennie, l'apparition des mauvaises herbes
résistantes aux herbicides, la nécessité d'optimiser les coûts de production et les
préoccupations de protection de l'environnement ont mis des pressions importantes
sur les producteurs pour réduire l'utilisation des herbicides de synthèse en ne traitant
que lorsque c'est nécessaire, avec la dose requise et sans sacrifier les rendements.
Ceci nécessite entre autres, le développement d'une technologie intégrant d'une part
un outil fiable de dépistage et de quantification des mauvaises herbes en début de
cycle de la culture, et d'autre part un modéle précis et versatile de prédiction des
pertes permettant de décider si oui ou non il faut intervenir. La surface foliaire des
mauvaises herbes s'est avérée comme étant un indice fiable pour prédire les pertes
de rendement des cultures. Cependant, la mesure de cette variable requiert
beaucoup de temps et de manipulations. La couverture foliaire (projection verticale
des plantes sur le sol) a été proposee comme une alternative à la surface foliaire et
son acquisition pourrait se faire rapidement par analyse d'images. Plusieurs modèles
empiriques ont été développés pour relier la présence des mauvaises herbes au
rendement des cultures. Ceux utilisant la surface foliaire des plantes ont été les plus
efficaces, mais peu pratiques a cause des difficultés d'acquisition de la variable.
Nos travaux ont été entrepris dans le but de contribuer au développement d'un
outil d'aide à la prise de décision permettant de prédire les pertes de rendement dues
aux mauvaises herbes a partir des images obtenues tôt en début du cycle de
croissance, afin de mieux cibler les interventions de désherbage. Les objectifs
spécifiques étaient : i) d'exploiter la technique d'analyse d'images pour estimer la
couverture foliaire des plantes et établir la relation entre ces données et les mesures
destructives de surface foliaire, ii) d'étudier et de comparer la performance des
estimés de couverture foliaire et celle des mesures de surface foliaire dans les
modèles prévisionnels, iii) de développer et de valider un modéle prévisionnel
performant et mieux adapt6 aux estimés de couverture foliaire et iv) d'étudier les
effets de la hauteur de prise de vue des images et du stade de croissance de la
culture sur la qualité des prédictions.
La capacité du système d'analyse d'images développé à estimer la couverture
foliaire a été testée par simulation et au champ. En simulation, le système présentait
à la fois une grande exactitude et une forte précision. La validation sur le terrain a
confirmé cette observation. La relation entre les estimés de couverture foliaire et les
mesures de surface foliaire variait en fonction de l'architecture des plantes et de leur
stade de développement. Les corrélations Btaient plus étroites aux stades précoces
de développement des plantes.
Une expérience au champ a été menée pour ktudier la performance des
estimés de couverture foliaire (obtenus par analyse d'images) et de surface foliaire
(mesurés au planimètre) sur les modèles prévisionnels. Cet essai a confirmé la
valeur prédictive de la surface foliaire relative des mauvaises herbes (rapport de la
surface foliaire des mauvaises herbes sur la surface foliaire totale des plantes). La
substitution de cette variable par la couverture foliaire relative des mauvaises herbes
a procuré un ajustement adéquat des modéles. Les valeurs de ? étaient du même
ordre de grandeur justifiant, dans les tests ult&ieurs, l'usage de la couverture foliaire
relative plus facile à mesurer.
Un nouveau modèle adapté à cette variable a été dérivé et validé. Ce modèle
sigmoïde à quatre paramètres intégrait les sous-modèles linéaire, hyperbolique,
sigmoïde symétrique et logistique asymétrique. Pendant la validation, le nouveau
modèle a supplanté tous les sous-modèles, A l'exception du type hyperbolique dont
les performances étaient comparables. La grande flexibilité du modèle et sa capacité
à détecter des cas particuliers, ont valu sa recommandation comme support à la prise
de décision.
AVANT-PROPOS
Cette thèse est constituée de quatre articles scientifiques formant chacun un
chapitre. Le style des chapitres correspond à celui exigé pour la soumission
d'articles dans les journaux Weed technology, Weed Science, Weed Research et
Crop Protection. Le premier article a été publié dans Weed technology (Volume
12:446-453). Le deuxiéme article est sous presse dans Weed Science (Volume
47:OOO-000). Le troisième article a été accepté pour publication dans Weed
Research. Le dernier a kt6 soumis pour publication dans Crop Protection.
REMERCIEMENTS
La réalisation de ce travail a At6 reridue possible grâce à la contribution de plusieurs
personnes morales et physiques que je ne pourrais entiérement citer ici. J'aimerais
cependant remercier particulièrement :
Mon épouse Ndongrno Babette Rita qui m'a incité à revenir aux études aprés
cinq années d'arrêt ; elle a accepte de passer toutes ces annees dans la solitude et
les canditions les plus difficiles tout en prenant bien soin de nos enfants et en gardant
un esprit de fer ;
Le gouvernement du Canada qui à travers la bourse de la francophonie m'a
permis de continuer mes études ;
L'Université de Dschang au Cameroun pour avoir bien voulu me libérer de mes
charges d'enseignement suite B l'obtention de ma bourse ;
Mes enfants Ngouajio Erica, Ngouajio Tankeu Boris Duvalier, Ngouajio Sokeng
Amanda Laurette, Ngouajio Téguiafa Lynne Lionnelle pour leurs encouragements a
travers les interminables coups de Méphone et toutes leurs performances ;
Le Dr Gilles Leroux, directeur de thèse, pour sa disponibilité, ses
encouragements et ses conseils ; au dela des activités académiques, son support
personnel m'a permis d'honorer beaucoup d'engagements sociaux trés importants ;
Le Dr Claudel Lemieux, codirecteur de thèse, pour avoir bien voulu
m'accepter au sein de son équipe de recherche, pour toute l'attention qu'il m'a
accorde, sa rigueur scientifique et son soutien total et multiforme ;
Le Centre de recherche et de développement sur les sols et les grandes
cultures d'Agriculture et Agroalirnentaire Canada et le Departernent de Phytologie de
l'université Laval pour toute la logistique mise à ma disposition ;
Le Dr Jean-Jacques Fortier et M. Denis Careau pour la mise en place et
l'optimisation du logiciel d'analyse d'images ;
Les Drs Daniel Dostaler (Directeur du programme de Biologie Végétale)
François Chalifour, Jean Collin et Guy Allard (membres de mon comité de pilotage)
pour les recommandations faites à mon projet et leurs conseils pendant mes 6tudes ;
M. Jocelyn Larnarre et Mme Michéle Martel pour leur assistance technique ;
les nombreux étudiants d'et6 pour leur aide ; mon collègue de tous les jours
Mohamed Ali Baghestani avec qui j'ai partagé de longues heures de laboratoire, de
compilation et de rédaction ;
Le Dr Guy Allard, pour la rigueur et les détails avec lesquels il a effectué la
prklecture de cette thèse ; le Dr Régis Baziramakenga qui a bien voulu apporter des
critiques aux manuscrits ;
Les familles Tchakounté, Defo et Djona ainsi que Mme Berthe Mouafo pour
leur amitié et leurs encouragements ;
Mme Isabelle Royer et Martin Brown pour leur précieuse amitié ;
Mes parents, mes frères, mes sœurs et tous mes amis pour leur soutien.
TABLE DES MATIÈRES
........................................................................................................ RÉSUMÉ COURT I
RÉSUMÉ LONG ......................................................................................................... Il AVANT-PROPOS ....................................................................................................... V
REMERCIEMENTS ................................................................................................... VI
TABLE DES MATIÈRES .......................................................................................... VI Il
........................................................................................... LISTE DES TABLEAUX XIV
LISTE DES FIGURES ............................................................................................. XVI
CHAPITRE 1
INTRODUCTION GÉNÉRALE PRÉDICTION DES PERTES DUES AUX
.......................... MAUVAISES HERBES ET ANALYSE D'IMAGES NUMÉRIQUES 1
.......................................... 1.2. Dépistage et quantification des mauvaises herbes 3
............................... 1.3. Estimation de la couverture foliaire par analyse d'images 5
1.4. Prédiction des pertes dues aux mauvaises herbes .......................................... 6
............................................................ Hypothèses et objectifs de recherche 1 1
............................................................................................... 1.5.1 . Hypothèses 12 ................................................................................................... 1.5.2. Objectifs. 1 3
..................................................................................................... 1 -6. Références 14
CHAPITRE 2
VALIDATION D'UN MODULE SEMI-AUTOMATISE D'ESTIMATION DE LA
COUVERTURE FOLIAIRE D'UNE CULTURE ET DES MAUVAISES
HERBES PAR ANALYSE D'IMAGES NUMÉRIQUES .............................................. 19
.................................................................................... 2.1. Résumé du chapitre 2 20
2.2. Validation of an Operator-Assisted Module to Measure Weed and Crop Leaf
........................................................................... Cover by Digital Image Analysis 22
...................................................................................... 2.2.2. INTRODUCTION 23
.................................................................. 2.2.3. MATERIALS AND METHODS 26 .......................................... 2.2.3.1 . l mage Acquisition. Storage. and Analysis 26
2.2.3.2. La boratory Experiment ....................................................................... 27 2.2.3.3. Field Experîrnents .............................................................................. 29
.................................................................................... 2.2.3.4. Data Analyses 30
2.2.4. RESULTS AND DISCUSSION ................................................................. 31 2.2.4.1 . Laboratory Experiment ....................................................................... 31 2.2.4.1 . Field Experiments .............................................................................. 31
................................................................................ 2.2.6. LITERATURE CfTED 36
CHAPITRE 3
PRÉDICTION DES PERTES DE RENDEMENT DU MA'& A PARTIR
D'OBSERVATIONS PRÉCOCES DE LA SURFACE FOLIAIRE RELATIVE
ET DE LA COUVERTURE FOLIAIRE RELATIVE DES MAUVAISES
HERBES ................................................................................................................... 45
3.1 . Résumé du chapitre 3 .................................................................................. 46
3.2. Prediction of corn (Zea mays) yield loss from early observations of the
..... ................................... relative leaf area and the relative leaf cover of weeds .. 48
3.2.1 . Abstract ............................................................................................... 4 8
3.2.2. Introduction ............................................................................................... 50
3.2.3. Materials and Methods .......................................................................... 52 3.2.3.1 . Experimental Sits ............................................................................... 52 3.2.3.2. Experimental Procedures ................................................................... 52 3.2.3.3. Data Analyses .................................................................................... 54
3.2.4. Results and Discussion .......................................................................... 5 5
3.2.5. Literature Cited ...................................................................................... 6 1
CHAPITRE 4
MODÈLE SIGMOTDE FLEXIBLE RELIANT LA COUVERTURE FOLIAIRE
RELATIVE DES MAUVAISES HERBES AU RENDEMENT DE LA CULTURE
................................................. ET COMPARAISON AVEC D'AUTRES MODELES 73
4.1. Résumé du chapitre 4 .................................................................................. 74
4.2. A flexible sigrnoidal model relating crop yield to weed relative leaf cover and
....................................................................... its cornparison with nested models 76
.................................................................................................. Summary 76
Introduction ............................................................................................... 77
............................................................................. Materials and methodç 79 ................................................................................. 4.2.3.1 . Model derivation 79
................................................................................. 4.2.3.2. Nested models 8 1 ...................................................... 4.2.3.3. Model Validation and cornparison 83
.............................................................................. 4.2.3.4.Statistical analyses 84
............................................................................. 4.2.4. Results and discussion 84 4.2.4.1. The performance of the model (unrestricted) ..................................... 84
.............................................................................. 4.2.4.2. Model cornparison 86
............................................................................................... 4.2.5. References 91
XII
CHAPITRE 5
EFFETS DE LA HAUTEUR DE PRISE DE VUE DES IMAGES ET DU
STADE DE CROISSANCE DE LA CULTURE SUR LES ESTIMES DE
COUVERTURE FOLIAIRE ET LEUR PERFORMANCE DANS LES
MODÈLES PRÉVISIONNELS ................................................................................ 101
5.1 . Résume du chapitre 5 .................................................................................. 102
5.2. Influence of images recording height and crop growth stage on leaf cover
estimates and their performance in yield prediction models ................................ 104
5.2.1. Abstract .................................................................................................. 104
.............................................................................................. 5.2.2 1 ntroduction 105
........................................................................... 5.2.3. Materials and Methods 107 ........................................ 5.2.3.1 . ExperÎmental site and growing conditions 107
................................................................. 5.2.3.2. Experimental procedures 108 .................................................................................. 5.2.3.3. Data analyses 110
5.2.4. Results and discussion ......................................................................... 111 ....................................................................... 5.2.4.1 . Leaf cover estimation 111
................................................................................ 5.2.4.2. Yield prediction 112
.............................................................................................. 5.2.5 References 117
CHAPITRE 6
CONCLUSION GÉNÉRALE (SYNTHÈSE) ............... ... .......................... ...... ...... .... . 129
REFERENCES BIBLIOGRAPHIQUES .... ...... ........ ... ... ......... ... ....... ....... ...... ..... . .... . 137
XIV
LISTE DES TABLEAUX
Chapitre 2
1. Total ar9a and range of size of cardboard pieces used in the laboratory
experiment conducted to test the effectiveness of the operator-assisted
module. The simulated conditions assumed no overiapping in the canopy.
They accounted for a crop at six different growth stages and a weed at
.............................................................................. different levels of infestation. 39
2. Corn and weed growth stages at the time of leaf area measurements in
field experiments conducted at Saint-Augustin (Quebec) in 1996. ..................... 40
Chapitre 3
1. Total monthly rainfall and mean temperature during the 1996 and 1997
growing seasons, and long term average (30 y e a r ~ ) ~ ........................................ 65
2. Chronology of events (sowing, emergence, sampling, and harvest) for
the 1996 and 1997 growing seasons .................................................................. 66
................................................... 3. Corn and weed growth stage at sampling time 67
4. Observed maximum corn grain yield loss, and parameter estimates for the
prediction model (equation 1) using the relative leaf area and the relative
Ieaf cover of weedsa .......................................................................................... 6 8
5. Cornparison of the residual mean squares (RMS) for corn grain yield and
corn total biornass, obtained from model fitting using the relative leaf area
and the relative leaf cover of weeds .................................................................. 6 9
Chapitre 4
1. Regression parameters obtained in maize yield prediction using the flexible
sigrnoïdal model (unrestricted model, equation 8) and nested models,
(restricted models, equations 9, 10 and 1 1). The data were recorded in
1996 and 1997, at the four- and at the eight-leaf stages (fully expanded
leaves) of maize. ................................................................................................ 96
2. The likelihood ratio (LR) and the Wald (W) test statistics for compatison of
the performances of the restricted models to the unrestricted model used
for maize yield prediction. .................................................................................. -97
Chapitre 5
1. Total monthly rainfall and mean temperature during the 1996 and 1997
growing seasons, and long term average (30 yearsIa ...................................... 122
2. Weed growth stage at the four-, six-, and eight-leaf stage of maize growth ..... 123
3. The effect of camera shooting height on the area covered by the picture,
...................... the spatial resolution of images and maize leaf wver estimates 124
4. The effect of the camera shooting height on maize average leaf cover
estimates (% ground cover) at different growth stages ..................................... 125
5. Regression parameters calculated from maize yield prediction using the
relative leaf cover of weeds and the sigmoidal model (equation 1).
Data were recorded at the six-leaf stage (fully expanded leaves) of maize
with the camera at 3.3 m above plant canopy. ................................................. 126
XVI
LISTE DES FIGURES
Chapitre 2
Relationship between !eaf cover estimated by the operator-assisted
module and leaf area measured with an optical area meter: data from
the laboratory experiment in which crop and weed populations were
...................................................................... simu lated with cardboard pieces. 4 1
Relationship between corn leaf cover estimated by the operator-assisted
module and leaf area measured with an optical area meter at two growth
stages of corn: corn was grown in cornpetition with common larnbsquarters,
barnyardgrass, or a mixture of both species (controlled weed populations),
or in cornpetition with naturally occurring weed species (natural weed
populations). ....................................................................................................... 42
Relationship between weed leaf cover estimated by the operator-assisted
module and weed leaf area measured with an optical area meter at two
growth stages of corn: corn was grown in competition with common
lambsquarters, barnyardgrass, or a mixture of both species. ............................. 43
Relationship between weed leaf cover estimated by the operator-assisted
module and weed leaf area measured with an optical area meter at two
growth stages of corn: data from a field experiment in which corn was
grown in cornpetition with a natural weed infestation .......................................... 44
XVI 1
Chapitre 3
Corn grain yield loss as a function of weed relative leaf area (-a-) and
relative leaf cover ( - - 0 - - ) determined at the four-leaf stage of corn growth
in 1996 and 1997 using a two-parameter empirical model
(YL= qLw/[l+(q/.-7)Lwn. Corn was infested with one or two weed
species, at different densities. ............................................................................ 70
Corn grain yield loss as a function of weed relative leaf area (-a-) and
relative leaf cover ( - - 0 - * ) determined at the eight-leaf stage of corn growth
in 1996 and 1997 using a ho-parameter empirical modei
(YL= qLw/[l+(q/m-7)Lw). Corn was infested with one or two weed
species, at different densities. ............................................................................ 71
Corn grain yield loss as a function of weed relative leaf area (--) and
relative leaf cover ( = - O - . ) detemined at the four- and at the eight-leaf
stages of corn growth in 1996 and 1997 using a Wo-parameter empincai
model (YL= qLw/[l +(q/m-7)Lw). Corn was infested with different densities
of a natural weed population ............................................................................... 72
Chapitre 4
1. The functional forms of the flexible sigmoidal model (unrestricted model) as
affected by the values of the parameters: with 6 = 1, the curve is either a
concave hyperbola (y' < 1), a straight line (y' = l), or a convex hyperboia
(y' > 1 ); the curve is either a symmetric (y' = 1 ) or an asymmetric (y' # 1 )
sigmoid, the upper portion being concave (6 > 1) or convex (6 < 1) to the
origin. For the purpose of this demonstration, crop yield is expressed in
................... t ha", and a and Y. are arbitrary set at 1 and 9 t ha-', respectively. 98
XVI II
2. Maize yield as a function of weed relative leaf cover recorded at the
four- and at the eight-leaf stages of maize growth in 1996. The non-linear
regression models are: the unrestricted model (-a-), the restricted
model 1 (- - l - -), the restricted model 2 (- -), and the restricted
mode1 3 (..... @..... ) ................................................................................................. 99
3. Maize yield as a function of weed relative leaf cover recorded at the
four- and at the eight-leaf stages of maize growth in 1997. The non-linear
regression models are : the unrestricted model (-e-), the restricted
model 1 (- - - -), the restricted mode12 (- -), and the restricted
mode1 3 (.. ...@ ..... ). .............................................................................................. 1 O0
Chapitre 5
1. Residual mean squares (RMS) obtained by fitting the yield prediction
model with maize yield and weed relative leaf cover. Leaf cover estimates
were obtained from images recorded at different heights and crop growth
stages, using a digital image analysis technique. The regression rnodel
used was: Y = [ Y ~ + ~ ( L J(I -LC)y)T1 [l + a ( ~ d ( l -~,)y)']. ........................................... 1 27
2. Maize yield as a function of weed relative leaf cover estirnated from
images taken 3.3 rn above the ground at the six-leaf stage of maize
development in 1996 and 1997. The rnodel used was the following :
Y=[Y~+U(L~(I - L& )~ I [1 +a(Ld(l -~&)q. ............................................................ 1 28
CHAPITRE 1
INTRODUCTION GÉNÉRALE
PRÉDICTION DES PERTES DUES AUX MAUVAISES HERBES
ET
ANALYSE D'IMAGES NUMÉRIQUES
1 .i Problématique
L'introduction à la ferme d'herbicides de synthése au lendemain de la
deuxième guerre mondiale a constitué un virage tres impoeant dans les systkmes de
production agricole. Les désherbages manuel et mécanique ont été progressivement
remplacés par la lutte chimique, avec pour avantage immédiat, une capacité accrue à
désherber de grandes superficies (Duke, 1996). La lutte chimique contre les
mauvaises herbes a connu une expansion tellement importante au cours des 50
dernières années, qu'aujourd'hui les herbicides représentent environ 60 à 70% du
volume total des pesticides utilisés en agriculture (Leroux et al., 1990; Duke, 1996).
En 1987, sur un total de 708 millions de dollars depenses par les agriculteurs
canadiens pour l'achat des pesticides, les herbicides ont compté pour S I 1 millions
(Anonyme 1, 1989). Face à t'importance des degâts causés par les mauvaises
herbes, les herbicides de synthèse grâce A leur grande efficacité, se sont imposés
comme outils de désherbage par excellence (Kropff et Lotz, 1992a; Swanton et al.,
1993; Lotz et al., 1995). Avec l'intensification de l'agriculture, les herbicides sont
rapidement devenus une partie intégrante du système de production chez la plupart
des fermiers. Ces derniers utilisent des applications prophylactiques de type «police
d'assurance » en prélevée de la culture pour se prémunir contre les effets néfastes
des infestations éventuelles (Lemieux et al., 1995). Cette pratique conduit
inévitablement a des traitements qui ne sont pas toujours justifiés, et avec comme
conséquence non seulement une augmentation des coûts de production, mais aussi
des effets potentiellement préjudiciables à I'environnement. Au cours de la dernière
décennie, l'apparition des mauvaises herbes resistantes aux herbicides, la nécessité
d'optimiser les coûts de production et les préoccupations de protection de
I'environnement ont mis des pressions importantes sur les producteurs pour réduire
l'utilisation des herbicides de synthèse (Swanton et Weise, 1991; Kropff et Lotz,
1992a, 1992b; Maxwell et Mortimer. 1994; Duke, 1996; Shaner, 1997;). Ceci a
conduit au développement du concept de lutte intégrée contre les mauvaises herbes,
concept qui vise entre autres la rationalisation de l'utilisation des herbicides, en ne
traitant que lorsque c'est nécessaire, avec la dose requise et sans sacrifier les
rendements (Swanton et Weise, 1991 ; Hall et al., 1992; Kropff et Lotz, 1992a, 1992b;
Dieleman et al., 1995; Lemieux et al., 1995; Lotz el al., 1995). Une réduction de la
fréquence et des doses d'utilisation des herbicides peut contribuer à coup sûr non
seulement à réduire les coûts d'opération de la ferme, mais aussi à améliorer la
qualité de l'environnement (Dieleman et al., 1995; Lemieux et al., 1995; Lotz et al.,
1995). Mais il incombe de s'assurer que ces modifications n'entraîneront pas des
pertes de rendement. On pourra sans doute y arriver en mettant a la disposition des
producteurs une technologie de prédiction des pertes et de prise de décision
suffisamment efficace pour convaincre ces derniers qu'il est possible d'abandonner
les traitements préventifs systématiques au profit des applications justifiées, faites en
postlevée. Cette technologie doit comporter d'une part, (1 ) un outil puissant, rapide,
peu coûteux et fiable de dépistage et de quantification des mauvaises herbes en
debut de cycle de la culture, et d'autre part, (2) un modèle précis et versatile de
prédiction des pertes dues aux mauvaises herbes permettant de décider si oui ou non
il faut intervenir.
1.2. Dépistage et quantification des mauvaises herbes
Bien que répondre a la question de savoir si oui ou non il y a des mauvaises
herbes dans une parcelle semble facile, il est cependant très difficile de déterminer le
taux d'infestation, c'est-à-dire de quantifier leur présence. Les variables les plus
couramment mesurées sont : la densité, la biomasse, la surface foliaire et la
couverture foliaire.
La détermination de la densité est une des méthodes classiques d'estimation
du taux d'infestation des mauvaises herbes. Ceci est géneralement fait en comptant
le nombre de plants dans des quadrats sélectionnés au hasard. Cependant, les
mauvaises herbes ont une distribution en grappe, et leur germination s'échelonne
généralement sur une période plus ou moins longue, ce qui empêche une estimation
précise et rapide de leur nombre (Brain et Cousens, 1990; Kropff et Spitters, 1991 ;
Kropff et al., 1992; Lemieux et al., 1992; Wiles et al., 1993; Knezevic et al., 1 995). La
densité représente donc un indicateur trks pauvre du taux d'infestation car elle ne
tient pas compte des espéces, de la période d'émergence, de la taille, de la
distribution spatiale et du stade de développement des mauvaises herbes (Kropff,
1988; Brain et Cousens, 1990; Kropff et Spitters, 1991; Kropff et al., 1992; Kropff et
Lotz, l992b; Morin et al., 1993; Wiles et al., 1993; Lotz et al., 1994; Knezevic et al.,
1995; Lemieux et al., 1 995).
La biomasse des mauvaises herbes permet de quantifier de maniére adkquate
leur taux d'infestation et leur impact sur les cultures (Wilson et al. 1995; Tanji et al.
1997). Cependant, a cause de sa nature destmctive et de l'ampleur des
manipulations requises, cette méthode est plus utilisée pour l'analyse de la
croissance des plantes que pour les prédictions de rendement.
La surface foliaire des mauvaises herbes s'est montrée comme étant un indice
très reprhsentatif de leur taux d'infestation (Lotz et al., 1994; Dieleman et al., 1995;
Knezevic et al., 1995). Cette variable se mesure généralement avec un planimètre,
après des prblèvements destructifs. L'obtention des données par cette méthode est
d'une application pratique tres limitée à cause des exigences en temps, de l'ampleur
des manipulations et de la nécessité de procéder a une coupe destructive de la
végétation.
Une méthode alternative à la surface foliaire est la determination de la
couverture foliaire des mauvaises herbes comme indice de prédiction (Kropff, 1988;
Lotz et al., 1995, 1994). La couverture foliaire est la surface obtenue par projection
verticale des feuilles sur le sol. La couverture foliaire des plantes, si elle était
mesurée, serait probablement tres proche de la surface foliaire aux stades précoces
de croissance (Kropff, 1988). Plusieurs techniques sont utilisées pour estimer la
couverture foliaire des mauvaises herbes, parmi lesquelles la plus simple est
l'estimation visuelle. Cette technique subjective fournit des données qui varient
beaucoup d'un observateur B l'autre (Kropff, 1988; Lotz et al., 1994). Certains
chercheurs ont détemin6 la couverture foliaire en plaçant un cadre quadrillé
directement sur la parcelle concernée et en comptant les carreaux couverts par
chaque espèce (Lotz et al., 1994, 1995). ou en faisant la même chose, mais plutôt
sur une photographie de la parcelle (Lutman, 1992). Ces techniques, bien que
fournissant des données de qualit&, restent cependant très exigeantes en temps et
en main d'œuvre et donc inappropriées pour une utilisation pratique. L'utilisation de
la réflectance spectrale comme méthode d'estimation de la couverture foliaire pourrait
être une technique très simple et très rapide, mais son efficacité est limitée par son
incapacité a distinguer la culture des mauvaises herbes (Lotz et al., 1994).
Du fait de toutes ces limitations, il devient primordial de trouver de nouvelles
méthodes pour évaluer l'importance des populations de mauvaises herbes. Ces
méthodes devront être rapides et objectives afin de pouvoir s'intégrer facilement A un
outil de prise de décision qui puisse être utilisé au champ.
1.3. Estimation de la couverture foliaire par analyse d'images
Aux vues des progrès dans les domaines de l'informatique et de l'imagerie,
Lemieux et ai. (1995) ont proposé d'utiliser l'analyse d'images numériques pour
déterminer la couverture foliaire des mauvaises herbes et de la culture au début du
cycle de croissance de la culture. La démarche proposée consiste à exploiter les
caractéristiques des images numériques. Ces demiéres sont composées d'un
ensemble de pixels dont chacun véhicule deux types d'informations : une information
spectrale (longueur d'onde) et une information spatiale (provenance de la longueur
d'onde) (Lemieux et al. 1995). La signature spatiale de l'image permet de
reconnaître la forme des objets, alors que la signature spectrale permet de distinguer
ces objets, en fonction de la longueur d'onde de la lumière réfléchie. Ces deux types
d'information peuvent être mis a profit pour différencier les plantes du sol et la culture
des mauvaises herbes.
Une des premières tentatives d'estimation de la couverture foliaire des plantes
A partir des images prises dans des parcelles a 6té r6alisée par Lutman (1992). Pour
le faire, ce dernier plaçait une grille avec 200 pointes sur une carte photo de la
parcelle et comptait le nombre de pointes correspondant A la culture, aux mauvaises
herbes et au sol. Depuis lors, la technique a évolué sensiblement et d'autres travaux
de recherche sur l'utilisation de l'analyse d'images pour determiner la couverture
foliaire des plantes ont été publiés (Carson et a/., 1995; Andreasen et al., 1997;
Andrieu et al., 1997). Carson et al. (1995) ont utilisé l'analyse d'image numérique
multispectrale de haute résolution pour détecter les populations de Hieracium
pratense. L'analyse d'images provenant d'une camera fixée sur un avion volant a 2,7
km d'altitude leur a permis de détecter les mauvaises herbes grâce au contraste de
couleur causé par leurs fleurs jaunes. Cette méthode reste cependant peu
appropriée comme technique de prédiction. En effet, pour être intégrée à un outil de
prise de décision, la détection doit se faire à l'échelle de la ferme et à des stades de
développement suffisamment précoces pour qu'il soit possible de mettre en place les
moyens de lutte les plus appropriés.
Andrieu et ai. (1997) de leur côté ont utilisé des photos prises sur des plus
petites parcelles pour estimer le recouvrement du sol par les plantes. Lemieux et al.
(1995) ont quant à eux proposé d'utiliser la signature spectrale des plantes afin
d'évaluer la proportion du sol occupée par les mauvaises herbes et par la culture.
Bien que les techniques proposées par les uns et les autres soient très prometteuses,
elles restent encore au stade de développement, et les travaux de validation en
conditions réelles n'ont pas encore été réalisbs. Par ailleurs, le d6veloppement d'un
outil d'aide a la décision n'est pas simplement dépendant de la disponibilité d'un
instrument de dépistage et d'évaluation des populations de mauvaises herbes, mais
aussi de la disponibilité d'un modèle de prédiction des pertes dues a ces dernières.
1.4. Prédiction des pertes dues aux mauvaises herbes
Plusieurs modèles empiriques ont ét6 développés pour relier la présence des
mauvaises herbes aux pertes de rendement (Dew, 1972; Zimdahl, 1980; Cousens et
al., 1984; Tisdell, 1984; Cousens, 1985a, 198513; Cousens et ai., 1987; Kropfi, 1988;
Spitters et al., 1989; Kropff et Spitters, 1991 ; Kropff et Lotz, l992a. 1992b; Lotz et al.,
1994, 1995; Swinton et Lyford, 1996). Ces modèles utilisent des variables comme la
densité des mauvaises herbes, leur pérÏode de lev6e, leur surface foliaire relative, ou
leur couverture foliaire relative.
Le modèle de prédiction le plus simple est celui proposé par Dew (1 972). 11 est
représent6 par l'équation suivante :
00 Y est le rendement de la culture, br l'indice de compétition et D la densité des
mauvaises herbes. L'indice de compétition est un paramètre déterminé
expérimentalement. Ce modèle est très peu réaliste car en plus d'être trop simpliste,
la courbe ne passe pas par l'origine, ce qui implique des pertes de rendement même
en l'absence de mauvaises herbes. La pente initiale de la courbe ainsi que son
asymptote sont infinies, ce qui rend le modèle inapproprié à la fois aux faibles et aux
fortes densités de mauvaises herbes. Par la suite, les travaux de Cousens et al.
(1984,1985a) ont mené à la proposition d'un modèle Ci deux paramètres, plus
élaboré, représenté par une équation hyperbolique reliant la densité des mauvaises
herbes au rendement de la culture :
avec YL le pourcentage de perte de rendement, D la densité des mauvaises herbes, i
le pourcentage de perte de rendement par plant de mauvaise herbe et par unité de
surface à mesure que D s'approche de zéro et a le pourcentage de perte de
rendement B mesure que D approche l'infini. Une autre version de cette équation a
été développée par Cousens (1985b) pour tenir compte de la densité de la culture :
avec c qui représente la densite de la culture, et p et q qui sont des paramètres.
Toutes ces équations (1, 2 et 3) se sont revélées trés peu efficaces comme
modèles de prédiction (Cousens et al., 1987; Brain et Cousens, 1990; Kropff et al.,
1992; Kropff et Lotz, 1992a; Morin et al., 1993; Wiles et al., 1993; Lot, et al.. 1994,
1995; Knezevic et d, 1995). 11 s'agit donc d'une autre démonstration à l'effet que la
densité n'est pas un bon indice de prédiction des dégâts causés par les mauvaises
herbes. Ce manque de précision est principalement dû au manque d'uniformité dans
la distribution spatiale et temporelle des mauvaises herbes dans les terres arables
(Brain et Cousens, 1990; Kropff et Spitters, 1991 ; Kropff et al., 1992; Wiles et al.,
1993; Knezevic et al.. 1995), jumelé avec la très grande plasticité phénotypique qui
caractérise les mauvaises herbes. Ainsi, plusieurs chercheurs considèrent que la
période relative de levée des mauvaises herbes et de la culture est un facteur
déterminant dans les phénomènes de compétition entre la culture et les mauvaises
herbes (Dew, 1 972; Cousens et al., 1 987; Brain et Cousens, 1990; Kropff et Spitters,
1991 ; Kropff et al., 1992).
Cousens et al. (1987) ont donc proposé une autre version de l'équation (2),
laquelle tient compte de la période relative de levée des mauvaises herbes par
rapport à la culture :
où YL est le pourcentage de perte de rendement, D la densite de mauvaises herbes,
T la durée de la période entre la levée des mauvaises herbes et celle de la culture et
enfin, a, b et c des coefficients de régression non linéaire. Cette nouvelle équation a
permis d'obtenir des résultats plus précis que ceux de l'équation initiale (Cousens et
al., 1987; Dieleman et al., 1995). Bien que ce modéle s'ajuste trés bien avec les
données de rendement obtenues expérimentalement, il requiert non seulement un
suivi quotidien de la culture mais aussi la détermination des densités, ce qui
nécessite beaucoup de temps et de travail (Kropff et al., 1992).
Dans une étude assez récente, Swinton et Lyford (1996) ont suggéré que les
modèles sigmoïdaux décrivent mieux la relation entre la densité des mauvaises
herbes et les rendements de la culture que les modèles hyperboliques. Ils ont
proposé l'utilisation de la densité des mauvaises herbes dans le modele de Morgan-
Mercer-Flodin ou modèle MMF (Morgan et al., 1975) pour prédire les rendements. Le
modèle prend la forme suivante :
où Y est le rendement de la culture. D est la densité des mauvaises herbes, a est le
rendement minimum ou l'asymptote inférieure lorsque la densité approche l'infini, P est le rendement maximum (en l'absence de mauvaises herbes), y est une mesure de
la courbature qui détermine le taux avec lequel le rendement atteint son asymptote
inférieure (a), et 6 est une mesure de la courbature qui détermine le point a partir
duquel le rendement commence à diminuer à un rythme croissant. Les études de
simulation ont montré que la validation d'un tel modèle nécessite une large gamme
de densités, soit environ 50 (Swinton et Lyford, 1996).
Par ailleurs, Kropff (1988) a démontré, à partir des donn6es provenant d'une
expérience de simulation, qu'il existe une relation étroite entre la surface foliaire
relative des mauvaises herbes et les rendements de la culture. Kropff et Spitters
(1991) ont développé un modèle simple de pr6diction des pertes bas6 sur une
évaluation precoce de la surface foliaire relative des mauvaises herbes. Ce modèle
est représenté par l'équation suivante :
où YL est le pourcentage de perte de rendement. Lw la surface foliaire relative des
mauvaises herbes et q la compétitivité des mauvaises herbes par rapport A la culture.
Ce modèle est utilisable en présence de plusieurs espèces de mauvaises herbes
(Kropff et Spitters, 1991). Les travaux de validation ont montré que ce modèle de
prédiction tient compte la fois de la densité des mauvaises herbes et de leur
période de germination par rapport A la culture (Kropff et Spitters, 1991; Kropff et al.,
1992b; Kropff et Lotz, 1992a; Lotz et al., 1994, 1995; Dieleman et al., 1995; Knezevic
et aL, 1995).
Une autre version de l'équation (5) a été récemment mise au point (Kropff et
Lotz, l992b; Lotz et al., 1992; Kropff et al., 1995). La grande nouveauté vient du fait
que ces auteurs ont tenu compte du fait qu'il existe une limite de perte de rendement
pour chaque situation. La nouvelle équation est la suivante :
ou m est la perte maximale relative de rendement.
second paramètre a permis d'améliorer la précision
L'incorporation a l'équation de ce
des ajustements des données de
rendement par rapport à l'équation (5) (Kropff et Lotz, l9Wb; Knezevic et al., 1995;
Lotz et al., 1995).
Les modèles de prédiction des pertes basés sur I'haluation de la surface
foliaire des mauvaises herbes prbsentent un potentiel réel pour une application
pratique. Malheureusement, le manque de technique rapide, précise et non
destructive d'estimation de la surface foliaire demeure une contrainte majeure à
l'utilisation de ces modèles (Lotz et al., 1994; Knezevic et al., 1995). Pour contourner
cette contrainte, Kropff et Lotz (1992a), Lotz et al. (1994, 1995) proposent la
substitution de la surface foliaire relative des mauvaises herbes par leur couverture
foliaire relative. Ainsi, les travaux réalisés par Lotz et al. (1994) ont prouvé qu'il
existe une étroite corrélation linéaire entre la surface foliaire des mauvaises herbes et
leur couverture foliaire, aux stades précoces de la culture. Ces constats suggèrent
donc la possibilité d'utiliser la couverture foliaire relative dans les modèles de
prédiction.
En exploitant les avantages de la technique d'analyse d'images et en
developpant des modèles appropriés, il et donc possible de mettre à la disposition
des producteurs un outil puissant leur permettant de prédire les pertes de rendement
en début de saison afin de décider si oui ou non des mesures d'intervention sont
nécessaires. Une telle technologie réduira la dépendance des producteurs aux
herbicides, et les retombées se feront sentir sur toute la cornmunaut&
1.5. Hypothèses et objectifs de recherche
Le dépistage et la détermination du taux d'infestation des mauvaises herbes
ainsi que le développement de modèles prévisionnels fiables adaptés à cette variable
restent donc des défis majeurs à relever pour notre agriculture. La mise à la
disposition des producteurs, d'un outil de prise de décision s'intégrant parfaitement
dans un programme de lutte intégrée, et permettant une meilleure rationalisation de
l'utilisation des herbicides de synthèse s'impose avec acuité. La couverture foliaire
des mauvaises herbes est un indice fiable de l'importance de ces plantes nuisibles,
mais son utilisation pratique reste cependant limitée par notre incapacit6 mesurer
cette variable de manière rapide et précise. De même, la plupart des modbles
prévisionnels utilisant la densite des mauvaises herbes sont peu pr6cis. et ceux
utilisant la surface foliaire sont limités par la difficulté d'acquisition de cette variable.
L'hypothèse générale de notre recherche était qu'il est possible de prédire les
pertes de rendement à partir d'images prises très tôt en début du cycle de croissance
de la culture.
Les hypothèses spécifiques étaient :
(1) La technique d'analyse d'images numériques permet d'estimer de manière
précise la couverture foliaire des plantes, et la relation entre ces estimés et
les mesures de surface foliaire est linéaire.
(2) La performance des estimés de couverture foliaire est comparable à celle
des mesures de surface foliaire dans les modales prévisionnels
(3) La qualité des prédictions peut être améliorée par le développement de
madèles plus appropriés aux estimbs de couverture foliaire
(4) La hauteur de prise de vue des images et le stade de croissance de la
culture ont des effets sur la qualité des prédictions.
De ces hypothèses ont découlé les objectifs de recherche.
1.5.2. Objectifs
L'objectif général de nos travaux était de contribuer au développement d'un
outil d'aide a la prise de decision permettant de prédire le rendement des cultures à
partir des images prises tôt en début de cycle de croissance afin de mieux cibler les
interventions de désherbage.
Les objectifs spécifiques étaient :
(1 ) Exploiter la technique d'analyse d'images pour estimer la couverture foliaire
des plantes et établir la relation entre ces données et les mesures
destructives de surface foliaire
(2) Etudier et comparer la performance des estimés de couverture foliaire et
celle des mesures de surface foliaire dans les modèles pr6visionnels
(3) Developper et valider un modèle prévisionnel performant et mieux adapté
aux estimés de couverture foliaire
(4) Étudier les effets de la hauteur de prise de vue des images et du stade de
croissance de la culture sur la qualit6 des prkdictions afin d'optimiser les
prédictions.
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CHAPITRE 2
VALIDATION D'UN MODULE SEMI-AUTOMATISE D'ESTIMATION DE
LA COUVERTURE FOLIAIRE D'UNE CULTURE ET DES MAUVAISES
HERBES PAR ANALYSE D'IMAGES NUMÉRIQUES
Ce chapitre a été publie dans Weed Technoiogy Vol. 72, pp.446-453, 1998 sous le
titre de 'Validation of an Operator-Assisted Module to Measure Weed and Crop Leaf
Cover by Digital Image Analysis.*
2.1. R6sum6 du chapitre 2
L'utilisation de la surface foliaire relative des maubaises herbes dans les
modèles mathématiques est un moyen efficace de prédiction de l'impact de ces
plantes sur le rendement des récoltes. Ceci peut contribuer à rationaliser l'utilisation
des herbicides et des autres moyens de lutte contre les mauvaises herbes.
Cependant, cet outil n'a pas reçu une reconnaissance pratique chez les producteurs,
à cause du manque de moyen rapide et précis pour estimer la surface foliaire des
plantes. La couverture foliaire (projection verticale des plantes sur le sol) a été
proposée comme méthode alternative pour estimer la surface foliaire des plantes aux
stades précoces de croissance. Un système automatisé de mesure de la couverture
foliaire base sur la technique d'analyse d'images numériques a été mis au point. Le
système comprend entre autre un module assisté par l'opérateur (OAM) dont le rôle
principal est de calibrer et valider les fonctions automatis8es. Le but de ce travail
était de démontrer la précision du module OAM sous différentes conditions
d'infestation des mauvaises herbes.
Un essai en laboratoire avec des cultures et des mauvaises herbes simulées a
été réalisé. De plus, deux expériences ont été mises en place sur le terrain, avec une
culture de maïs en compétition avec : (1) le pied de coq [Echinochloa crus-galli (L.)
Beauv], le chénopode blanc (Chenopodium album L.), et un mélange des deux
espèces, et (2) une population naturelle de mauvaises herbes.
En laboratoire, une étroite corrélation a été observée entre la couverture
foliaire estimée avec le module OAM et la surface foliaire mesurée avec un
planimètre optique (?>0,98). Dans les conditions de champ, la régression entre la
couverture foliaire du maïs (Zea mays) estimée avec le module OAM et la surface
foliaire du maïs mesurée au planimétre n'a pas donné des résultats aussi fiables
(?<0,55). Cette moindre performance du module OAM sur les données du maïs était
2.2. Validation of an Operator-Assisted Module to Measure Weed and Crop Leaf
Cover by Digital Image ~nalysis'
MATHIEU NGOUAJIO, CLAUDEL LEMIEUX, JEAN-JACQUES FORTIER,
DENIS CAREAU, and GILLES O. LEROUX*
2.2.1. Abstract
The practical application of yield loss prediction models using relative leaf area of
weeds is limited due to the lack of a quick and accurate method of leaf area
estimation. Leaf cover (the vertical projection of plant canopy on the ground) can be
used to approximate leaf area at early stages of plant development. An automated
digital image analysis system for measuring leaf cover has been developed. The
system has an operator-assisted module aimed at validating the autornated functions.
The objective of this research was to demonstrate the accuracy of the operator-
assisted module under different weed-crop conditions. A laboratory experiment was
conducted using simulated weed-crop populations. Two additional field experiments
were conducted using corn in cornpetition with: (1) common lambsquarters,
barnyardgrass, or a mixture of both species, and (2) a natural weed community. In
the laboratory experiment, a narrow linear relation was observed between leaf cover
estimated with the operator-assisted module, and leaf area measured with an optical
area meter (? > 0.98). In field experiments, the regression between corn leaf cover
estimated by the operator-assisted module and corn leaf area measured with the
'~eceived for publication August 4, 1997, and in revised f o m March 24, 1998. Contribution 574 of Soils and Crops Research and Developrnent Centre.
*~raduate Research Assistant, Department of Phytology, Laval University, Quebec, QC, Canada G1 K 7P4; Research Scientist, Agriculture and Agri-Food Canada, 2560 Hochelaga Boulevard, Sainte-Foy, QC, Canada G1V 2J3; SociBté de Mathématiques Appliquées Inc., 59 d'Auteuil Street, Québec, QC, Canada G1 R 4C2; and Professor, Department of Phytology, Laval University, Quebec, QC, Canada G1K 7P4.
optical area meter was not as good (? < 0.55). The poor performance of the module
was probably due to the overlapping and the architecture of corn leaves (especially
unexpanded leaves). Nevertheless, the system showed high precision in estimating
leaf area of both grassy weeds and broadleaf weeds (+ > 0.89). Generally, the
accuracy of the estimates decreased as the growth stage became more advanced.
Apart from its initial purpose as a calibration tool for the automated system, the
operator-assisted module can have several potential research applications. It can be
used: (1) as an alternative to destructive leaf area measurement at early stages of
plant development, (2) as a tool in the study of plant cornpetitive ability, and (3) as an
objective and quantitative support to visual observations.
Nomenclature: Common lambsquarters, Chenopodium album L. #3 CHEAL;
barnyardgrass, Echinochloa cms-galli (L.) Beauv. # ECHCG; corn, Zea mays L.
Additional index words. Machine vision, pixel classification, leaf area, leaf cuver,
CHEAL, ECHCG.
2.2.2. INTRODUCTION
Crop yield loss prediction is a major component of rational weed control decision
making. Ta decide whether or not a weed should be controlled, it is necessary to
quantify its interference (Cousens 1 985a, 1985b; Kropff and Spitters 1991 ). This task
is usually achieved through the development of empirical models (Cousens 1985a,
1985b; Dew 1972; Kropff and Spitters 1991; Kropff et al. 1995; Lotz et al. 1992,
1995). However, lheir predictive values are highly dependent on the ability to quantifi
weed interference with adequate precision.
3~etters following this symbol are a WSSA-approved cornputer code from Composite List of Weeds. Revised 1989. Available from WSSA, 81 0 East 10th Street, Lawrence, KS 66044-8897.
Several variables including plant density and leaf area have been used to evaluate
weed interference. Weed density was the variable used in the early models of weed-
crop cornpetition (Cousens 1985a; Cousens et al. 1984; Dew 1972). However,
density does not take into account differences in weed species, size, distribution, and
time of emergence relative to the crop. Not only is accurate density estimation
difficult due to the patchy distribution of weeds in fields (Brain and Cousens 1990;
Wiles et al. 1993) but. also. weeds usually emerge in successive flushes, making
density difficult to use.
Relative leaf area of the weed was used to develop yield loss prediction models.
These models showed some limitations, but they accounted for variations of both
density and relative time of weed emergence (Dieleman et a1.1995; Knezevic et al.
1995; Kropff and Lotz 1 W2a, 1992b; Lotz et al. 1994, 1995). Despite their predictive
capacity, the potential of using these models in weed management programs is
limited due to the lack of accurate, quick, and non-destructive methods to estimate
leaf area (Knezevic et al. 1995; Lotz et al. 1994).
So far, precise leaf area measurement required destructive sampling and laborious
manipulations to process foliage through an area rneter. As an alternative to leaf
area, one can use leaf cover, the vertical projection of the canopy of individual
species on the ground surface. Previous studies have shown that there is a close
relationship between leaf area and leaf cover (Kropff 1988; Lotz et al. 1994).
However, there are limitations associated with the measurement of this variable as
well. The visual estimation of leaf cover is quick but the method is subjective (Kropff
1988; Lotz et al. 1994). Some objective methods of rneasurement include the use of
a frame with cross wires on experimental plots (Lotz et al. 1994) and the use of a grid
on photographs of experimental plots (Lutman 1992). Nevertheless, these methods
are as labodous as conventional leaf area rneasurements (Lotz et al. 1994). Viewing
the recent progress in the area of irnagery, Lemieux et al. (1995) had investigated the
possibility of using digital image analysis to detemine leaf cover of weeds and crop at
an early stage of plant development.
Digital images are made up of a certain number of pixels, each carrying various
types of information. Among them are the spatial and the spectral signatures. The
analysis of the spatial information is ach ieved by stud ying the geometric
characteristics of individual groups of pixels associated with a given object. The
analysis of the spectrai information is achieved by studying the characteristics of
individual pixels, i.e., the nature of the radiation wming from the objects (Lemieux et
al. 1995). With that in mind, we initiated a study for developing an automated image
analysis system for the purpose described above. As part of this study, we needed a
tool to determine the exact proportion of weed cover and crop cover in the images.
The exact proportions are needed as a control to test and validate the automated
system. Thus, we designed a module that requires input from a qualified operator to
manually classify individual pixels in the image. The method can be defined as an
ope rat or-assisted classification me thod, and the image analysis module is referred to
as the operator-assisted module.
The objective of this work was to determine the accuracy of the operator-assisted
module, i.e., to determine whether or not the operator-assisted module could be used
as a validation tool for the autornated system.
2.2.3. MATERIALS AND METHODS
2.2.3.1. Image Acquisition, Storage, and Analysis
Image acquisition was performed using a high resolution color digital camera4
equipped with a 28-mm ultrafast auto focus lens. The camera uses a charged
coupled device with 1,012 rows and 7,524 columns, corresponding to a theoretical
resolution of about 1.54 rnegapixels. Each sensor records data in one of the three
following wave bands: red, green, or blue. The images are stored on a high-capacity
rernovable PCMCIA hard disk card, which is used for downloading to a cornputer.
A camera-supporting device was designed and built to meet a series of
requirements. The device allowed us to (1) take frames at three different heights (1.5,
1 -9, and 3.3 m); (2) maintain the camera parallel to the ground surface, irrespective of
the ground slope; and (3) mark with precision the ground area included in individual
images.
The operator-assisted module was developed on the basis of the law of large
numbers, in which the error of estimation of the proportion of different classes (soil,
crop, or weed) is given by the formula:
where E is the error in estirnating a class, p is the proportion of the variable being
estimated in the class, q is the proportion of the same variable in the remaining
classes (1 - p), and n is the sample size. According to the formula, the maximum
4 ~ o d a k professional DCS420c digital camera. Kodak Canada Inc., Toronto, Ontario, Canada, M6M 1V3.
error is obtained when p = q = 0.5. With the operator-assisted module set to select
1,000 pixels a i random, the maximum error at 95% confidence intewal is thus 3.2%.
Although an increase in the number of pixels reduces the error term, according to
preliminary tests (data not shown), 1,000 pixels was the best compromise in terms of
precision and length of time required to process an image. Besides the intrinsic error
described above, an additional source of error is due to the operator wrongly
classifying weed, crop, and soil pixels. This operator error has been estimated (data
not shown) to be an additional 1.8%, which means that the overall error of estimation
is around 5%.
The operator-assisted module also included a computer interface that allowed the
operator to proceed to pixel classification. The operator had to manually classify
each of the randomly selected pixels in one of the classes retained for analysis. In
this case, each pixel was classified as soil, crop, or weed. The output of the operator-
assisted module is the number of pixels in each of the classes.
These proportions were then converted to coverage. With the camera secured at a
height of 1.9 ml the area covered by each image was 5,400 cm2 (60 by 90 cm). By
using 1,000 pixels to estimate an area of 5,400 cm2, each pixel represents 5.4 cm2.
To convert the output of the operator-assisted module to coverage data, the number
of pixels in each class was multiplied by this factor (5.4).
2.2.3.2. Laboratory Experiment
Initial tests were conducted in the laboratory to evaluate the efficiency of the
operator-assisted module. The experiment consisted of simulating plant canopy a t
different growth stages using cardboard pieces of different sizes. Cardboard pieces
of different calors, blue for the crop and red for the weed, were used to simulate the
presence of both groups of plants.
In a preliminary experiment conducted by our group (unpublished), we observed
that corn leaf area varied from 50 to 200 cm2 at the four-leaf stage, and from 1,000 to
3,000 cm2 at the eight-leaf stage. In latter work, weed leaf area varied from 5 to 200
cm2 at the four-leaf stage of corn, and from 200 to 2,000 cm2 at the eight-leaf stage of
corn. These values were used as general guidelines to prepare 30 simulated
treatments: six simulated growth stages of the crop, and for each growth stage, five
weed infestation levels (Table 1). Actual simulated leaf area of the crop ranged from
50 cm2 at growth stage 1, the eariiest simulated growth stage, to 1,500 cm2 at growth
stage 6, the latest simulated growth stage, while that of the weed ranged from 10 to
1,700 cm2. Furthermore, to account for the variation of individual leaf size that may
be observed under natural conditions, we used cardboard pieces of different sizes as
well. Thus, within each treatment, the size of individual cardboard pieces contributing
to total crop and weed simulated area also varied. For example, at growth stage 1,
cardboard pieces simulating the crop ranged from 1 to 20 cm2. At the same growth
stage, for a simulated weed infestation level of 80%. cardboard pieces simulating the
weed ranged from 0.5 to 5 cm2. The range of sizes of individual cardboard pieces
simulating the weed and the crop within the 30 treatments is presented with more
detail in Table 1.
For each treatment, cardboard pieces were hand cut with scissors and measured
using an optical leaf area meter.' They were then rnixed and arranged randomly on a
60- by 90-cm flat sheet, avoiding overlapping. A digital image of each arrangement
was then recorded from a height of 1.9 m. The images were processed through the
operator-assisted module to obtain estimated coverage data of each component:
sirnulated crop and simulated weed.
-
'LI-COR Inc., P.O. Box 4425, Lincoln, NE 68504.
2.2.3.3. Field Experiments
Two field experiments were conducted at the Agronomy Station of Laval University
located at Saint-Augustin (Quebec). The soi1 at this site was a sandy loam. Corn
hybrid 'Pioneer 3967' was grown according to the provincial recornmendations
(Anonymous 1984). Corn was seeded May 8, 1996, at a density of 66,000 plantslha,
in rows 75 cm apart.
The first experiment included 15 levels of weed infestation. Total weed densities
retained were: 0, 5, 10, 15, 20, 30, 40, 50, 75, 100, 125, 150, 200, 250, and 300
plantslm2. Treatments also included three types of weed infestation, i.e., common
lambsquarters, barnyardgrass, or both species at equal densities, for a total of 45
treatments. Weed seeds were broadcast at the time of crop planting. The final weed
densities were achieved by successive hand weeding of the plots. Initial thinning was
conducted between 1 and 2 wk after emergence.
The second experiment also included various levels of weed infestation. Total
weed densities retained were: 0, 2, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 60, 70, 80,
90, 100, 125, 150, 200, 250, 300, and 400 plants/m2. In this experiment, the type of
weed infestation was not controlled and weed species naturally occumng on the site
were used. Final densities were achieved by successive hand weeding. The major
weed species present on the site included: common lambsquarters. barnyardgrass,
wild mustard [Brassica kaber (DC.) L. C. Wheeler], false charnomile (Matricana
mantirna L.), cornmon chickweed [Steilana media (L.) Cyrille], redroot pigweed
(Amaranthus retroflexus L.), ladysthumb (Polygonum persicana L.), and pale
smarhveed (Polygonum scabrum Moench) (Table 2).
In both experiments, treatments were assigned to 3- by 8-rn plots (four corn rows),
arranged in a completely randomized design. Digital image acquisition was done at
two different sampling dates: the four-leaf stage and the eight-leaf stage (fully
expanded leaves) of corn (Table 2). Images were taken as previously described,
each wvering an area of 60- by 90-cm. In each case, the camera-supporting device
waç positioned to include the right-hand side rniddle row of each plot. lmmediately
following image acquisition, the area covered by the image was marked, al! plants
(weeds and crop) were clipped at ground levei, and leaf area was measured using an
optical leaf area meter?
2.2.3.4. Data Analyses
The ability of the operator-assisted module to estimate leaf areas in both field and
laboratory conditions was tested by fitting simple linear regressions relating measured
Ieaf area to estimated leaf cover. The F-test and t test were used to determine the
significance of the reg ressions and regression parameters, respective1 y. Whenever
appropriate, the hornogeneity of slopes was tested by cornparhg a model with a
common slope (y j = ai + PX, + ei ) to models with individual slopes
(Y, = ai + p& + E,) (Snedecor and Cochran 1980). All calculations and statistical
analyses were performed using SAS^^ (SAS 1989).
2.2.4. RESULTS AND DISCUSSION
2.2.4.1. Laboratory Experiment
For both components of the simulated populations, the crop and the weed, there
was a strong relationship between leaf area measured with an optical area meter and
leaf cover estimated by the operator-assisted module (Figure 1). The linear
regressions between the two variables were highly significant (P < 0.0001) and
characterized by coefficients of determination (3) of 0.99. In both cases, the slopes
differed from zero (P < 0.0001) and were very close to one. Even though these
relations are narrow, they are not perfect, and one can note that the area of both
components seems to be overestimated slightly; the intercepts were 11.5 and 17.9
cm2 for the simulated crop and weed, respectively. However, the t test on the
intercepts were not significant, P = 0.15 and P = 0.16 for the simulated crop and
weed, respectively, indicating that the apparent overestimation reported above is not
a problem.
In this laboratory experiment, parameters have been set so that cover was
equivalent to area. The data reported above demonstrate clearly that under these
conditions, the cover estimates supplied by the operator-assisted module correlate
perfectly with the exact area of the different components of the images. This means
that the operator-assisted module is performing as expected and is capable of
estimating cover with high precision.
2.2.4.1. Field Experiments
In field experiments, overlapping is the rule, and comparing leaf cover
measurernents with leaf area measurements will allow one to determine how different
these two measurements are. With respect to corn, cover values supplied by the
image analysis system did not correlate well with leaf area measurements obtained
with a planirneter, regardless of the type of weed infestation and regardless of the
crop growth stage (Figure 2). The variation explained by the linear regression models
was less than 55% in al1 cases. This is possibly due to overiapping leaves and plant
architecture. In the case of overlapping, one could expect to obtain better estimates
at the four-leaf stage than at the eight-leaf stage. However, this was not the case,
suggesting that leaf overiapping may not be the major cause of the observed
discrepancy. The most probable explanation resides in foliar architecture of corn and
is related to the way corn leaves expand. As each new corn leaf expands, it also
rernains rolled up for a while. As a consequence, corn leaf wver is not a good
estimate of corn leaf area, even at early stages of plant development. However, one
must note that our final goal is to predict yield losses. In this context, it is not certain
that additionai information concerning hidden leaf area, especially that from rolled up
leaves, would be of any interest. But additional work is needed to demonstrate that
point.
With respect to weed populations, the poor correlation discussed above was not
observed, and weed cover measurements obtained with the operator-assisted
module can be used to estimate weed leaf area (Figures 3 and 4). In all cases, the
linear regressions between the two variables were highly significant (P < 0.0001) and
characterized by coefficients of determination (P) of 0.90 or higher. According to the t
tests, the slopes of these regressions were always different from zero (P < 0.0001).
while the intercepts were not at the 0.05 level of significance.
When species and densities were controlled, as was the case for the first field
experiment, the test for homogeneity of slopes revealed a differential response of the
operator-assisted module, Le., the slopes differed significantly for different growth
stages (P = 0.0516) or weed populations (P c 0.0001) (Figure 3). At the four-leaf
stage of corn, the operator-assisted module underestimated the leaf area of common
lambsquarters populations (slope = 0.90) and overestimated the leaf area of
barnyardgrass (slope = 1.31) and mixed weed population (slope = 1.23). This means
that bamyardgrass leaf area measured with the optical area meter was lower than
leaf cover estimates obtained with the operator-assisted module. This was probably
due to the rolling of leaves after they were cut, a situation not observed with cornmon
lambsquarters. At the eight-leaf stage of the crop, the leaf area of the weeds was
underestirnated, regardless of the type of weed infestation present in the plot. The
slope of the regression lines ranged from 0.52 to 0.66. This trend was expected,
since we anticipated more and more overlapping of the leaves as the growing season
went on.
When natural multispecific weed communities were present and only total weed
densities were controlled, as was the case in the second field experiment, the
proportions of the variance explained by the regression models were very high: 99%
at the four-leaf stage and 96% at the eight-leaf stage (Figure 4). Results from this
experiment were quite similar to those observed with the mono- or bispecific weed
populations. The test for homogeneity of slopes revealed a significant difference
(P < 0.0001) between growth stages. At the four-leaf stage, the operator-assisted
module overestimated weed leaf area with a slope of 1.31, as was the case for the
barnyardgrass and mixed weed populations in the first experiment. Again, the rolling
of young grass leaves after cutting could explain this trend. At the eight-leaf stage,
leaf cover data provided by the operator-assisted module were lower than the
measured leaf area, as indicated by the low slope of the regression line (0.60).
These observations agree with those found in the first experiment. They reflect a
situation that has been anticipated, since an increase of leaf overlapping is expected
as plant canopy expands.
The results of the laboratory experiment dernonstrate clearly that the operator-
assisted module can provide precise and accurate estimates of leaf cover. The
operator-assisted module can thus be used as a validation tool for the automated
system that is under development. The results of the field experiments showed that
weed leaf cover data are reliable estimates of weed leaf area, but the estimates so
obtained are biased, as they overestimate some components and underestimate
others. Similar results have been reported by Lotz et al. (1994), who suggested the
use of a correction factor to account for weed architecture when leaf cover is used.
For the purpose of crop loss prediction, these findings are very positive as they
confirm, at least in the case of weeds, that objective measurernents of plant cover can
potentially be substituted for leaf area measurements in model development.
However, our results also demonstrated that the correlation between corn leaf cover
and corn leaf area was not as good as the one observed with weeds. The
implications of such discrepancies for the purpose of crop loss prediction will have to
be addressed in subsequent work. It is noticeable that most of the problems
observed with the operator-assisted module will be encountered with the final
automated image analysis system. Thus, the latter constraint will have to be ruled out
first.
Considering the data presented herein, we are suggesting that the operator-
assisted module, apart from its original purpose, can find other research applications:
it can be a valuable alternative to destructive leaf area measurement at eariy stages
of plant development; it can serve as a tool in the study of plant cornpetitive ability;
and it can be used as an objective and quantitative support to visual observations.
ACKNOWLEDGMENTS
Funding for this research was provided in part by the Matching Investment Initiative
of Agriculture and Agri-Food Canada. The senior author is a recipient of a
scholars hip from the "Programme Canadien des Bourses d'Excellence de la
Francophonie." We thank Mr. Jocelyn Lamarre and Ms. Michèle Martel for technical
and professional assistance and summer students for field plot work, especially hand
weeding and vegetation sampling.
Anonymous. 1984. Maïs, Culture. Agdex 1 1 1120. Québec, Canada: Conseil des
Productions Végetales du Québec. 21 p.
Brain, P. and R. Cousens. 1990. The effect of weed distribution on predictions of
yield loss. J. Appl. Ecol. 2717350742.
Cousens, R. 1985a. A simple model relating yield loss to weed density. Ann. Appl.
Biol. 107:239-252.
Cousens, R. 1985b. An empirical model relating crop yield to weed and crop density
and a statistical cornparison with other rnodels. J. Agric. Sci. 105:513-521.
Cousens, R., N.C.B. Peters, and C. J. Marshall. 1984. Models of yield loss-weed
density relationships. In proceedings of the 7th International Symposium on Weed
Biology, Ecology and Systematics. Paris: Columa-EWRS. pp. 367-374.
Dew, D. A. 1972. An index of cornpetition for estimating crop loss due to weeds.
Can. J. Plant Sci. 52:921-927.
Dieleman, A., A. S. Hamill, S. F. Weise, and C. J. Swanton. 1995. Empirical models
of pigweed (Amaranthus spp.) interference in soybean (Glycine max). Weed Sci.
43:612-618.
Knezevic, S. Z., S. F. Weise, and C. J. Swanton. 1995. Cornparison of ernpirical
models depicting density of Amaranthus retroflexus L. and relative leaf area as
predictors of yield loss in maize (Zea mays L.). Weed Res. 35207-214.
Kropff, M. J. and L.A.P. Lotz. 1992a. Optimization of weed management systems: the
role of ecological models of interplant cornpetition. Weed Technof. 6:462-470.
Kropff, M. J. and L.A.P. Lotz. 1992b. Systems approach to quantify crop-weed
interactions and their application to weed management. Agric. Syst. 40:265-282.
Kropff, M. J., L.A.P. Lotz, S. E. Weaver, H. J. Bos, J. Wallinga, and T. Migo. 1995. A
two-parameter model for prediction of crop loss by weed cornpetition from eariy
observations of relative leaf area of weeds. Ann. Appl. Biol. 126:329-346.
Kropff, M. J. and C.J.T. Spitters. 1991. A simple model of crop loss by weed
competition from early observations of relative leaf area of the weeds. Weed Res.
31 197-1 05.
Kropff, M. J. 1988. Modeling the effects of weeds on crop production. Weed Res.
28:465-471.
Lemieux, C., B. Panneton, and D. Benoit. 1995. L'analyse d'image en malherbologie.
ln actes Colloque international sur la prévision et le dépistage des ennemis des
cultures, Quebec, October 10-1 2. pp.201-208.
Lotz, L.A.P., M. J. Kropff, B. Bos, and J. Wallinga. 1992. Prediction of yield loss
based on relative leaf cover of weed. Proc. First Int. Weed Control Congr.,
Melbourne, February 17-22. 2:290-293.
Lotz, L.A.P., M. J. Kropff, J. Wallinga, H. J. Bos, and R.M.W. Groeneveld. 1994.
Techniques to estimate relative leaf area and cover of weeds in crops for yield
prediction. Weed Res. 34: 1 67-1 75.
Lotz, L.A.P., J. Wallinga, and M. J. Kropff. 1995. Crop-weed interaction:
quantification and prediction. In O. M. Glen, M. P. Greaves and H. M. Anderson
eds. Ecology and lntegrated Farming Systems. London: J. Wiley. pp. 3147.
Lutman, P.J.W. 1992. Prediction of the cornpetitive ability of weeds on the yield of
several spring-sown arable crops. ln actes lXBme colloque international sur la
biologie des mauvaises herbes, Dijon, Paris, France. pp. 337-345
[SAS] Statistical Analysis Systems. 1989. SASISTAT User's Guide, Version 6, 4th
ed. Volume 2. Cary, NC: Statistical Analysis Systems Institute. 846 p.
Snedecor, G. W. and W. G. Cochran. 1980. Statistical Methods. 7th ed. Ames,
Iowa State University Press. 507 p.
Wiles, L. J., H. J. Gold, and G. G. Wiikerson. 1993. Modeling the uncertainty of weed
density estimates to improve post-ernergence herbicide control decisions. Weed
Res. 33:241-252.
Table 1. Total area and range of size of cardboard pieces used in the laboratory
experhent conducted to test the effectiveness of the operator-assisted module. The
simulated conditions assumed no overlapping in the canopy. They accounted for a
crop at six different growth stages and a weed at different levels of infestation.
Range of size of Weed Total areaC cardboard pieces
Growth infestation Treatment stagea levelb Crop Weed C ro p Weed
- -
a Arbitrary growth stages ranging from 1 (earliest) to 6 (latest). Arbitrary infestation level (proportion of weed leaf area to crop leaf area). Area measured with an optical leaf area meter.
Table 2. Corn and weed growth stages at the time of leaf area measurements in field
experiments conducted at Saint-Augustin (Quebec) in 1996.
S pecies 6 June, 1996 19 June, 1996
c o n
common larnbsquarters
barnyardgrass
wild mustard
common chickweed
redroot pigweed
ladysthumb
pale srnartweed
Number of fully expanded
4
2to 10
2 to 6
2 to 5
5t0 12
2 to 8
5 to 20
4 to 8
leaves
8
14 to40
i t o 14
7to II
15 to 30
5 to 12
20 to 40
7 to 15
Simulated crop
Simulated weed
O 400 800 1 200 1680 20'00 Leaf area (cm2)
Figure 7. Relationship between leaf cover estimated by the operator-assisted module
and leaf area measured with an optical area meter: data from the laboratory
experiment in which crop and weed populations were simulated with cardboard
pieces.
& Controlled weed populations Y=32.4+0.67X; r2=0.47
*q m. Natural weed populations Y=18.1 : 377x3 r2=0.53 O
Four-leaf stage of corn
U *.= ... - Controlled weed populations
3 Y=598.0+0. 1 7X; r2=0.50 . . G a
Natural weed populations Y=218.0+0.31X; r2=0.51
0 1000 20'00 3000 4000 50'00 Corn leaf area (cma)
Figure 2. Relationship between corn leaf cover estimated by the operator-assisted
module and leaf area measured with an optical area rneter at WO growth stages of
corn: corn was grown in competition with cornmon larnbsquarters, barnyardgrass, or a
mixture of both species (controlled weed populations), or in competition with naturally
occurring weed species (natural weed populations).
Four-leaf stage of corn Eight-leaf stage of corn
E. cnrs-galli populations 15. cnrsqelli populations Y r 7.13 + 1.31X Y = 97.0 + 0.52X
O 1 r f = 0.94
O.
Mixed weed populations Y = -4.47 + 1.23X ? = 0.90
Mixed weed poputairans Y = 33.5 + 0.66X ? = 0.97
l f
O 50 100 150 200 250 300 O 500 1000 1500 2000 2500 3000
Weed leaf area (cm2) Weed leaf area (crn2)
Figure 3. Relationship between weed leaf cover estimated by the operator-assisted
module and weed leaf area measured with an optical area meter at two growth stages
of corn: corn was grown in cornpetition with common lambsquarters, bamyardgrass,
or a mixture of both species.
stage of corn /
Eig ht-leaf stage of corn
Weed leaf area (cm2)
Figure 4. Relationship between weed leaf cover estimated by the operator-assisted
module and weed leaf area measured with an optical area meter at two growth stages
of corn: data from a field experiment in which corn was grown in cornpetition with a
natural weed infestation.
CHAPITRE 3
PRÉDICTION DES PERTES DE RENDEMENT DU MAIS À PARTIR
D'OBSERVATIONS PRÉCOCES DE LA SURFACE FOLIAIRE
RELATIVE ET DE LA COUVERTURE FOLIAIRE RELATIVE
DES MAUVAISES HERBES
Ce chapitre est sous presse dans Weed Science Vol. 47, No 00, pp.000-000, 1999
sous le titre de "Prediction of corn (Zea mays) yield loss from early observations of
the relative leaf area and the relative leaf cover of weeds."
3.1. Résume du chapitre 3
La surface foliaire relative des mauvaises herbes (rapport de la surface foliaire
des mauvaises herbes sur la surface foliaire de la culture et des mauvaises herbes)
est un indice fiable de mesure des effets de la compétition entre les mauvaises
herbes et les cultures. Cet indicateur n'est toutefois pas utilisé comme outil de prise
de décision dans les programmes de lutte integr&e, à cause du manque de moyen
rapide de mesure de la surface foliaire des plantes. Un systéme rapide et précis
permettant de mesurer la couverture foliaire a partir d'images numériques a été mis
au point et validé. Les données fournies par le systéme ont permis de démontrer qu'il
existe une étroite corrélation entre la surface foliaire et la couverture foliaire des
plantes à leurs stades précoces de croissance. Cela suggère la substitution de la
surface foliaire relative des mauvaises herbes par leur couverture foliaire relative
dans les modèles prévisionnels. Une telle opération ne peut cependant être justifiée
que par des tests de validation dans des conditions variées d'infestation et
d'environnement. C'est dans cette optique que cette recherche a été menée pour
tester et comparer l'efficacité de la surface foliaire relative et de la couverture foliaire
relative des mauvaises herbes pour prédire les pertes de rendement du maïs (Zea
mays).
Des expériences en champ ont été réalisées en 1996 et 1997 avec des
densités variables de chénopode blanc (Chenopodium album L.), de pied de coq
[Echinochloa cnisgalli (L.) Beauv], d'un mélange des deux espèces, et d'une
population naturelle de mauvaises herbes. La surface foliaire et la couverture foliaire
des plantes étaient échantillonnées aux stades quatre et huit feuilles entièrement
étalées du maïs. La surface foliaire était mesurée avec un planimètre optique. alors
que la couverture foliaire était estimbe par la technique d'analyse d'images
numériques. Un modèle prévisionnel hyperbolique à deux paramètres a été utilisé
pour ajuster les données de rendement du maïs et de surface/couverture foliaire
relative des mauvaises herbes.
Le rendement en grain du maïs ainsi que la biomasse des parties aériennes
variaient avec l'année et le type d'infestation des mauvaises herbes. Les valeurs du
paramètre q (coefficient de dégâts relatif des mauvaises herbes) étaient plus petites
en 1997 qu'en 1996. Pour les deux années, l'efficacité de la surface foliaire relative
des mauvaises herbes à prédire les rendements a été cunfirmée (? de 0,61 à 0,92).
La précision des prédictions était indépendante de la période d'6chantillonnage de la
surface foliaire (stade quatre- ou huit-feuilles entièrement étalées du maïs). La
substitution de la surface foliaire relative des mauvaises herbes par leur couverture
foliaire relative s'est soldée par une baisse de la valeur des paramètres q et m (perte
de rendement maximale) du modèle. En dépit de cette obsenration, le pourcentage
de variation expliqué par le modéle (de 0,67 a 0,90) était du même ordre de grandeur
que les valeurs obtenues avec la surface foliaire relative. Sur la base de la somme
des carrés des résidus, aucune variable ne pouvait être d6clarée supérieure à l'autre
en prédiction des pertes de rendement. Cela suggere la possibilité de remplacer la
surface foliaire relative des mauvaises herbes par leur couverture foliaire relative
(plus facile à mesurer) dans les modèles prévisionneis.
L'utilisation de la couverture foliaire relative des mauvaises herbes dans les
modèles prévisionnels comme outil de prise de décision pourrait encore nécessiter
des améliorations majeures avant que ce dernier ne trouve une niche dans les
programmes de répression des mauvaises herbes. De telles am6liorations incluent
entre autres des meilleures techniques d'échantillonnage et d'analyse d'image, le
développement et la validation de modèles empiriques appropriés à chaque situation,
et un meilleur ciblage du stade de croissance de la culture auquel l'estimation de la
couverture foliaire des plantes doit être faite. Ces travaux supplémentaires devront
tenir compte de la logistique de chaque unité de production, de la résolution et de la
précision du système d'analyse d'images utilisé, et des limitations imposées par
l'usage des herbicides de postlevée et des méthodes alternatives de lutte.
3.2. Prediction of corn (Zea mays) yield loss from early observations of the
relative leaf area and the relative leaf cover of weeds
Mathieu Ngouajio, Claudel Lemieux and Gilles D. Leroux
3.2.1, Abstract
The relative leaf area of weeds is a good predictor of the outcome of weed-crop
cornpetition. However, this variable has not been used in decision making tools for
integrated weed management because leaf area can not be measured quickly. A
quick and accurate image analysis system for measuring leaf cover (the vertical
projection of plant canopy on the ground) has been developed and validated. This
research was conducted to compare the efficiency of weed relative leaf area and its
relative leaf cover in predicting corn yield loss. Field studies were conducted in 1996
and 1997, using varying densities of common lambsquarters, barnyardgrass,
common lambsquarters plus barnyardgrass, and a natural weed community. Corn
grain yield and biomass loss varied with the weed infestation type and the year.
Values of the relative damage coefficient of weeds (q) were smaller in 1997
compared to 1996. For both years, the relative leaf area of weeds was a good
predictor of corn yield loss (? varied from 0.61 to 0.92). The precision of the
predictions was not influenced by the leaf area sampling period (four- or eight-leaf
stages of corn). In general, smaller values of q and rn (predicted maximum yield loss)
were obtained as a consequence of using the relative leaf cover of weeds in model
fitting. However, percentages of variation explained by the model (from 0.67 to 0.90)
were similar to values obtained with the relative leaf area. On the basis of the
residual mean squares, none of the variables wuld be declared superior to the other
in yield loss prediction. The development of weed control decision making tools using
the relative leaf cover of weeds may still require additional improvements prior to
being used in weed management systems. Such improvements would include
appropriate sampling and image processing techniques. development and validation
of empirical rnodels specific to individual situations, and proper identification of the
crop growth stage at which leaf cover assessrnent has to be done.
Nomenclature: Corn, Zea mays L. 'Pioneer 3967'; common lambsquarters,
Chenopodium album L. CH EAL; barnyardgrass, Echinochloa cnrsgalli (L.) Beauv.
ECHCG.
Key words: lntegrated weed management; weed wntrol decision making; yield loss
prediction; empirical models; biomass reduction; CHEAL; ECHCG.
3.2.2. Introduction
Reducing herbicide inputs for weed control is one of the major concerns in
modern agriculture. For decades, the extensive use of these chemicals has led to the
creation of resistant weed biotypes and has contributed to the contamination of the
environment (Duke 1996; Maxwell and Mortimer 1994). As a general practice, most
herbicides used in many field crops in developed countries are applied
preemergence, regardless of the type of weed present, and regardless of the
potential outcome of their competition on the crop (Kropff and Lotz 1992a; Lemieux et
al. 1995).
The development of weed control programs with minimum herbicide inputs
requires the adoption of both an integrated weed management systern and a well
designed decision making tool based on postemergence observations of weed
infestation (Knezevic et al. 1997; Kropff and Lotz 1992a; Lemieux et al. 1995). The
forecasting system should be accurate and quick, and should predict the outcome of
weed-crop competition earîy enough to allow adequate time for control measures to
be taken (Knezevic et al. 1997).
Several empirîcal models relating crop yield losses to the presence of weeds
have been proposed (Dew 1972; Cousens 1985a, 1985b; Cousens et al. 1984, 1987;
Kropff and Spitters 1991 ; Kropff et al. 1995; Lotz et al. 1992, 1995). These models
use weed density (Dew 1972; Cousens 1985a; Cousens et al. 1984), weed and crop
densities (Cousens 1985b), weed density and relative time of emergenca compared
to the crop (Cousens et al. 1987), and relative leaf area of weeds (Kropff and Spitters
1991; Lotz et al. 1992) as predictors of crop yield loss. With field validation data,
models using the relative leaf area of weeds have gained growing attention due to
their high predictive capacity (Dieleman et al. 1995; Knezevic et al. 1995; Kropff and
Lotz 1992a, 1992b; Lotz et al. 1995, 1996). However, practical use of these models
has been limited due to the lack of a quick and accurate method of leaf area
estimation (Knezevic et al. 1995; Lotz et al. 1994). So far, precise leaf area
measurement has relied mainly on destructive sampling, followed by laborious
manipulations to process foliage through an area meter. As an alternative to leaf
area, one can use leaf cover. the vertical projection of individual species on the
ground (Kropff 1988). However, the measurement of leaf cover is as laborious as
conventional leaf area measurements (Lotz et al. 1994; Lutman 1992).
Possibilities of using spatial and spectral information of digital images for leaf
cover measurements have been suggested (Lemieux et al. 1995). This technique
has the advantage of being both quick and non destructive. Recent progress in this
area has led to the development of an image analysis system. Laboratory and field
validation experiments of the systern showed high precision in estimating leaf cover,
and high linear correlation between weed leaf area and leaf cover at early stages of
plant development (Ngouajio et al. 1998). In field experiments, leaf cover values
were shown to be generally smaller than leaf area, yet a high correlation was
obsewed between the two variables.
The narrow linear relationship between weed leaf area and leaf cover suggests
that relative leaf cover could be substituted for relative leaf area in yield loss
prediction models. This could facilitate crop monitoring in integrated weed
management programs for on time decision making, thereby contributing to a more
rational use of herbicides. However, such substitution can only be supported by
extensive field validations under different weed infestations and environrnental
conditions. This study was therefore conducted to test and compare the efficiency of
weed relative leaf area and weed relative leaf cuver in predicting corn yield losses
under different weed infestation conditions.
3.2.3. Materials and Methods
3.2.3.1. Experimental Site
Two field experiments were conducted in 1996 and 1997 at the Agronomy
Station of Laval University located at Saint-Augustin (Quebec). The soi1 at this site
was a sandy loam with 3.9% organic matter and a pH of 6.3. The major weed species
present on the site included: common lambsquarters, barnyardgrass, wild mustard
[Brassica kaber (DC.) LC. Wheeler], false charnomile (Matricaria maritirna L.),
common chickweed [Stellaria media (L. ) Cyrille], redroot pigweed (Amaranthus
retroflexus L.), ladysthumb (Polygonum persicaria L.) and pale smartweed
(Polygonum scabrum Moench).
Except for the month of May 1997, the temperatures over the two growing
seasons were similar to the long-term average. Rainfail varied in total amount and
pattern (Table 1). In 1997, snow accumulation was exceptionally high (data not
shown). The average temperature of May was below normal (Table 1), and caused a
delay in the sowing date and in weed emergence date (Table 2). The late weed
emergence (1 997) was followed by 15 days of hot and dry weather (June 01 to 15).
These conditions caused crust formation at the soi1 surface, which affected plant
growth. As a consequence of these growing conditions, at equivalent growth stages,
corn and weeds were smaller in 1997 ihan in 1996. This difference in plant size was
visible throughout the first month of the growing period. and faded out afterwards.
3.2.3.2. Experimental Procedures
The site was fall moldboard plowed and cultivated, and corn hybrid 'Pioneer
3967' was grown according to the provincial recommendations (Anonymous 1984).
Corn was seeded May 8, 1996 and May 15, 1997 (Table 2), at a density of 66,000
plants ha", in rows 75 cm apart.
The first experiment included fifteen levels of weed infestation. Total weed
densities retained were: 0, 5, 10, 15, 20, 30, 40, 50, 75, 100, 125, 150, 200, 250, and
300 plants ma'. Treatments also included three types of weed infestation, i.e.
cornmon lambsquarters, barnyardgrass, or both species at equal densities, for a total
of 45 treatments. Weed seeds were broadcast at tirne of corn planting.
The second experiment also included various levels of weed infestation. Total
weed densities retained were: 0, 2, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 60, 70, 80,
90, 100, 125, 150, 200, 250, 300, and 400 plants ma2. In this experiment, the type of
weed infestation was not controlled and weed species naturally occurring on the site
were used (Table 3). We tried to attain equal proportions of the species, especially at
higher densities.
In both experirnents, the final weed densities were achieved by successive
hand weeding of the plots. Initial thinning was conducted between 1 and 2 wk after
weed emergence. Weeds emerged three days pnor to the crop in 1996 and one day
after the crop in 1997 (Table 2). Emergence dates were based on visual estimates of
50% emerged plants. In both experiments, the treatments were assigned to 3- by 8-m
plots (four corn rows), arranged in a completely randomized design.
Leaf Area and Leaf Cover Sampling
Leaf area and leaf cover were sarnpled at the four-leaf stage and at the eight-
leaf stage of corn development (Tables 2 and 3). These records fall within the critical
period of weed control in corn (Hall et al. 1992) and within some of the
postemergence corn herbicides application windows. Only fully expanded leaves
were included in the count when recording the crop growth stage. At each sampling,
a digital image covering an area of 60- by 90-cm and including the right-hand side
middle corn row of each plot was taken. A portion of 60 cm of the corn row was
included in the images. lmmediately following image acquisition, the area covered by
the image was marked and al1 plants (weeds and crop) were clipped at the soi1
surface. Leaf area was measured using an optical leaf area meter' and leaf wver
estimated using an image analysis system2. Details of the image acquisition and
analysis procedures have been provided in a previous study (Ngouajio et al. 1998).
Final Harvest
Corn was hawested by hand from the middle two rows of each plot on October
12, 1996 and October 1, 1997. Shoots were clipped at ground level for biomass
determination. Grains and shoots were dried at 50°C for 10 days and grain and total
above ground dry weight determined.
3.2.3.3. Data Analyses
Data were analysed separately for each year and weed infestation type, using
the non-linear regression mode1 proposed by Kropff and Spitters (1991), and Lotz et
al. (1 992):
where Y 2 is the yield loss by weed cornpetition, Lw is either the relative leaf area (L,)
or the relative leaf cover (L,) of weeds, q is the relative damage coefficient of weeds.
and m is the maximum relative yield loss of the crop. Parameters L, and L, were
computed using equations 2 and 3:
where LAI is the leaf area index and LCi the leaf cover index. YL was derived from
yield data using equation 4:
where Y. is crop yield or biomass in the weed-free plots and Y, the observed yield or
biomass in weed-infested plots.
The F test and t test were used to determine the significance of the
regressions and regression parameters, respectively. Performances of the leaf area
and leaf cover variables in mode! fitting were compared with a sign test, using the
residual mean squares (Lotz et al. 1996). All statistical analyses were performed
using the non-linear regression procedure of SASTM (SAS lnstitute Inc. 1989).
3.2.4. Results and Discussion
The sarnpled area (quadrat) was 60- by 90-cm, and included a 60 cm portion
of a corn row. With a quadrat of that size, the number of corn plants per sampled
area was variable, and ranged from 1 to 7 plants. This affected individual values of
the corn leaf area and leaf cover, and consequently the relative leaf area and the
relative leaf cover of the weeds. As a result, the quality of the predictions was very
poor when individual values of corn leaf area and leaf cover were used (data not
shown), probably due to the size of the sampled area. The large variability of leaf
area and leaf cover data was however not observed with weed populations. To solve
the problem, corn leaf area and leaf cover averaged over al1 plots were used in lieu of
individual plot values in the computation of the relative leaf area and the relative leaf
cover of weeds. That improved the quality of the predictions. Kershaw (1973), and
Lernieux et al. (1992) showed that the sample size has a considerable effect on the
mean and the variance of data obtained when the distribution of individuals within a
population is not random. This was the case in Our experiment where corn population
was not randomly distributed in the plots. The high variance of corn data (stand, leaf
area and leaf cover) suggested that the size of the quadrats used (60- by 90-cm) was
far from being optimum, and that a larger size quadrat should be used. This concem
will be addressed in future work.
The variable response of corn to weed populations between the two
experirnental years as well as the great differences of regression parameters for
different weed populations did not justify pooling the data for the different years and
weed populations. From a statistical point of view, equation 1 fitted well the data.
And since corn grain yield and biomass data responded in a similar way, only crop
grain yield data are reported in details herein (Table 4; Figures 1-3).
Common lambsquarters infestations were not well described by the model.
The observed values of ? ranged from 0.61 to 0.77 for the relative leaf area and the
relative leaf cover of the weed during both growing seasons (Table 4). This low
performance of the model was probably due to the high heterogeneity (size and
fitness) of weeds at the experimental site. With the exception of data recorded at the
four-leaf stage of corn in 1997, the use of relative leaf cover of common
lambsquarters in lieu of its relative leaf area improved the precision in predicting corn yield loss (Table 5). Corn response to wmmon lambsquarters infestations varied
between growing seasons, as indicated by the overall shape of the regression lines
(Figures 1 and 2). The curves were convex in 1996 and concave in 1997.
The effect of barnyardgrass on corn was well described by the yield prediction
model. The percentage of variation explained by the model ranged from 0.67 to 0.92
(Table 4). Although years did not affect the functional forms of the curves, the 1996
growing season provided better predictions than the 1997 growing season (Figures 1
and 2, Table 4). The use of relative leaf cover of weeds as model variable performed
as well as relative leaf area in yield prediction (Table 5).
In plots infested with both common lambsquarters and bamyardgrass,
coefficients of determination obtained from the regression varied between 0.67 and
0.86. The weed variable used (relative leaf area or relative leaf cover) did not affect
the precision of the regressions. However, effects of the growing season were
observable on the functional form of the curves as indicated earlier for the common
lambsquarters infestation (Figures 1 and 2). The curves were concave to the origin in
1996 and convex in 1997.
With the natural weed population, ? values varied from 0.65 to 0.88. With the
exception of data collected at the four-leaf stage of corn in 1996, using the relative
leaf cover of weeds improved the predictions (Table 5). Again, the effect of the
growing season resulted in concave and convex regression lines for the 1996 and
1997 data, respectively (Figure 3).
The results reported above confirmed the high predictive capacity of the model,
and its potential practical use for yield loss prediction in an integrated weed
management system (Dieleman et al. 1995; Knezevic et al. 1995; Kropff and Lotz
1992a, 1992b; Lotz et al. 1995, 1996). Generally, the percentage of variation
explained by the model (?) ranged from 0.61 to 0.92 for grain yield (Table 4). The
adjustment of the model with the 1997 data (except for data of plots infested with
barnyardgrass alone) resulted in concave shaped curves. This was usually found
when q values were lower than one. As a consequence of that, values of the
predicted maximum yield loss (m) were very high and unrealistic.
According to Kropff and Spitters (1991), concave curves associated with low
values of relative damage coefficients of weeds (q) indicate situations where the crop
is a stronger cornpetitor than weeds. With respect to Our work, the one day delay
between corn and weed ernergence in 1997 (Table 2), coupled with the long, dry, and
hot weather (15 days) following weed emergence could have favored the crop over
the weeds during that growing season. The observed maximum grain yield loss and
biomass reduction was lower in 1997 with al1 weed populations, confiming the
hypothesis of corn being more competitive in 1997 compared to 1996 (Table 4). The
differential response of corn to weed competition during the two experimental years is
a serious handicap to practical application of the yield loss prediction model.
Performance of the model has been shown to Vary with environmental
conditions, and weed and crop species (Lotz et al. 1996). In 1996, data from plots
infested with bamyardgrass provided the best fit for the model, with ? values of 0.89
and 0.92 at the four-leaf stage and eight-leaf stage of corn, respectively. In 1997,
however, data fitting was better in plots infested with the mixture of common
lambsquarters and barnyardgrass. The i! was 0.86 at both sampling dates. In
general, precision of the predictions using the relative leaf area of weeds was not
influenced by the sarnpling date. Fitting of the data with the model was equally good
at both stages of corn developrnent.
With the exception of plots infested with comrnon lambsquarters in 1996 (four
leaf-stage of corn), values of the regression parameters (q and m) were smaller when
the relative leaf cover of weeds was used for model fitting compared to using relative
leaf area of weeds (Table 4). The observation was consistent over both years, with
al1 weed populations, and it applied to grain yield as well as to the total plant biomass.
Regardless of that fact, the precision obtained with the relative leaf cover of weeds
was not affected, the values of ? being in the same range as those obtained with the
relative leaf area (Table 4). As observed with the leaf area, precision of the
predictions using the relative leaf cover of weeds was not influenced by growth stage
at which the leaf cover was recorded. Normally, one would expect to obtain better
predictions with leaf cover data collected at the four-leaf stage of corn growth, since
there was little leaf overlapping at that stage compared to the eight-leaf stage.
However, this was not the case. The results of this study suggest that the hidden leaf
area caused by increasing leaf overlapping as growth stage progresses may not
contribute to the competitive ability of plant species. This might be particularly true
when a single weed cohort is considered as was the case in the present study.
The performance of relative leaf cover in model fitting was compared to that of
relative leaf area using a sign test based on the residual mean squares (Table 5).
Differences between the residual mean squares obtained with the two variables, were
very small in general. Out of 16 comparkons, the relative leaf cover performed better
than the relative leaf area eight times. and the Mo variables had equal performances
once, when grain yield was used in model fitting. Using corn biomass, the precision
of the relative leaf cover was higher seven times and equal to that of the relative leaf
area once (Table 5). This observation, coupled with the small differences between
the residual mean squares obtained with the two variables indicate with little doubt
that the relative leaf cover of weeds is as good as relative leaf area in ftting yield loss
prediction models.
Leaf cover estimation by digital image analysis has lifted some of the major
constraints imposed by the use of relative leaf area of weeds in yield loss prediction
models. This work has revealed that leaf cover estimates may perform as well as leaf
area. These facts may constitute an opened avenue for the practical use of yield loss
prediction models in integrated weed management systems, with the objective of
reducing herbicide inputs. However, the implementation of such technology may still
require some ground work including: the development and validation of empirical
models specific to individual situations e-g. crop. weed, environment etc.; the
appropriate choice of both the quadrat (image) size and the sample size when
collecting images; the proper identification of the crop growth stage at which leaf
cover assessrnent has to be done. Additional work should take into acwunt the
logistics of individual production units, the resolution of images. the precision of the
image analysis system, and the limitations imposed by the use of postemergence
herbicides and other weed wntrol options.
Sources of Materials
' LI-COR Inc., P.O. Box 4425, Lincoln, NE 68504.
~urfaces~ro@, Sociéte de Mathématiques Appliquees Inc., 59 d'Auteuil Street,
Quebec, QC, Canada G1 R 4C2.
Acknowledgements
Funding for this research was provided in part by the Matching lnvestment Initiative
of Agriculture and Agri-Food Canada. The senior author is a recipient of a
scholarship from the Programme Canadien des Bourses d'Excellence de la
Francophonie D. We thank Mr. Jocelyn Lamarre and Ms. Michéle Martel for technical
and professional assistance and summer students for field plot work, especially hand
weeding and vegetation sampling. The weather data were supplied by Dr. Philippe
Rcchette.
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des Productions Végétales du Québec. 21 p.
Cousens, R. l985a. A simple rnodel relating yield loss to weed density. Ann.
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Cousens, R. 1985b. An empirical model relating crop yield to weed and crop
density and a statistical comparison with other models. J. Agric. Sci. IO5:513-521.
Cousens, R., N.C.B. Peters, and C. J. Marshall. 1984. Models of yield
loss-weed density relationships. ln Proceedings of the 7th International Symposium
on Weed Biology, Ecology and Systematics. Paris: Columa-EWRS. pp. 367-374.
Cousens, R., P. Brain, J.T. O'Donovan, and P.A. OrSuIlivan. 1987. The use of
biologically realistic equations to describe the effects of weed density and relative
time of emergence on crop yield. Weed Sci. 35:720-725.
Dew, D. A. 1972. An index of cornpetition for estimating crop loss due to
weeds. Can. J. Plant Sci. 52:921-927.
Dieleman, A., A. S. Hamill, S. F. Weise, and C. J. Swanton. 1995. Empirical
models of pigweed (Amaranthus spp.) interference in soybean (Glycine max). Weed
Sci. 43:612-618.
Duke, S.O. 1996. Herbicide resistant crops : background and perspectives. in
S.O. Du ke ed. Herbicide-resistant Crops: Agricultural, Environmental, Economic,
Regulatory, and Technical Aspects. Boca, Raton, Florida: CRC Press. p 1-3.
Hall, M.R., C.J. Swanton, and G.N. Anderson. 1992. The critical period of weed
control in grain corn (Zea mays L.). Weed Sci. 40:441-447.
Kershaw, K.A. 1973. Quantitative and dynamic plant ecology, 2nd ed. New
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Knezevic, S.Z., M.J. Horak, and R.L. Vanderlip. 1997. Relative time of redroot
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Table 1. Total monthly rainfall and mean temperature during the 1996 and 1997
growing seasons, and long term average (30 y e a r ~ ) ~
Rainfall (mm) Temperature ( O C )
Month
Long Long
1996 1997 te rrn 1996 1997 te rrn
May 73.1 96.0 108.2 10.7 8.8 10.8
June 142.5 62.0 111.3 17.8 17.1 16.4
July 235.8 69.0 125.4 19.3 19.3 19.2
August 76.0 166.0 11 6.3 19.1 17.8 17.9
September 108.0 68.0 11 8.3 14.3 13.3 12.5
October 86.0 48.0 98.1 6.3 6.7 6.4
a Data recorded at the Quebec City airport about 10 km from the experimental plots.
Table 2. Chronology of events (sowing, emergence, sampling, and harvest) for the
1996 and 1997 growing seasons
Year
- -
Emergence date Sampling date
Sowing Hawest
date Corn Weeds First Second date
1996 08 May 23 May 20 May 06June 18June 12 October
1997 15 May 31 May 01 June 11 June 23 June 01 October
Table 3. Corn and weed growth stage at sarnpling time
First samplingb Second sampling
Experimenta Species
1 Corn
Common lam bsquarters
Barn yardgrass
2 Corn
Common lambsquarters
Barnyardgrass
Wild mustard
Common chickweed
Redroot pigweed
Ladysthumb
Pale smartweed
- Number of fully expanded leaves - 4 4 8 8
2 to 10 2 to 6 14to40 8to18
2 to 6 2 to 4 7 to 14 6to10
4 4 8 8
2to 10 2 to 6 14to40 8to18
2 to 6 2 to 4 7t0 14 6 to 10
2 to 5 3 to 5 7 to11 8to12
5 to 12 4 to 8 15to30 l o to20
2 to 8 1 to4 5to 12 2 to lO
5 to 20 3to10 20to40 12to20
4 to 8 2 to 4 7 to15 5to10
aExperiment 1 included 15 plots common lambsquarters, 15 plots of barnyardgrass
and 15 plots of a mixture of both species grown at equal densities, while experiment 2
had a natural weed infestation.
b ~ h e first sampling was conducted on June 06 (1996) and June 11 (1 997) and the
second sarnpling on June 18 (1996) and June 23 (1997).
PPPP P P P P
P P P P
PPPP P P P P
P P P P P P P P
Table 5. Cornparison of the residual mean squares (RMS) for corn grain yield and
corn total biornass, obtained from model fitting using the relative leaf area and the
relative leaf cover of weeds
Type of weed infestation
RMS for yield RMS for biomass
Leaf Leaf na Leaf Leaf a area cover (+ or -) area cover (+ or -)
1996, four-leaf stage of corn Common lambsquarters Barnyardgrass Common larnbsquarters + barnyardgrass Natural population
1997, four-leaf stage of corn Common lambsquarters Barnyardgrass Common lambsquarters + barnyardgrass Natural population
1996, eight-leaf stage of corn Common lambsquarters Barnyardgrass Common lambsquarters + barnyardgrass Natural population
1997, eight-leaf stage of corn Common lambsquarters Barnyardgrass Common lambsquarters + barnyardgrass Natural population
a a is the difference behiveen the RMS (x 100) calculated with the relative leaf area and the RMS calculated with the relative leaf cover of weeds. The sign + indicates that the leaf cover provided a better fit of the model, - indicates that the leaf area was better, and O means that the two variables performed equally.
Comrnon lambsquarters populations
Barn yardgrass populations
1 { " Common lambsquarters + 10
O barnyardgrass
O 1 / , I
populations
0.0 0.2 0.4 0.6 0.8
Comrnon lam bsquarters populations
Common larnbsquarters + barn yard grass populations
40 - Barnyardgrass
Relative leaf arealleaf cover of weeds
30
Figure 1. Corn grain yield loss as a function of weed relative leaf area (-a-) and
relative leaf cover (-a.--) determined at the four-leaf stage of corn growth in 1996 and
1997 using a two-parameter empirical mode1 (YL= qLw/[7+(q/m-l)Lwn. Corn was
infested with one or two weed species, at different densities.
populations
Common Iambsquarters populations
Barnyardgrass populations
Common lam bsquarters
- 1;. 0 Common lambsquarters +
barn yardgrass O , populations
i
Barnyardgrass populations
Common lambsquarters +
barnyardgrass populations . a;
Relative leaf arealleaf cover of weeds
Figure 2. Corn grain yield loss as a function of weed relative leaf area (-a-) and
relative leaf cover ( -O.- - ) determined at the eight-leaf stage of corn growth in 1996
and 1997 using a two-parameter empirical model (YL= qLw/[l+(q/m-l)Lw). Corn was
infested with one or two weed species, at different densities.
Four-Ieaf stage of corn Natural weed populations
50 .
40 . 30
20
Four-leaf stage of corn 10 - Natural weed populations
1 4
Eig h t-leaf stage of corn 10
Natural weed populations O v
Eight-leaf stage of corn Natural weed populations
Relative leaf area/leaf cover of weeds
Figure 3. Corn grain yield loss as a function of weed relative leaf area (-a-) and
relative leaf cover (- - -O- ) determined at the four- and at the eight-leaf stages of corn
growth in 1996 and 1997 using a two-parameter empirical model (YL= qL,/[l+(q/m-
7 ) ) Corn was infested with different densities of a natural weed population.
CHAPITRE 4
MODÈLE SIGMO~DE FLEXIBLE RELIANT LA COUVERTURE
FOLIAIRE RELATIVE DES MAUVAISES HERBES AU RENDEMENT
DE LA CULTURE ET COMPARAISON AVEC
D'AUTRES MODÈLES
Ce chapitre a été accepté pour publication à la revue Weed Research Vol. 39, No 00,
pp.000-000, 1999 sous le titre de "A flexible sigmoidal mode1 relating crop yield to
weed relative leaf cover and its cornparison with nested models."
4.1. Résume du chapitre 4
Plusieurs modèles empiriques reliant la présence des mauvaises herbes au
rendement des cultures sont proposés dans la littérature. La plupart de ces modèles
sont soit des équations Maires simples, soit des équations non linéaires
hyperboliques ou logistiques. En dehors de la capacité intrinsèque de ces modèles à
prédire les rendements, la forme fonctionnelle de leur courbe peut jouer un rôle
décisif si ceux-ci sont associés à des outils de prise de décision. Les modèles
linéaires simples sont peu efficaces. Les modèles hyperboliques ne permettent pas
une asymptote aux faibles quantites de mauvaises herbes, ce qui surestime très
souvent l'impact de ces plantes sur les rendements en réduisant le seuil de contrôle.
Les modèles logistiques quant à eux sont biologiquement très rationnels, mais
souffrent d'un manque de flexibilité. L'impact de la compétition entre les cultures et
les mauvaises herbes varie avec plusieurs facteurs incluant les espèces végétales en
présence, les techniques cülturales, la localité, la saison et les conditions
environnantes. La complexité des interactions entre ces differents facteurs exclut
l'usage d'un modèle simple ou statique.
L'objectif principal de cette étude était de développer et de valider un modèle
flexible reliant la présence des mauvaises herbes au rendement des cultures. II etait
aussi question de comparer l'efficacité du modèle développé a celle d'autres sous-
modèles qui lui sont intégrés.
Un modèle empirique, flexible et sigmoïdal reliant la couverture foliaire relative
des mauvaises herbes au rendement des cultures a été dérivé. II a été démontré que
ce modèle intègre les modèles non linéaires hyperbolique, sigmoïdal symétrique et
logistique asymétrique, ainsi que le modèle linéaire simple comme cas spéciaux
(sous-modèles). Des données colligées en 1996 et 1997 dans des expériences en
champ ont été utilisées pour valider le modèle. Dans ces essais, le maïs (Zea mays
L.) était cultivé en présence de densités variables (15 à 25) de chénopode blanc
(Chenopodium album L.), de pied de coq [Echinochloa crus-galli (L.) Beauv], d'un
mélange des deux espèces, et d'une population naturelle de mauvaises herbes. La
couverture foliaire des plantes était échantillonnée aux stades quatre et huit feuilles
entièrement étalées du maïs et la technique d'analyse d'images numériques etait
utilisée pour les estimations.
Le modèle comportait quatre paramétres. Lors des travaux de validation,
l'estimation des paramètres a été réalisée au moyen de la procédure de régression
non linéaire. L'ajustement des données au modéle était bon pour tous les types
d'infestations de mauvaises herbes (les valeurs du P variaient entre 0,68 et 0,90).
Lorsque comparé aux autres modèles emboîtés et restreints (sous-modèles), le
modèle sigmoïde flexible s'est avéré plus performant que les sous-modèles sigmo'idal
symétrique et logistique asymétrique. Par contre, le rejet de l'hypothèse nulle d'une
réponse hyperbolique des rendements n'a été possible qu'une fois sur 16. Cette
observation indique que le modèle sigmoïde flexible et le sous-modèle hyperbolique
ont des valeurs prédictives comparables. La complexité accrue du modèle sigmoïde
flexible (quatre paramètres) placerait ainsi le choix de la plupart des investigateurs
sur le modèle hyperbolique plus simple (trois paramètres). L'échec du modèle
complet à supplanter le sous-modèle hyperbolique Btait surtout dû aux faibles valeurs
du paramètre 6 (responsable de la réponse sigmoïdale) associées à la petite taille
des échantillons utilisés. Toutefois, si le modèle doit être inséré dans un programme
informatique de support a la prise de dkcision, le modèle sigmoïde flexible pourrait
s'avérer plus approprié car une plus grande taille des échantillons est requise dans
un tel cas. La grande flexibilité du modèle pourrait ainsi permettre de détecter les cas
particuliers et réduire au minimum les risques de mauvaises décisions.
4.2. A flexible sigmoidal model relating crop yield to weed relative leaf cover
and its cornparison with nested rnodels
M. NGOUAJIO, G. D. LEROUX AND C. LEMIEUX
4.2.1. Summary
A flexible sigmoidal model relating crop yield to relative leaf cover of weed was
derived. The model was shown to embody an hyperbolic, a symmetric sigmoidal and
an asyrnmetric logistic model as special cases. Data from field experiments
conducted in 1996 and 1997 on maize (Zea mays L.) in competition with various
weed infestation conditions were used to validate the rnodel. A high accuracy was
observed for yield prediction, and the four parameters of the mode1 were estimated
easily using a non-linear regression procedure. When compared to other (nested and
restricted) models, a better fit of the data was obtained cornpared to the symmetric
sigmoidal and the asymmetric logistic models. Rejection of the nuIl hypothesis of
hyperbolic yield response was observed only in one case out of 16, rneaning that both
the hyperbolic and the flexible sig moidal rnodels have comparable yield pred ictive
capacities. The increased wmplexity due to the extra (fourth) parameter in the
flexible sigmoidal model rnay favour the use of the hyperbolic model by most
investigators. Failure of the unrestricted model to outperform the hyperbolic model
was prirnarily due to the small values of the sigmoidal response parameters (6),
associated with the small sample sizes. However, when the model is to be
embedded in a decision support computer program, the flexible sigmoidal model may
be more appropriate since large sample sizes are required. The high flexibility of the
model may allow to detect special cases, and then reduce the rîsk of a wrong
decision to a minimum.
4.2.2. Introduction
Several empirical models relating crop yield to the presence of weeds are proposed in
the literature (Dew, 1972; Cousens et al., 1984; Cousens, 1985a, l985b; Cousens et
al., 1987; Kropff & Spitters, 1991 ; KropfF & Lotz, 1992b; Lotz et al., 1992, Kropff et al.,
1995; Lotz et al., 1995). These models are based on the estimates of weed density
(Dew, 1972; Cousens et al., 1984; Cousens, 1985a), weed and crop densities
(Cousens, 1985b), or the relative leaf area of weeds (Kropff & Spitters, 1991 ; Kropff &
Lotz, 1992b; Lotz et al., 1992, 1995). Models using the relative leaf area of weeds
have shown high predictive capacity in field experiments (Kropff & Lotz, 1992a,
l99Zb; Dieleman et al., 1995; Knezevic et a l , 1995; Lotz et a/., 1995, 1996). At low
densities or at early stages of plant development, leaf cover is similar to leaf area
index (Lotz et al., 1994; Andreasen et al., 1997) and both variables have comparable
performances in yield loss prediction models (Ngouajio et al., 1999). Leaf cover
estimation has the advantages of being both non-destructive and easy to measure.
Research efforts in recent years have led to the developrnent of techniques of leaf
cover estimation (Lutman, 1992; Lotz et al., 1994; Carson et al., 1995; Ruget et al.,
1 996; Andrieu et al., 1 997; Ngouajio et al., 1 998).
Most yield prediction models use either simple linear equations (Dew, 1972) or
hyperbolic equations (Cousens et al., 1984; Cousens, 1985a, 1985b; Cousens et al.,
1987; Kropff & Spitters. 1991 ; Kropff & Lotz, 1992b; Lotz et al., 1992; Kropff et al.,
1995; Lotz et al., 1995). Apart from the intrinsic capacity of these models to desctibe
yield, their functional f o m can play a decisive role in weed control recommendations,
especially when the models are embedded in a decision support cornputer program
(Swinton & Lyford, 1996). This is particulariy important since, for the same weed
infestation level, a slight change in the initial dope of a curve (determined by its
functional form) may result in a major change in the predicted threshold level of weed
control. Simple linear models of yield prediction have little rational biological
backbones, and as such, have often resulted in low performances (Cousens et al.,
1984). Hyperbolic yield functions on the other hand have an asymptote at high weed
infestation levels; however, their initial slope does not allow a yield asymptote at the
low weed infestation end of the curve. This may result in an overestimation of the
impact of weeds thus, reducing the threshold level of control (Swinton & Lyford,
1996).
Major biological phenomena conceming both bacteria and higher plants have
shown logistic types of response (Morgan et al., 1975). Logistic models
accommodate two asymptotes, one at limiting resources and the other at saturating
resources (Morgan et al., 1975; Silvertown, 1982). It might be expected that the
response of crops to weed competition should exhibit similar trends. Direct
application of logistic models is precluded as they allow very srnall Rexibility, and
their curves are forced through the origin of the coordinate axes (Morgan et al., 1975).
In experimental data, curves representing yield response to weed competition rarely
pass through the ongin of the axes.
The outcome of weed competition on crops varies with several factors
including crop and weed species, management techniques, location, year, and
environmental conditions. The highly complex interactions between those factors
preclude the use of a simple or static model. A more appropriate model should be
flexible, and able to accommodate linear, hyperbolic and logistic models as special
cases. In addition, if the model is to be used with the relative leaf cover of weeds, the
independent vanable should Vary between zero and one, with the upper asymptote
(maximum yield) at zero and the lower asymptote (minimum yield) at one (Lotz et al.,
1994). The Morgan-Mercer-Flodin or MMF model (Morgan et al., 1975; Ratkowsky,
1983; Swinton & Lyford, 1996) meets the first set of requirements, but not the second.
In the present paper, a flexible sigmoidal model relating crop yield to the
relative leaf cover of weeds is derived from the MMF rnodel. The model is
demonstrated to embody linear, hyperbolic and logistic models of yield loss based on
the relative leaf cover of weeds. Finally, the model is validated and compared to
other nested rnodels using field data on maize in competition with Chenopodium
album L., Echinochloa crus-galli L. Beauv., the mixture of C. album and E. cmsqalli,
and a natural multispecies weed cornrnunity.
4.2.3. Materials and methods
4.2.3.1. Model derivation
Swinton & Lyford (1996) proposed the use of weed density in the MMF modei
(Morgan et al., 1975) for yield description. The model takes the fom:
where Y = crop yield, D = weed density, a = minimum yield or lower asymptote as
weed density approaches infinity, P = maximum yield (weed-free yield), y = cur~ature
measure that detemines the rate at which yield reaches its lower asymptote (a ) i.e.,
the lower curvature of the sigmoid, and 6 = cuwature measure that determines the
point at which yield begins to decline at a decreasing rate (Le., the upper curvatura of
the sigmoid). From equation 1, a new equation using the relative leaf cover of the
weed is derived, using a series of assumptions.
(a) Yield is not related only to weed density (D,), but also to crop density (D,)
(Cousens, 1985b), and mainly to the ratio of the two variables. Using that
assumption, equation 1 becomes:
(b) Plant density is lineariy related to the leaf area index (LAI) and leaf area is a
better yield descriptor than density (Kropff & Spitters, 1991; Kropff & Lotz, 1992a,
l99Zb; Dieleman et al., 1995; Knezevic et al., 1995; Lotz et al., 1995, 1996). After
replacing weed and crop densities in equation 2 with their leaf area indices, the
following equation is obtained:
(c) The share in total leaf area of weed species or the relative leaf area of
weeds (RLA,) may be easier to measure than the leaf area indices (Kropff & Spitters,
1991). The relation between leaf area indices and relative leaf area of weeds is as
follows:
After replacement of the crop leaf area index (LAI,) in equation 3 and rearrangement
using X = RU,, equation 5 is obtained:
Equation 5 is a flexible sigmoid equation, using the relative leaf area of the weed
instead of weed density as was the case for the MMF model. The relative leaf cover
of weeds can be substituted for their relative leaf area, since both variables have
comparable performance at earîy growth stages (Ngouajio et al., 1999).
4.2.3.2. Nested models
Kropff & Lot- (1992b) suggested an hyperbolic rnodel relating crop yield to the
relative leaf area of weeds. This model which has been shown to exhibit high
predictive capacity takes the following form when expressed in terms of yield:
where Y = crop yield, Y. = maximum yield or yield in weed-free conditions,
X = relative leaf area of weeds, 1 = relative damage coefficient of weeds (a measure
of the cornpetitive ability of weeds), and A = minimum yield (lower yield asymptote) as
the relative leaf area of weeds approaches unity. Equation 6 can be rewritten in the
form of equation 5 (Swinton & Lyford, 1996) as follows:
where a =Yo(l-A), fl =Yo, y =NI, and 6 =l. This indicates that equations 5 and 6 are
nested, equation 6 being a special case of equation 5.
Equation 5 was reparameterized to reduce the non-linearity effects of the
parameters (Ratkowsky, 1983; Swinton & Lyford, 1996). The reparameterized
version, where y is substituted for = y ', takes the following form:
The parameters have the following biological interpretation: Y = predicted crop yield,
Y. = maximum yield or yield in weed-free conditions (upper asymptote), a = minimum
yield or the lower asymptote as weed relative leaf area approaches unity, i.e., X/(1-X)
approaches infinity, y' = value of (1-X)/X at which half of the yield is lost (the
corresponding value of X is 1/(1+ y')), and 6 = measure of the sigrnoid curvature. 6
rnay also be used as a measure of the cornpetitive ability of the weeds compared to
the crop. Values of 6 lower than unity but higher than zero may represent situations
where weeds are more cornpetitive than the crop, and is illustrated by a concave
upper portion of the sigmoid (Fig. 1). Values of 6 higher than unity may represent
cases where the weed is less cornpetitive than the crop, and the upper portion of the
sigmoid is convex to the origin.
When 6 is equal to unity, the curve is an hyperbola similar to Kropff & Lotz
(1992b) model in equation 6:
For uniformity of the parameters, equation 9 will be used in place of the Kropff & Lotz
(1992a) model in equation 6 for model cornparison.
When y' is equal to unity, the curve is the following symmetrîc sigmoid:
With a equal to zero, the cuve becomes an asymmetric logistic dose response
Equation 8 is a flexible sigmoid (unrestricted model) that embodies the hyperbolic
model in equation 9 (restricted model 1 ), the symmetric sigmoidal model in equation
10 (restricted model 2). and the asymmetric logistic mode1 in equation 11 (restricted
model 3), as special cases, respectively when 6 is equal to unity, y ' is equal to unity,
and a is equal to zero (Fig. 1). This rnay represent a more versatile predictor of yield
than either individual rnodel. It rnay also have sorne advantages in explaining
biolog ical interactions between weeds and crops.
4.2.3.3. Model Validation and cornparison
The unrestricted model (equation 8) was validated and compared to the restricted
models using data from field experiments conducted in 1996 and 1997. Maize was
grown in cornpetition with C. album, E. crus-galli, a mixture of C. album and E. c m -
gallî, or with a natural multispecies weed community. Fifteen weed densities were
used for the first three weed infestation types, and 25 densities for the natural weed
population. Leaf cover was estirnated at the four- and at the eight-leaf stages of
maize development. Detail of the experimental procedures and data collection has
been described by Ngouajio et a/. (1 998, 1999).
4.2.3.4. Statistical analyses
Field experiment data were fitted to the rnodels (equations 8, 9, 10, and Il ) using the
non-linear regression procedure of SASTM (SAS lnstitute Inc., 1989). The nested
statistical analyses using the likelihood ratio and the Wald tests (Judge et al., 1988,
Borowiak, 1989; Swinton & Lyford, 1996) were used for model discrimination.
Cornparisons between the hyperbolic model (restricted model 1) and the flexible
sigmoidal model (unrestricted model) were performed by testing the nuIl hypothesis of
6 = 1, in the complete model. An identical test was conducted with the symmetric
sigrnoidal model (restricted model 2) using the nuIl hypothesis of y ' = 1 in the
complete model. Cornparison with the asymrnetric logistic model (restricted model 3)
was made using the nuIl hypothesis of a = O in the complete model. All statistical
tests were conducted at 5 and 1 % levels of probability.
4.2.4. Results and discussion
4.2.4.1. The performance of the model (unrestricted)
The four parameter flexible sigmoidal model was derived from the MMF model
(Morgan et al., 1975; Ratkowsky, 1983; Swinton 8 Lyford, 1996), for use with the
relative leaf cover of weeds. The derivation was made based on some biological
factors governing weed-crop cornpetition. The model can then be regarded as a
semi-empirical model. The importance of using biologically realistic models to
describe the impact of weeds on crop yield has been demonstrated previously
(Cousens et al., 1984; Cousens. 1985a; Cousens et al., 1987; Kropff & Spitters,
1991 ).
The model fitted the experimental data very well (Table 4 , Figs 2 and 3). All
parameters were estimated easily, using a non-linear regression procedure. The
competitive ability of weeds measured with parameter 6 varied with weed species,
year, and leaf cover assessment period (Table 1). C. album in mixture with E. crus-
galli was generally more aggressive towards maize than either species grown alone
or the natural weed population. In plots infested by a mixture of the two species. the
value of 6 varied from 0.8 to 2.71. Higher values of 6 were recorded in 1997,
indicating lower weed competitive ability. In general, the 1997 growing season was
favourable to rnaize compared to weeds. The low weed competition in 1997 may be
attributed to unfavourable weather conditions during and imrnediately following weed
emergence (Ngouajio et al., 1999). Early leaf cover estimation (four-leaf stage of
maize) resulted in higher weed competitive ability. This may represent a very
important observation, as the value of 6 determines the functional shape of the
regression curve, and ultirnately, the predicted threshold level of weed control. In this
regard, the appropriate timing of leaf cover assessment becomes one of the major
components of good performances of the model, especially when the data are used in
weed control decision making tools. This timing should, as much as possible, be
related to the physiological stages of crop development rather than the weed, or the
number of days after weed or crop emergence.
With the exception of C. album for data wllected at the four-leaf stage of maize
in 1997 (with 4.82), the values of parameter y' (indicator of the value of relative leaf
cover at which half of the yield is lost) are higher for plots infested with the natural
weed population, compared to other weed infestation types (Table 1). The values
range from 3.50 to 6.90. Higher values of y' (more than one) indicate that half of the
reduction in yield is achieved at relatively low weed infestation levels. The
combination of low values of 6 (less than 0.5) and high values of y' (more than one),
represent situations where weed interference is very damaging to the crop. Such a
situation is illustrated by the data on natural weed populations recorded in 1996 at the
four-leaf stage of maize development where 6 is 0.46 and y' is 3.65 (Table 1, Figs 2
and 3).
The percentage of variation explained by the regression model is variable
(Table 1). The values range from 70 to 78 for C. album, from 68 to 90 for E. crus-
galli, from 75 to 89 for the mixture of C. album and E. crvsgalli, and from 66 to 90 for
the natural weed infestation. This is probably due to the large variation in the
environmental conditions prevailing during the experiments in both years. It may also
be due to the differences in weed species or experirnental and measurement error.
4.2.4.2. Model comparison
The restricted model 1 (equation 9), the restricted model 2 (equation 10). and the
restricted model 3 (equation 1 l), were derived from the unrestricted model (equation
8) by restricting some of the parameters of the unrestricted (complete) model to fixed
values,
Since the restricted models are nested within the unrestricted model, the
residual surn of squares is not an appropriate criteria on which to judge the goodness
of fit, as the more complex model will generally turn out to be the best. In such
circumstances, the likelihood ratio and the Wald test statistics are more appropriate
for model discrimination (Judge et al., 1988; Borowiak, 1989; Swinton & Lyford,
1996). These test statistics are presented in Table 2. The critical x2 (Chi square)
values are 3.84 and 6.63, respectively, at the 5 and 1% levels of probability.
Fitting of data with the unrestricted model produced the smallest of the residual
sum of squares, irrespective of year, weed infestation type and year. An associated
increase in the percentage of variation explained by the models was observed (Table
1). These results were predicted since the more complex model generally results in a
better fit of data when the models are nested.
The imposition of the restriction 6 = 1 (restricted model 1 ) significantly
increased the residual sum of squares for data recorded in 1996, at the eight-leaf
stage of maize in plots infested with the mixture of C. album and E. crus-galii. This
results in higher and significant values of the likelihood ratio (5.28) and the Wald
(4.63) test statistics (Table 2). This case indicates that the unrestricted model is
better than the restricted model 1. Apart from this case, the restriction 6 = 1 increases
the residual sum of squares and reduces the percentage of variation explained by the
model (Table 2). However these changes are not large enough to be statistically
significant. In those cases, the two models have statistically equal performances,
putting the choice of the investigator on the less cornplex rnodel (restricted model 1).
With the restricted model 2 (y' = 1). the conclusions of the two statistical tests
are not always concordant in model comparison. The two tests indicate that the
unrestricted model is significantly better than the restricted rnodel 2, for the natural
weed population at the four-leaf stage of maize in 1997, and for the mixture of
C. album and E. crvs-galli at the eight-leaf stage of maize in 1996. The likelihood
ratio and the Wald test statistics were respectively, 27.36 and 10.52 for the natural
weed population, and 6.53 and 148.18 for the mixture of the two weeds. Fitting of the
data collected at the eight-leaf stage of maize in 1997 from plots infested with the
natural weed population, is significantly better for the unrestricted model using the
l i kelihood test statistics (8.76), while the two models are declared comparable using
the Wald test statistics (0.08). A reverse situation is found in 1996 with E. crus-galli,
the mixture of C. album and E. crus-gaili at the four-leaf stage of maize, and C. album
at the eight-leaf stage of maize. In those cases, the likelihood ratio test declares the
two models equal, and the Wald test finds the unrestricted model better.
Cornparisons of the restricted model 3 with the unrestricted model indicate
that, out of 16 cases, both statistical tests declare two cases where the unrestricted
model is significantly better than the restricted rnodel 3, and six cases where the two
models are comparable. In addition, there are eight cases where the unrestricted
model is more appropriate for data fitting according to the Wald test. The lack of
concordance between the two tests in cornparhg the models has also been obsewed
with the restricted model 2.
Irrespective of the statistical test used. data collected in 1996 at the eight-leaf
stage of maize from plots infested with the mixture of C. album and E. crus-galli are
shown to be better described by the unrestricted model than either of the restricted
models (Table 2). On the other hand, al1 four rnodels provide comparable fitting of the
data for C. album (four-leaf stage of maize in 1996 and 1997), and the natural weed
population (eight-leaf stage of maize in 1996). For the remaining 12 cases, either the
unrestricted model or the restricted rnodel 1 is more adapted to the data.
Aithough it is relatively easy to declare that the unrestricted model is preferable
to the restricted models 2 and 3, it is very difficult to choose between the unrestricted
model and the restricted model 1. The unrestricted model generally reduced the
residual sum of squares and increased the proportion of the variation explained by
the model, but the complexity of the model caused by the estimation of a fourth
parameter may discourage most investigators from using it. Failure of the
unrestricted model to outperfon the restricted model 1 was primarily due to the small
values of the sigmoidal response parameters (6). Swinton & Lyford (1996) have
demonstrated that under conditions of high data variability and weakly sigmoidal yield
response (6 close to one), a sample size of more than 50 may be required to identify
sigmoidal response parameters with 95% confidence. With the data sets used in this
test, the value of 6 is generally close to one (Table 1) and the sarnple sires are 15
and 25 with highly variable weed populations (Ngouajio et al., 1998). If the mode1 has
to be included in a weed control decision making tool, the unrestricted model may be
preferred over the restricted mode1 1 for several reasons: (1) sufficient data points
must be used to reduce the risk of a wrong decision as a result of a poor estimate;
such large sample size should be easy to collect with the recent techniques of leaf
cover estimation by digital image analysis; (2) to reduce the risk of a wrong decision,
a model that can encompass most possible situations is necessary.
This last statement can be observed cleariy with the data sets presented in this
paper. In Figs 2 and 3, the threshold level of weed control would be highly influenced
by the model used in plots infested by the mixture of C. album and E. crvs-galli at the
eight-leaf stage of maize growth. In Fig. 2, the graph obtained with the mixture of
C. album and E. cmsgalli as well as the different statistical tests show that the yield
response is sigmoidal rather than hyperbolic. Detection of such special cases which
would otherwise lead to wrong decisions, car; only be possible through the use of a
more versatile model.
The flexible sigmoidal model of crop yield prediction presented here is shown
to embody an hyperbolic, a symmetric sigmoidal and an asymrnetric logistic models.
Our validation results indicate that the flexible sigmoidal model provides a better fit of
the data compared to the symmetric sigmoidal and the asymmetric logistic models.
However, the model fitted the data significantly better than the hyperbolic model only
in one out of 16 cases. Failure to reject the nuIl hypothesis of hyperbolic yield
response is rnainly due to the weakly sigmoidal yield response associated with the
high data variability and the srnall sarnple sizes. An appropriate cornparison between
the hyperbolic and the flexible sigmoidal model would require experiments specifically
designed for the purpose. Detection of the sigmoidal yield response requires sample
sizes larger than the usual practice in field experiments for weed competition. Large
samples are required to reduce the risk of a wrong decision when the model is used
for weed control decision making. In such a situation the use of the flexible sigmoidal
model may be preferred over that of the hyperbolic model.
Acknowledgements
Funding for this research was provided in part by the Matching lnvestment Initiative of
Agriculture and Agri-Food Canada. The senior author is a recipient of a scholarship
from the (( Programme Canadien des Bourses d'Excellence de la Francophonie ».
We thank Mr. Jocelyn Lamarre and Ms. Michéle Martel for technical and professional
assistance and summer students for field plot work. especially hand weeding and
vegetation sarnpling. We than k Dr. Régis Baziramakenga for its critical review of this
manuscript.
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tD ul
Table 1. Regression parameters obtained in maize yield prediction using the flexible sigmoidal model (unrestricted model. equation 8) and nested models, (restricted models, equations 9. 10 and 11). The data were recorded in 1996 and 1997, at the four- and at the eight-leaf stages (fully expanded leaves) of rnaize.
- - - -- - - - -- - - - - -
Regression parameters a*b
Type of Unrestricted Restricted Restricted Restricted
weed Model rnodel 1 mode1 2 mode13 infestation (sigrnoidal) (hyperbolic) (symmetric sigrnoidal) (asymmetric logistic)
a Y. 6 y* r2 a Y. y' r2 a Y. 6 r2 Y. 6 y' r2
1996, four-leaf stage of rnaize C. album E. crus-galli C album + E. crus-galli Natural population
1997, four-leaf stage of maize C. album E. crus-galli C. album + E. crus-galli Natural population
1996, eight-leaf stage of maize C. album E. crusqalli C. album + f. crus-galli Natural population
1997, eight-leaf stage of maize C. album E. crusqalli C. album + E. crusqalli Natural population
a In the restricted model 1, 6 = 1 ; in the restricted model 2, y' = 1 ; and in the restricted model 3, a = 0. b ? values are multiplied by 100.
Table 2. The likelihood ratio (LR) and the Wald (W) test statistics for cornparison of
the performances of the restricted models to the unrestricted model used for maize
yield prediction.
Test statistics a
Type of Rest ricted Restricted Restricted
weed rnodel 1 mode12 mode13 infestation
LR W LR W LR W
1996, four-leaf stage of maize C. album E. crvsgalli C. album + E. crus-galli Natural population
1997, four-leaf stage of maize C. album E. crus-galli C. album + E. crus-galli Natural population
1996, eight-leaf stage of maize C. album E. crus-galli C. album + E. cmsgalli Natural population
1997, eight-leaf stage of maize C. album E. crus-galli C. album + E. crus-galli Natural population
a In the restricted model 1, 6 = 1; in the restricted model 2, y' = 1 ; and in the restricted model 3, a = O. ' and " indicate that the unrestricted model (equation 8) is significantly better than the restricted model, respectively, at the 5 and 1 % levels of probability. The critical x2 values are 3.84 and 6.63 at the 5 and 1% levels of probability, respectively.
0.0 0.2 0.4 0.6 0.8 1.0
Weeds relative leaf cover
Figure 1. The functional forms of the flexible sigrnoidal model (unrestricted rnodel) as affected by the values of the parameters: with 6 = 1, the curve is either a concave hyperbola (y' c l ) , a straight line (yJ = i), or a convex hyperbola (y'> 1); the cuwe is either a symmetric (y' = 1) or an asymmetric (y'# 1) sigrnoid. the upper portion being concave (6 > 1 ) or convex (6 < 1) to the origin. For the purpose of this demonstration, crop yield is expressed in t ha", and a and are arbitrary set at 1 and 9 t ha-', respectively .
Four-leaf stage of maize
6 C. album
Eight-leaf stage of rnaize
C. album and
population ' \\
Weed relative leaf cover
Figure 2. Maize yield as a function of weed relative leaf cover recorded at the four and at the eight leaf stages of maize growth in 1996. The non-Iinear regression models are: the unrestricted model (-a-), the restricted model 1 (- - a - -), the restricted model 2 (- -), and the restricted model 3 (----- ).
tour-leaf stage of maize
C. album ! C. album
C. album and
Natural weed population
G .
Weed relative leaf cover
77 Natural weed
population \
Figure 3. Maize yield as a function of weed relative leaf cover recorded at the four
and at the eight leaf stages of maize growth in 1997. The non-linear regression
models are : the unrestricted model (-a-), the restrkted model 1 (- - - -), the
restricted model 2 (- = * a - - -), and the restricted model 3 (-=--*--).
CHAPITRE 5
EFFETS DE LA HAUTEUR DE PRISE DE VUE DES IMAGES ET DU
STADE DE CROISSANCE DE LA CULTURE SUR LES ESTIMÉS DE
COUVERTURE FOLIAIRE ET LEUR PERFORMANCE DANS LES
MODÈLES PRÉVISIONNELS
Ce chapitre a été soumis pour publication à la revue Crop Protection Vol. 00, No 00,
pp.000-000, 1999 sous le titre de "Influence of images recording height and crop
growth stage on leaf cover estimates and their performance in yield prediction
models."
5.1. Résumé du chapitre 5
Au cours de travaux antérieurs, il a été démontré qu'aux stades précoces de
croissance des plantes, les estimés de couverture foliaire d6temiinés par analyse
d'images fournissaient une bonne estirnatio:: de la surface foliaire. De plus, la
couverture foliaire relative des mauvaises herbes et leur surface foliaire relative ont
montré des performances comparables pour leur utilisation dans les modèles
pr6visionnels. Ces travaux recommandaient l'usage de la couverture foliaire (plus
facile à mesurer) à la place de la surface foliaire dont la mesure est non seulement
destructive mais aussi très laborieuse. L'utilisation des données de couverture
foliaire des plantes dans les outils de prise de décision nécessite cependant
l'acquisition de connaissances additionnelles en rapport avec les effets de plusieurs
facteurs parmi lesquels, la période d'échantillonnage des images et la hauteur de
prise de vue de ces dernières. La période d'échantillonnage doit non seulement être
dictée par la précision des estimés obtenus, mais aussi elle doit tenir compte des
systèmes de production, et être sufTisamment précoce afin de laisser assez de temps
pour la mise en place des interventions. La hauteur de prise de vue affecte la
résolution des images et peut avoir un grand impact à la fois sur les estimés obtenus
et sur leurs valeurs prédictives. Cette recherche avait pour objectifs : (1) d'étudier
I'effet de la période d'échantillonnage de la couverture foliaire et I'effet de la hauteur
de prise de vue des images sur les estimés obtenus, et (2) de tester la performance
de ces estimés sur les modèles prévisionnels.
Des expériences en champ ont été menées en 1996 et 1997 avec le maïs en
compétition avec des densités variables (O à 300 plants/m2) de chénopode blanc
(Chenopodium album L.), de pied de coq [Echinochloa crvsgalli (L.) Beauv] et d'un
mélange des deux espèces. La couverture foliaire de la culture et des mauvaises
herbes était échantillonnée aux stades quatre- six- et huit-feuilles du maïs. A chaque
période d'échantillonnage, des images étaient prises à la hauteur de 1'5; 1'9 et 3'3 m
dans chaque parcelle. La couverture foliaire était deteminée par la technique
d'analyse d'images décrite dans des travaux antérieurs (Ngouajio et al. 1998). Un
modèle prévisionnel sigmoïde a quatre paramètres, très versatile, a ét6 utilisé pour
ajuster les données de rendement du maïs aux couvertures foliaires relatives des
mauvaises herbes.
Les estimés de la couverture foliaire du mai's étaient très variables, Ils ont été
affectés par la période d'échantillonnage des images et par la hauteur de prise de
vue. Les données provenant des images prises à 3,3 m Btaient plus fiables que
celles obtenues à partir d'images prises plus près du sol (1'5 et 1'9 m).
L'échantillonnage prbcoce (stade quatre-feuilles du maïs) a produit des estimés
moins variables que l'échantillonnage plus tardif. En ce qui concerne les prédictions
des pertes de rendement, la période d'échantillonnage de la couverture foliaire a eu
peu d'effets sur l'ajustement du modéle. Cependant, du point de vue pratique, les
échantillonnages au stade six-feuilles de la culture pourraient être plus appropriés
que des échantillonnages hâtifs ou tardifs. A ce stade, la plupart des herbicides de
postlevée peuvent encore être utilisés. Indépendamment du type de mauvaises
herbes et du stade de croissance du maïs, les images prises à 3,3 rn au-dessus du
sol ont généralement permis d'obtenir de meilleures prédictions que lorsque les
images étaient prises de plus près.
Les résultats des travaux présentés ici démontrent qu'il est possible
d'améliorer les estimés de couverture foliaire des plantes et ultimement leur
performance dans les modèles prévisionnels grâce à un choix judicieux de la période
d'échantillonnage des images et de leur résolution. De telles améliorations,
associées aux techniques d'analyses d'images plus précises et au développement de
modèles de prédiction précis, flexibles et versatiles contribueront Ci la mise sur pied
d'un outil efficace d'aide à la prise de décision. Un tel outil permettra de faire passer
la lutte contre les mauvaises herbes de l'étape de la prévention à celle des
interventions mieux ciblées.
5.2. Influence of images recording height and crop growth stage on leaf cover
estimates and their performance in yield prediction models
M. Ngouajio, G. D. Leroux, and C. Lemieux
5.2.1. Abstract
Field experiments were conducted in 1996 and 1997 to study the effects of crop
growth stage and images recording height on the estimates of leaf cover obtained
through digital image analysis techniques, and to test the effectiveness of these data
in maize yield prediction. Maize leaf cover estimates were highly variable and the
precision was influenced by both the crop growth stage and the camera recording
height. Images recorded at 3.3 m above the ground produced more reliable
estimates than those taken at lower heights. Early timing of leaf cover assessment
produced estimates with smaller variability than later timings. Maize yield prediction
was slightly affected by the timing of leaf cover sampling. However, sampling at the
six-leaf stage of maize may be more appropriate from a practical stand point than
earlier or later samplings. While being compatible with many control options, this
would allow enough weed seeds to germinate. Increasing the images recording
height improved the accuracy of yield predictions. Data from images taken at 3.3 rn
fitted the mode1 better than those from images recorded at 1.5 and 1.9 m. These
results indicate that appropriate timing of leaf cover assessment and appropriate
selection of image shooting height may help improve the accuracy of crop yield
prediction, and thereby, reduce the risk of making wrong weed control decisions.
Key words: lntegrated weed management; Zea mays; yield prediction
Abbreviated title: Influence of height and crop growth stage on yield prediction
5.2.2 Introduction
The major cause for crop yield reduction by weeds is competition for growth limiting
resources of light, water and nutrients. For decades, weed control in major
agronomic crops has relied solely on herbicide use (Leroux, Laganiere and Vanasse,
1990; Duke, 1996). In recent years, however, reports of herbicide resistance and
environmental concerns have drawn attention to the development of integrated weed
management programs with a more rational herbicide input (King, Lybecker,
Schweizer and Zimdahl, 1986; Kropff, 1988; Brain and Cousens, 1990; Hall, Swanton
and Anderson, 1992; Kropff and Lotz, 1992a; Kropff, Weaver and Smits, 1992; Wiles,
Gold and Wilkerson, 1993; Lemieux, Panneton and Benoit, 1995; Baziramakenga and
Leroux, 1998). The implementation of such strategies requires the integration of
multiple factors including the prediction of the effects of weed wmpetition on crop
yield. A well designed decision making tool capable of predicting the outwme of
weed competition with adequate precision is a major key to ensure success of
integrated weed management programs (Kropff and Lotz, 1992a; Lemieux et al.,
1995; Knezevic, Horak and Vanderlip, 1997). For this purpose, several models
relating crop yield to the presence of weeds have been developed. These models
use either the estimates of weed density (Dew, 1972; Cousens, Peters and Marshall,
1984; Cousens, 1985a; Cousens, Brain, O'donovan and O'Sullivan, 1987; Swinton
and Lyford, 1996). the estimates of weed and crop densities (Cousens, 1985b), or the
relative leaf area of weeds (Kropff and Spitters, 1991; Kropff and Lotz, 1992b; Lotz,
Kropff, Bos and Wallinga, 1992; Kropff, Lotz, Weaver, Bos, Wallinga and Migo, 1995;
Lotz, Wallinga and Kropff, 1995). lrrespective of the input variables used, the major
constraint to practical applications of yield loss prediction models remains the labour
intensive and tirne consuming acquisition of accurate estirnates (Wiles et al., 1993;
Lotz, Kropff, Wallinga, Bos and Groeneveld, 1994; Knezevic, Weise and Swanton,
1995; Andreasen, Rudemo and Sevestre, 1997). Weed density estimation by field
scouting is inaccurate due to their patchy distribution (Brain and Cousens, 1990;
Wiles et al., 1993), and destructive leaf area measurements is unrealistic due to the
amount of work required to harvest and process individual plants (Lotz et al.. 1994;
Knezevic et al., 1995). In order to overcome these constraints, leaf cover estimation
by digital image analysis has been suggested (Lemieux et al., 1995). Recent
progress in this area have yielded powerful techniques of leaf cover estimation
(Lutman, 1992; Lotz et al., 1994; Carson, Lass and Callihan, 1995; Andreasen et al.,
1997; Andrieu, Allirand and Jaggard, 1997; Ngouajio, Lemieux, Fortier, Careau and
Leroux, 19963. Although these techniques have been dernonstrated to be quick and
accu rate, several questions need to be addressed to improve performances of the
estimates in yield loss prediction models. The intent of this work was to address two
of these questions.
The first question refers to the timing of leaf cover estimation: what is the
influence of crop growth stage on the estimates of leaf cover and the quality of yield
predictions? Timing of measurements should take into account the critical period of
weed interference (Hall et al., 1992) and should be done eariy enough to allow time
for the implementation of control measures (Knezevic et al., 1997). In fields, weeds
usually ernerge in Rushes (Kropff and Spitters, 1991 ; Kropff et al., 1992; Knezevic et
al., 1995), and too eariy leaf cover estimation may underestimate the importance of
weeds, leading to inadequate control decisions. Use of references such as the
number of days after planting or the nurnber of days after emergence are not
appropriate for timing of leaf cover estimation as they do not provide a reliable
representation of the actual situation in the field and therefore cannot allow
cornparison of data from different experiments.
The second question concems the resolution of images used for leaf cover
estimation: what is the influence of image resolution on estimates of leaf cover and on
quality of yield predictions? On the basis of individual images, accuracy of estimates
is closely linked to the size of the smallest detectable plant part. However, when an
entire field is considered, the area included in each image becomes an important
factor. Apart from the type of cainera and lens used, both the resolution and the area
covered Vary with the height at which images are taken. For weed detection in
pastures and forests, Carson et al. (1995) proposed the use of an airplane Rying at
2.7 km for a resolution of 1 m2. In Our previous work with maize (Ngouajio et al.,
1998). a height of 1.9 m (1 mm2 resolution) was used. Andrieu et al. (1997) used
photographs taken at 2.5, 5 and 10 m to estimate maize and sugar beet (Beta
vulgaris) leaf cover. At low height, smaller plant parts are readily detectable, due to
the high resolution of images. However, estimates obtained rnay not be
representative of the actual weed infestation in the field, due to patchy weed
distribution (Brain and Cousens, 1990; Wiles et al., 1993), and to smaller area
included in each image (Kershaw, 1973; Lemieux, Cloutier and Leroux, 1992).
Conversely, when height is too important, the area per photograph increases, but
precision may be lost, due to low resolution. The appropriate choice of height at
which images are taken is therefore very important and should take into accounts
both the situation under investigation and the logistics of the farm production unit.
Objectives of the present study were (1) to determine the effect of crop growth
stage and image recording height on estimates of leaf cover obtained by digital image
analysis, and (2) to test the performance of these estimates in a yield prediction
model.
5.2.3. Materials and Methods
5.2.3.1. Experimental site and growing conditions
Field experirnents were conducted in 1996 and 1997 at the Agronorny Station of
Laval University located at Saint-Augustin (Quebec). The soi1 at this site is a sandy
loam with 3.9% organic matter and a pH of 6.3 and was fallowed each of the previous
two years. Except for the month of May 1997, the temperatures over the two growing
seasons were similar to the long-term average. Rainfall varied in total amount and
pattern (Table 1). In 1997, snow accumulation was exceptionally high (data not
shown). The average temperature in May was below normal (Table 1 ) and caused a
delay in the sowing date and in weed emergence. The late weed ernergence (1997)
was followed by 15 days of hot and dry weather (from June O1 to 15). These
conditions caused a crust formation at the soi1 surface, which affected plant growth,
mainly the newly emerged weeds. At equivalent growth stages, maize and weeds
were smaller in 1997 compared to 1996 during the first month of growth.
5.2.3.2. Experimental procedures
Maize hybrid 'Pioneer 3967' was grown according to the provincial recornmendations.
The crop was seeded May 8, 1996 and May 15, 1997, at a density of 66,000
plantslha, in rows 75 cm apart. The site had been previously fall mouldboard plowed
and cultivated.
The experiments included three types of weed infestation (comrnon
lambsquarters: Chenopodium album L, bamyardgrass: Echinochloa cmsgalli (L.)
Beauv. and both species at equal densities). Fifieen weed densities for each
infestation type were used: 0, 5, 10, 15, 20, 30, 40, 50, 75, 100, 125, 150, 200, 250,
and 300 plants mm*.
The final weed densities were achieved by successive hand weeding of the plots.
Initial thinning was conducted between 1 and 2 wk after emergence. In 1996, weeds
emerged on May 20, three days prior to the crop while in 1997, they emerged on
June 01, one day after the crop. Emergence dates were based on visual estimates of
50% emerged plants. The experiments were additive series, and the treatments were
assigned to 3- by 8-m plots (four maize rows), arranged in a completely randomized
design.
Lea f cover sampling and estimation
Leaf cover was measured at the four-, six- and eight-leaf stage of maize development
(Table 2). These stages fall within the critical period of weed wntrol in maize (Hall et
al., 1992) and within most postemergence maize herbicides application window. Only
plants with fully expanded leaves were included in the count when recording the crop
growth stage. Images were recorded using a high resolution color digital camera
(Kodak professional DCS420c digital camera, Kodak Canada Inc., Toronto, Ontario,
Canada, M6M 1V3) equipped with a 28-mm ultra-fast lens. The camera uses a
charged couple device with 1,012 rows and 1,524 columns corresponding to a
theoretical resolution of 1.54 megapixels. However, the practical resolution was only
one third (0.514 rnegapixels). The camera supporting device was custom-built and
allow to take horizontal frames at different heights. At each sarnpling date, three
digital images were recorded in each plot at heights of 1.5, 1.9 and 3.3 ml with
corresponding resolutions of 0.6, 1 .O and 3.2 mm2, respectively (Table 3). The
camera was positioned to allow the maize rows to be parallel to the width of the
images. Images taken at 1.5 and 1.9 m included one maize row (the right-hand side
middle row) and those taken at 3.3 m included two maize rows (the middle rows).
The camera was positioned in such a way that the area covered by the images taken
at 1.5 rn was included in the images taken at 1.9 m which was in tum included in the
images taken at 3.3 m. The leaf cover was estimated using a digital image analysis
system (Su rfacesProTM, Société de Mathématiques Appliquées Inc., 59 d'Auteuil
Street, Quebec, QC, Canada G1R 4C2). Detail of the images acquisition and
analysis procedures have been provided in a previous study (Ngouajio et al,, 1998).
For images recorded at different heights, the proportion occupied by an average
maize plant differed, and this proportion also differed from that occupied by the same
rnaize plant in the field. To account for this effect, a correction factor was used (Table
3). This correction was not required for weeds as their stands were uniform on the
plots.
Final hantest
Maize was hand-hawested from the middle two rows of each plot on October 12,
1996 and October 1, 1 997. Grains were dried at 50°C for 1 0 days prior to weig hing.
5.2.3.3. Data analyses
All maize and weed leaf cover were expressed as percent ground cover to allow
cornparisons at different camera shooting heights. Average maize leaf cover was
computed, and the precision of the estimates evaluated using either the standard
error of the means or the coefficient of variation (CV). For yield prediction,
regressions of weed relative leaf cover (weed leaf cover divided by total plant leaf
cover) on rnaize yield data were performed, using the non-linear regression mode1
proposed by Ngouajio, Leroux and Lemieux (1 999):
where Y is the predicted crop yield, Y. is the maximum yield or yield in weed-free
conditions (upper asymptote), a is the minimum yield or the lower asymptote as weed
relative leaf cover (Lc) approaches unity, i.e. Lcl(1-Lc) approaches infinity, y is the
value of (1-Lc)lLc at which half of the yield is lost (the corresponding va!ue of Lc is
1/(1+ y)), and 6 is a measure of the sigmoid curvature and is used as a measure of
the cornpetitive ability of the weeds compared to the crop.
The F-test and t test were used to determine the significance of the
regressions and reg ression parameters, respectively. The rZ values were calculated
according to the following equation: P = 1 -(residual sum of squares/total corrected
sum of squares) (Chisrn, Birch and Bingham, 1992; Baziramakenga and Leroux,
1998). The performance of the leaf cover variables in the yield prediction model was
compared, using the residual mean squares (Lotz, Christensen, Cloutier, Quintanilla,
Légère, Lemieux, Lutman. Iglesias, Salonen. Sattin, Stigliani and Tei, 1996). All
regression analyses were performed using the nonlinear regression procedure of
SASTM (SAS Institute Inc., 1989).
5.2.4. Results and discussion
The regression analyses were run separately for individual year, maize growth stage,
camera shooting height and weed infestation type.
5.2.4.1. Leaf cover estimation
One of the objectives of this work was to study the effect of plant growth stage and
the camera shooting height on the precision of leaf cover estimates. The coefficient
of variation (CV) was used for comparison of leaf cover estimates at different crop
growth stages and at different camera shooting heights. Within the same maize
growth stage, the standard error of the means was used to study the effect of the
camera shooting height.
Within crop growth stage, leaf cover estimates from images recorded at 3.3 m
above plant canopy were less variable than estimates from images recorded at 1.5 or
1.9 m (Table 4). At the four-leaf stage of maize, CV of the estirnates was 26.3 for
images recorded at 3.3 rn compared to 31.4 and 34.6 for those recorded at 1.5 and
1.9 m. respectively. The same trend was observed at the six-leaf stage of maize. At
the eight-leaf stage, precision of the estirnates slightly improved with increasing
camera shooting height (Table 4). These observations suggest that by increasing the
camera shooting height. more reliable leaf cover estirnates may be obtained. On the
basis of image resolution (Table 3), it was expected that precision of leaf cover
estimates will decrease with increasing camera shooting height. However, at the
different resolutions used (0.6, 1 .O and 3.2 mm2), the image analysis system was able
to detect maize plant part equally well at al1 camera shooting heights. This could
have been different if there had been very small or germinating plants in the plots. In
a previous study, it was shown that the image analysis system can detect plant parts
as small as 0.5 cm2 from images recorded at 1.9 rn with high precision (Ngouajio et
al. 1998).
The red uced variability of the estimates with increasing camera shooting height
was more likeiy due to the size of area included in the images. The smaller size of
area included in images recorded at 1.5 or 1.9 m (Table 3) associated to a lack of
uniformity of rnaize stands within individual row resulted in high variability in the
number of maize plants per image. This variability was less important for images
recorded at 3.3 m. The importance of using large sample sizes have been addressed
by Kershaw (1 973) and Lemieux et al. (1 992).
The precision of maize leaf cover estimates was affected by growth stage
(Table 4). The coemcient of variation ranged from 26.3 to 31.4 at the four-leaf stage,
from 40.0 to 49.3 at the six-leaf stage and from 39.8 to 42.7 at the eight-leaf stage of
maize. This indicates that sampling at the earliest growth stage produced more
reliable estimates. This observation is in agreement with results from previous
studies (Ngouajio et al. 1998). It was shown that leaf overlapping resulting from later
plant growth stages reduces the precision of leaf cover estimates. In the same study,
it was shown that plant architecture rnay also have an important effect. In the present
work, CV values are higher than the norm usually accepted for field experiments
(Gornez and Gornez, 1984). These large values may be attributed to maize leaf
architecture (some plants with rolled leaves and others with fully expanded leaves).
The observations reported indicate that leaf cover estimates obtained by digital
image analysis are affected by both the camera shooting height and the timing (crop
growth stage) at which images are recorded. This may have an impact on yield
prediction since those estimates are used as input variable in yield prediction models.
5.2.4.2. Yield prediction
In general, better yield predictions were obtained in 1997 compared to 1996,
irrespective of weed infestation type (Figure 1) . Values of residual mean squares
calculated from mode1 fitting varied from 92,635 to 626,603 in 1996 and from 39,739
to 227,293 in 1997. Plots infested with C. album or E. cms-galli resulted in maize
yield predictions with a higher degree of precision than plots infested with a mixture of
both weed species (Figure 1).
Effect of crop growth stage
The crop growth stage at which the images were sampled had little effect on yield
prediction (Figure 7). Values of residual mean squares for the different weed species
were in the same order for data collected at the four-, six- or eight-leaf stages of
maize. The exception to this general observation was with plots infested with the
mixture of both C. album and E. cnisgalli, and that was found only in 1996 (Figure 1).
In those plots, data from images recorded at the four-leaf stage of maize were not as
reliable as those from images recorded at later growth stages, especially with a low
camera recording height.
It was expected that since precision of leaf cover estimation was better at the
four-leaf stage of maize, the same observation could apply to yield predictions.
However, this was not the case, and in general al1 crop growth stages produced
comparable predictions. The lost of precision in the estimation of leaf cover caused
by increased leaf overlapping at increasing growth stages seerned to have had little
effect on plant competition. This suggests that the hidden leaf area caused by leaf
overlapping did not contribute much to the cornpetitive ability of the plants.
Aithough our results suggest that for yield prediction purposes leaf cover
sampling can be done at any time, for a practical point of view early evaluations
should be recommended in order to allow time for the implementation of control
measures (Knezevic et al., 1997). For this reason the eight-leaf stage of maize must
be ruled out. Under natural conditions, weeds usually emerge in flushes (Kropff and
Spitters, 1991 ; Kropff et al., 1992; Knezevic st al., 1995). In our experiments weed
emergence was uniform and as such the effect of late emerging weeds was absent.
However, in field conditions this effect may reduce the quality of prediction when leaf
cover is evaluated too early. For this reason it might be more appropriate to sample
leaf cover at the six-leaf stage of maize rather than at the four-leaf stage. The six-leaf
stage of maize falls within the application window of most postemergence herbicides
and allow the use of other weed control options such as mechanical weed control
methods (Anonymous, 1995). The timing of leaf cover sampling at the six-leaf stage
of maize for control decisions may then be compatible with integrated weed
management programs aiming at reducing the use of herbicides.
Effect of camera shooting height
As indicated earlier, estimates of leaf cover obtained using different camera shooting
heights (Table 3) were affected by this factor (Table 4). This was reflected in the
fitting of the yield prediction model (Figure 7). Generally, the best fitting of the model
within individual year and weed infestation type was obtained with data from images
taken at 3.3 m above plant canopy. With very few exceptions, an increase in the
camera shooting height resulted in an improvement in model fitting. These results
were expected since the increase in the camera shooting height increases the area
included in individual images, and consequently reduces the variability of the leaf
cover estimates. As mentioned earlier, this observation was more likely related to the
sampling technique rather than being in herent to the resolution of images which
would have probably resulted in a reverse situation. The image resolution used in
this work (Table 3) did not affect leaf cover estimates and fitting of the model since
plant detection was good at al! camera shooting heights.
Our results indicate that an image recording height of 3.3 m above the ground
(corresponding to a resolution of about 3.2 mm2) should be preferred to lower heights.
In addition. for a practical stand point, the six-leaf stage of maize may be more
appropriate for leaf cover sampling. The combination of those two factors provided
adequate fitting of the yield prediction model (Figure 2). Values of the variation
explained by the model (P) varied between 0.73 and 0.91, irrespective of the growing
season and type of weed present in maize plots (Table 5). Although it might be easy
from a practical point of view to agree that the six-leaf stage of maize is an adequate
timing for leaf cover sarnpling, it rernains difficult to Say that a height of 3.3 m was the
most appropriate for images recording. Since 3.3 m was the highest setting used in
this work, one could suspect that increasing further the performance of the yield
prediction mode1 could be done by increasing the image recording height (reducing
the resolution of the images). Andrieu et ai. (1997) obtained good estimates of maize
and sugar beet leaf cover from photographs taken at 10 m above the ground. Carson
et ai. (1995) demonstrated that it was possible to detect heavy infestations of yellow
hawkweed (Hieracium pratense) with high accuracy in pastures and forests using
images taken from a camera attached to an airplane flying at 2.7 km above the
ground. However, the low resolution of the images taken at such a distance
(1 m2/pixel) may not provide reliable detection of weed at early growth stages or at
moderate infestation levels. In addition, the extra cost associated with the operation
of an airplane may not be justified. It is clear that the height at which images are
taken and consequently their resolution, depends mainly on the situation being
investigated and the logistics used. At a small farm scale, a height of up to 10 m
above the ground may be envisaged since a well designed camera supporting device
attached to a tractor rnay allow to reach this height conveniently. Leaf cover
estimates from such images would probably be affected by image resolution and their
performance in yield prediction rnodels will need to be evaluated.
Acknowledgements
Funding for this research was provided in part by the Matching lnvestment Initiative of
Agriculture and Agri-Food Canada. The senior author is a recipient of a scholarship
frorn the «Programme Canadien des Bourses d'Excellence de la Francophonie)). We
thank Mr. Jocelyn Lamarre and Ms. Michèle Martel for technical and professional
assistance and summer students for field plot work, especially hand weeding and
vegetation sampling. The weather data were supplied by Dr. Philippe Rochette.
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Table 1. Total monthly rainfall and rnean temperature during the 1996 and 1997
growing seasons, and long term average (30 years)=
Rainfall (mm) Temperature (OC)
Month
1996 1997 Long 1996 1997 Long
term term
May 73.1 96.0 108.2 10.7 8.8 10.8
June 142.5 62.0 111.3 17.8 17.1 16.4
July 235.8 69.0 125.4 19.3 19.3 19.2
August 76.0 166.0 11 6.3 19.1 17.8 17.9
September 108.0 68.0 II 8.3 14.3 13.3 12.5
October 86.0 48.0 98.1 6.3 6.7 6.4
'Data recorded at the Quebec City airport about 10 km from the experimental plots.
Table 2. Weed growth stage at the four-, six-, and eight-leaf stage of maize growth
Weed
speciesa
Maize growth stageb
Fou r-leaf Six-leaf Eig ht-leaf
Number of fully expanded leaves
1996
Chenopodium album 2to 10 6 to 22 14 to 40
Echinochloa crus-galli 2 to 6 5to 12 7 to 14
1997
Chenopodium album 2 to 6 5to 10 8 to 18
Echinochloa crus-galli 2 to 4 4 to 7 6 to 10
'The experiments included 15 plots of Chenopodium album, 15 plots of Echinochloa
crvs-ga//i and 15 plots of a mixture of both species grown at equal densities.
b ~ a i z e reached the four-leaf stage (June 06 in 1996 and June 11 in 1997), the six-
leaf stage (June 12 in 1996 and June 16 in 1997), and the eight-leaf stage (June 18 in
1996 and June 23 in 1997).
Table 3. The effect of camera shooting height on the area covered by the picture, the
spatial resolution of images and maize leaf cover estimates
Camera Area per image Image Maize leaf
s hooting spatial cover correction
heig ht Length Width Area resolutiona facto?
(m) (ml (m) (m2) (mm2 pixel-') (?"d
a The image spatial resolution was obtained by dividing the area included in the
image by the number of pixels in the image (514,096).
The correction factor (in percent) at a given height was calculated as the difference
between the area occupied by a maize plant in each image and the area occupied by
a maize plant at the field scale.
Table 4. The effect of the camera shooting height on maize average leaf cover
estimates (% ground cover) at different growth stages
Maize growth Heighta Mean Standard c.v.~ stage (m) error
Six- leaf
Eig ht-leaf
a Camera shooting height
C.V. coefficient of variation.
Table 5. Regression parameters calculated from maize yield prediction using the
relative leaf cover of weeds and the sigmoidal model (equation 1). Data were
recorded at the six-leaf stage (fully expanded leaves) of maize with the camera at 3.3
rn above plant canopy.
Year Weed
infestation
Regression parameters
1996
C. album
E. crus-galli
C. album + E. crus-galli
C. album
E. crus-galli
C. album + E. crus-galli
30 l C. album
E. crus- galli
C. album
E. crus- galli
C. album and E. crus- galli
Maize growth stage
Figure 1 . Residual mean squares (RMS) obtained by fitting the yield prediction rnodel
with maize yield and weed relative leaf cover. Leaf cover estimates were obtained
from images recorded at different heights and crop growth stages, using a digital
image analysis technique. The regression mode1 used was:
Y=[Yo+a(L J(l -~~)y) ' ] / [1 +a(L J(I - Q y ) Y .
] C. album . 5
I I 1 I
C. album ~ l u s
C. album
E. crus-galli
C. album plus E. crus-galli
Weeds relative leaf cover
Figure 2. Maize yield as a function of weed relative leaf cover estimated from images
taken 3.3 m above the ground at the six-leaf stage of maire development in 1996 and
1997. The model used was the following :
Y=[Yo+a(L J(l - L , ) ~ ) ~ I [1 +a(L J( l - ~ , ) ~ ) q .
CHAPITRE 6
CONCLUSION GÉNÉRALE
(SYNTHÈSE)
Au cours de la dernière décennie, l'apparition de mauvaises herbes résistantes
aux herbicides, la nécessité d'optimiser les coûts de production et les préoccupations
de protection de l'environnement ont mis des pressions importantes sur les
producteurs pour réduire l'utilisation des herbicides de synthèse (Swanton et Weise,
1991 ; Kropff et Lotz, 1992a, 1992b; Maxwell et Mortimer, 1994; Duke, 1996; Shaner,
1997). Parmi les pistes de solution envisagées pour atteindre ce but, la rationalisation
de I'utilisation des herbicides, qui consiste à ne traiter que lorsque c'est nécessaire,
avec la dose requise et sans sacrifier les rendements, figure en bonne place
(Swanton et Weise, 1991; Kropff et Lotz, 1992a, 1992b; Dieleman et al., 1995;
Lemieux et a1.,1995; Lotz et al., 1995). Toutefois, la seule façon de convaincre les
producteurs de remplacer la pratique géneralisée de traitements préventifs en
prélevée par des traitements curatifs de postlevée est de mettre à leur disposition un
outil efficace et fiable de dépistage et de quantification des mauvaises herbes et un
modèle de prédiction des pertes. Le présent travail a été entrepris dans le but de
contribuer au développement d'une telle technologie.
La surface foliaire des mauvaises herbes a déjà été démontrée comme étant
un indice fiable de leur taux d'infestation (Lotz et ai., 1994; Dieleman et al., 1995;
Knezevic et al., 1995). Cependant, à cause de son caractère destructif et de
l'ampleur des matripulations requises, une variable alternative à savoir la couverture
foliaire a été proposée (Kropff, 1988; Lotz et al., 1994, 1995). La couverture foliaire
est la surface obtenue par projection verticale des feuilles sur le sol. Plusieurs
chercheurs ont développé des méthodes d'estimation de la couverture foliaire des
plantes. Ces méthodes sont soit tout simplement visuelles soit font recours à un
cadre quadrillé que l'on place sur la parcelle (Lotz et al., 1994, 1995 ou sur une
photographie de cette dernière (Lutman, 1992), afin de compter les carreaux couverts
par chaque espèce. Ces techniques restent très exigeantes, et donc, inappropriées
pour une utilisation pratique. Lemieux et al. (1995) ont proposé I'utilisation de
l'analyse d'images numériques pour déterminer la couverture foliaire des plantes.
Notre première série d'expériences consistait donc a Btudier cette technique.
Entre autres, il était question (1) de savoir si oui ou non les donnbes obtenues par
analyse d'images fournissaient une bonne reprbsentation de la couverture foliaire
réelle et (2) d'étudier la relation qui existe entre la couverture foliaire ainsi obtenue et
la surface foliaire.
Grâce à notre essai de laboratoire avec des cultures et des mauvaises herbes
simulées nous avons démontré de maniére convaincante que le système d'analyse
d'images développé était efficace et fiable. La technique d'analyse d'image a permis
de détecter avec grande précision des parties de plantes aussi petites que 0'5 cm2.
Les régressions linéaires simples entre les données fournies par le système et les
données réelles ont produit des valeurs de ? supérieures B 0'98. Une telle précision
en laboratoire était nécessaire pour statuer définitivement sur la fiabilité du systéme.
Récemment. d'autres travaux de recherche sur I'utilisation de la technique d'analyse
d'images pour déterminer la couverture foliaire des plantes ont été publiés (Carson et
ai., 1995; Andreasen et al., 1997; Andrieu et al., 1997). Ces travaux ne font toutefois
aucune corrélation entre les données obtenues par analyse d'images et les données
réelles. A notre avis, cette démonstration devrait constituer un préalable à l'utilisation
des techniques développées in situ. La validation du systerne d'analyse d'images sur
le terrain nous a démontré de manière indéniable qu'aux stades précoces de
croissance, la couverture foliaire des plantes était fortement corrélée à leur surface
foliaire, et que cette relation pouvait être affectée par l'architecture des plantes
étudiées. Que ce soit en infestation contrôlée ou naturelle, nous avons observe des
valeurs de ? supérieures a 0.89. Toutefois, la prkision de ces estimés diminuait
avec l'avancement du stade de croissance des plantes, et l'écart entre la surface
foliaire et la couverture foliaire devenait de plus en plus grand. Cet écart entre les
deux variables était de toutes les façons prévisible dans la mesure ou la
superposition des feuilles augmente avec l'avancement du stade de croissance des
plantes.
Les résultats de nos essais sur le terrain nous ont définitivement convaincu de
la qualité du système d'analyse d'images. Ce système pourrait d'ailleurs trouver
d'autres applications potentielles en recherche, notamment (1 ) comme outil dans
l'étude de la compétitivité entre les espéces végétales, et (2) comme support objectif
et quantitatif aux obsewations visuelles de la végétation.
Ainsi, dans le premier volet de nos travaux, nous avons démontr6 de maniére
indéniable que les données de couverture foliaire fournies par le système d'analyse
d'images sont précises d'une part, et d'autre part qu'elles sont fortement corrélées
aux données de surface foliaire. Aussi, la technique d'analyse d'images est à la fois
non destructive et moins laborieuse que la mesure de la surface foliaire. Ces
observations, associées aux propositions d'autres chercheurs (Lotz et al., 1994,
1995; Kropff, 1998) nous ont amené logiquement à envisager de remplacer la surface
foliaire relative des mauvaises herbes par leur couverture foliaire relative dans les
modèles prévisionnels. Une telle opération ne pouvait cependant être justifiée que
par des tests de validation dans des conditions variées d'infestation et
d'environnement. Pour répondre à cette exigence, une série d'essais au champ a été
menée en 1996 et 1997, pour tester et comparer l'efficacité de la surface foliaire
relative et de la couverture foliaire relative des mauvaises herbes en prédiction des
pertes de rendement chez le maïs (Zea mays).
Les résultats de ces travaux ont démontré que la surface foliaire relative des
mauvaises herbes est un bon indice de mesure de l'effet de la compétition entre les
mauvaises herbes et les cultures. Les régressions avec le modèle hyperbolique à
deux paramètres (Kropff et Lotz, 1992b; Lotz et al., 1992; Kropff et al.. 1995;) ont
donné des coefficients de détermination entre 0'61 et 0,92 au cours des deux années
et sous des conditions d'infestation très variables. Cette observation en elle-même
ne constituait pas une nouveauté dans la mesure ou des résultats similaires ont été
précédemment rapportés par d'autres chercheurs (Lotz et al.. 1994; Dieleman et ai.,
1995; Knezevic et al., 1995). Par contre. l'efficacité de la couverture foliaire relative
des mauvaises herbes dans les modèles prévisionnels restait à démontrer. La
substitution de la surface foliaire relative des mauvaises herbes par leur couverture
foliaire relative s'est soldée par une baisse de la valeur des paramétres q et m
(coefficient de dégâts relatif des mauvaises herbes et perte maximale prédite de
rendement) du modèle. En dépit de cette observation, le pourcentage de variation
expliqué par le modéle (de 0,67 à 0,90) était du même ordre de grandeur que les
valeurs obtenues avec la surface foliaire relative. Sur la base de la somme des
carrés des residus, aucune variable ne pouvait être déclarée supérieure à l'autre en
prédiction des pertes de rendement. Ces r6sultats nous ont permis de demontrer
l'efficacité des données de couverture foliaire en prédiction des pertes de rendement,
justifiant ainsi leur utilisation potentielle dans les modèles prévisionnels.
Si dans le premier volet étudié nous avons démontré qu'il est possible
d'estimer la couverture foliaire des plantes de manière rapide et pr6cise par anelyse
d'images, dans le second nous avons demontré que les données ainsi obtenues
permettent de prédire efficacement les rendements des cultures. Ces deux faits
constituent une importante ouverture pour l'utilisation pratique de la couverture
foliaire des plantes pour prédire les pertes de rendement dans des systèmes de lutte
intégrée qui visent la réduction des intrants en herbicides. Cependant, la mise sur
pied d'une telle technologie nécessiterait des raffinements majeurs parmi lesquels (1)
l'amélioration des techniques d'échantillonnage et d'analyse d'images, (2) le meilleur
choix de la période d'échantillonnage et (3) le developpement et la validation des
modèles empiriques appropriés.
Le troisième volet de notre travail a été initie afin d'apporter une réponse à ce
dernier point. II a porté sur le développement et la validation d'un modèle de
pr&d iction des pertes utilisant la couverture foliaire relative des mauvaises herbes.
A l'issue de cette étape, un modèle semi-empirique, sigmoïdal et flexible a été
dérivé à partir du modèle proposé par Morgan et al. (1975) et repris par Swinton et
Lyford (1996). La construction du modèle s'est faite en tenant compte de plusieurs
facteurs qui gouvernent la compétition entre les espèces végétales. Ceci constitue à
notre connaissance le premier modèle de prédiction des pertes expressément
développé pour la couverture foliaire relative des mauvaises herbes. Une
démonstration a été faite pour prouver que ce modèle comportait plusieurs sous-
modèles qui lui sont emboîtés, parmi lesquels le modéle linéaire simple, le modèle
hyperbolique, le modèle sigmoïde symétrique et le modéle logistique asymétrique.
Lors de tests de validation avec les données de terrain, les performances du rnodéle
ont supplanté celles de tous les sous-modèles à l'exception du modéle hyperbolique
avec lequel il était difficile de se prononcer sur la base de nos données. Le sous-
modèle hyperbolique (à trois paramètres) se positionnait aussi bien que le modèle
complet (A quatre paramètres). Mais compte tenu du caractère semi-empirique du
nouveau modèle (modèle complet). de sa grande flexibilité et de sa capacité A tenir
compte des cas spéciaux qui échapperaient au modèle hyperbolique. nous avons
recommandé son utilisation comme support à la prise de d8cision. Ceci pourra
amener à réduire au minimum les risques d'une mauvaise décision. En dehors de
l'optimisation du modèle prévisionnel, ces risques seront davantage réduits si le choix
de la période d'échantillonnage des images et leur résolution étaient également
optimis6.
Cette préoccupation Ci fait l'objet du quatrième volet de notre travail. II semblait
évident qu'6chantillonner les plantes trop tard en saison ne servirait ii rien, car il
serait inutile d'intervenir. De même, un échantillonnage trop hâtif nous priverait d'une
partie de l'information utile. II fallait donc trouver un compromis entre ces deux
extrêmes, en tenant compte de l'efficacité des interventions. En ce qui concerne la
résolution des images nous savions qu'avec une grande hauteur de prise de vue, il
est difficile de détecter des plantes individuelles; par contre, la superficie couverte par
chaque image est plus grande. Au fur et a mesure que la hauteur est réduite, il est
de plus en plus facile de détecter les mauvaises herbes de plus petite taille, mais la
surface couverte par chaque image est réduite. Une fois de plus il fallait trouver un
compromis entre ces situations extrêmes, et garder à l'esprit l'aspect pratique de la
chose.
Les résultats obtenus lors de ce quatriéme et dernier volet de notre travail
nous ont clairement démontre que pour prédire les pertes de rendement du maïs, la
période d'échantillonnage de la couverture foliaire a peu d'effet. Cependant, pour
des raisons pratiques dont I'effkacitb des interventions, le stade six-feuilles de la
culture serait mieux approprié. Ce stade est propice dans la mesure où il se situe
d'une part dans la pkriode critique de nuisibilité des mauvaises herbes sur le maïs
(Hall et ai., 1992), et d'autre part à l'intérieur de la fenêtre d'application d'un grand
nombre d'herbicides de postlevee.
Pour ce qui est de la hauteur de prÎse de vue, les meilleures prédictions ont été
obtenues avec les images prises à 3,3 m du sol. Malheureusement, ceci représentait
la hauteur maximale de prise de vue testée lors de nos essais. II serait interessant
de voir ce qui se passe avec les images prises plus haut. Toutefois, dans le choix de
la hauteur de prise de vue, il faudra toujours avoir présent B l'esprit la logistique
requise et l'aspect pratique de la chose dans une unité moyenne de production.
Nous estimons qu'a 10 m de hauteur et moins, il est possible de concevoir un support
à caméra portable par un tracteur agricole. Au-delà de cette limite, il faudra sûrement
envisager d'autres types de systèmes pour porter la caméra.
La combinaison de la période optimale d'échantillonnage (stade six-feuilles du
maïs), de la meilleure hauteur de prise de vue des images (3'3 m) et l'utilisation du
nouveau modèle prévisionnel ont amélioré de manière satisfaisante les prédictions de
rendement du mals. Les ajustements des donnees au modèle ont permis d'obtenir
des coefficients de détermination de 0'73 0'91, indépendamment du type
d'infestation des mauvaises herbes et de la saison de culture. Ces résultats étaient
très satisfaisants et nous ont permis de démontrer qu'il est tout à fait possible
d'améliorer les prédictions de rendement des cultures en choisissant judicieusement
certains facteurs et en les optimisant.
L'ensemble des résultats présentés dans cette thèse démontre qu'avec la
technique d'analyse d'images il est possible d'estimer rapidement et avec précision la
couverture foliaire des plantes, d'utiliser les données ainsi obtenues dans des
modéles mathématiques appropriés pour prédire les rendements des cultures tôt au
début de la saison. et d'améliorer la qualité des prédictions grâce Ci un choix judicieux
de la période d'échantillonnage des images et de leur résolution. La mise en
commun de tous ces éléments pourra conduire A la mise au point d'un outil
permettant de décider si oui ou non une intervention est justifide. Ce n'est qu'à ce
moment que l'on pourra entrevoir le passage de la lutte contre les mauvaises herbes
de l'ère des traitements préventifs de prélevée A celle des interventions curatives de
postlevée. Mais avant d'y arriver, la recherche devra relever des défis majeurs. Des
études sérieuses devront être entreprises afin d'automatiser complètement les
analyses d'images. Les analyses d'images devront être intégrées aux modèles
prévisionnels appropriés pour des prises de décision en temps réel. L'outil développé
devra quitter le milieu expérimental pour des tests extensifs de validation a la ferme.
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