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Multispectral classification of grass weeds and wheat (Triticum durum) crop using 1

linear and nonparametric functional discriminant analysis, and neural networks 2

F. López-Granados*, J. M. Peña-Barragán, M. Jurado-Expósito, M. Francisco-3

Fernández1, R. Cao1, A. Alonso-Betanzos2, O. Fontenla-Romero2 4

Department of Crop Protection, Institute for Sustainable Agriculture, CSIC, P.O. Box 5

4084, 14080-Córdoba, Spain. 6

1 Department of Mathematics, Campus de Elviña, Nº 5, La Coruña, 15071, La Coruña, 7

Spain. 8

2 Department of Computer Science, Campus de Elviña, Nº 5, La Coruña, 15071, La 9

Coruña, Spain. 10

* Corresponding author. 11

Abstract 12

Field research was conducted to determine the potential of multispectral 13

classification of late-season grass weeds in wheat. Several classification techniques 14

have been used to discriminate differences in reflectance between wheat, and wild oat, 15

canarygrass, ryegrass and rabbit foot in the 400-900 nm spectrum, and to evaluate the 16

accuracy performance for a spectral signature classification into the plant species or 17

group to which it belongs. Fisher linear discriminant analysis, nonparametric functional 18

discriminant analysis and several neural networks have been applied, either with a 19

preliminary principal component analysis or not and in different scenarios. Fisher linear 20

discriminant analysis, feedforward neural netwroks and one-layer neural network, aal of 21

them with a principal component analysis, showed classification percentages of between 22

90% and 100%. Generally, a preliminary computation of the most relevant principal 23

components considerably improves the correct classification percentage. These results 24

are promising because wild oat and ryegrass, two of the most problematic, clearly 25

Manuscript

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patchy and expensive to control weeds in wheat, could be successfully discriminated 1

from wheat in the 400-900 nm range. Our results suggest that mapping grass weed 2

patches in wheat is feasible with high-resolution satellite imagery acquired in mid-May 3

under our conditions. 4

Keywords: wild oat (Avena sterilis L.), canarygrass (Phalaris brachystachis Link), 5

ryegrass, (Lolium rigidum Gaudin), wheat (Triticum durum L. cultivar Mexicali), rabbit 6

foot (Polypogon monspeliensis L. Desf.). 7

1. Introduction 8

Wheat is the most important winter cereal crop in Spain, with over 5 M ha 9

grown annually (Anonymous, 2004). Wild oat (Avena sterilis L.), canarygrass (Phalaris 10

brachystachis Link) and ryegrass (Lolium rigidum Gaudin) are the most common grass 11

weeds in cereal crops and have been found in 65%, 34% and 32% of the arable fields in 12

southern Spain, respectively (Saavedra et al., 1989). Recently, the spreading of rabbit 13

foot (Polypogon monspeliensis L. Desf.) in wheat is increasing due to it being a grass 14

weed usually associated with rice and this is being included in crop rotation in southern 15

Spain. The patchy distribution of wild oat and ryegrass in winter cereals has already 16

been demonstrated (Barroso et al., 2004b; Blanco-Moreno et al., 2006a, 2006b). One of 17

the main implications of a spatially aggregated pattern is to reduce the herbicide 18

application only to the patches with a weed density which is higher than the economic 19

threshold (Jurado-Expósito et al., 2003b; Francisco-Fernández et al., 2006), which is 20

one of the main principles of site-specific weed management (SSWM). The economic 21

benefits of the patch spraying of broad-leaved and grass weeds in winter cereals 22

(Timmermann et al., 2003), and of wild oat in winter barley (Barroso et al., 2004a; Ruiz 23

et al., 2006) have supported the feasibility of using SSWM to control worldwide weeds. 24

A key component of SSWM is that accurate, appropriate and timely weed maps are 25

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required to take full advantage of site-specific herbicide applications. Rew and Cousens 1

(2001) reviewed discrete and continuous sampling and concluded that mapping weed 2

patches based on ground survey techniques (discrete sampling) is time consuming and 3

expensive on a large scale. They also argued that continuous sampling, such as remote 4

sensing, is more appropriate and cost-effective for SSWM. Remote sensing data can 5

come from ground-based sensors mounted on field equipment, aerial or satellite 6

platforms. The importance of remote sensing in SSWM has been reviewed by 7

Andreasen et al. (1997), Brown and Noble (2005), Felton et al. (2002), Radhakrishnan 8

et al. (2002), Thorp and Tian (2004), Yang et al. (2000). Detection of late-season weed 9

infestation with aerial remote sensing has tremendous possibilities when spectral 10

differences between crops and weeds prevail, and before crop and weeds are turning 11

yellow in colour at the same time (Koger et al., 2003; López-Granados et al., 2006). 12

Taking into account that wild oat (Barroso et al ., 2004b) and other weed infestations 13

can be relatively stable from year to year (Jurado-Expósito et al., 2004; Wilson and 14

Brain, 1991), late-season weed detection maps can be used to design site-specific 15

control methods in the coming years. 16

Girma et al. (2005) studied optical spectral signatures of cheat (Bromus 17

secalinus L.) and ryegrass under greenhouse conditions; however, it would be necessary 18

to explore whether spectral identification is robust under field conditions. López-19

Granados et al. (2006) studied multispectral bands and aerial photographs for 20

discriminating wheat and wild oat, canarygrass and ryegrass, showing significant 21

differences through the visible and near-infrared wavebands at late-season. However, 22

one of the keys to establishing SSWM is, not only to detect significant differences, but 23

also to develop an algorithm that can successfully classify crops and weeds, i.e., to 24

classify a spectrum into the specific group or species to which it belongs. Analysis of 25

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variance has been used for spectral discrimination of corn caraway (Ridolfia segetum 1

Moris.) and other weeds in sunflower, and several multivariate methods and artificial 2

neural networks (ANNs) have also been investigated for image recognition or spectral 3

classification of crop and different weed species (Borregaard et al., 2000; Goel et al., 4

2003; Jurado-Expósito et al., 2003a; Kavdir, 2004; Peña-Barragán et al., 2006; Yang et 5

al., 2000; 2002). However, some works support the idea that SSWM does not require 6

differentiation between weed species, but rather between crops and monocot and dicot 7

weeds for reducing nontarget spraying (Gibson et al., 2004; Thorp and Tian, 2004). No 8

information has been found about applications of ANN and other multivariate analyses 9

for classifying grass weeds in winter wheat under field conditions. 10

If we consider that wild oat can be controlled with specific and expensive 11

herbicides, and ryegrass has been reported as one of the weed species to have evolved 12

resistance to several herbicides (Wakelin and Preston, 2006; Broster and Pratley, 2006), 13

this could justify the interest in discriminating these most problematic grass weed 14

species to reduce herbicide use and cost, or to plan a specific application for herbicide 15

resistant ryegrass. Thus, it is crucial to explore the potential for identifying variations in 16

the spectral signatures of the plant species studied, indicating the wavelengths suitable 17

for species discrimination and classification. 18

The objectives of this research were: 1) to evaluate the potential of classic 19

methods of discriminant analysis, as well as more recent algorithms for the 20

classification of wheat, wild oat, canarygrass, ryegrass, rabbit foot and soil on the basis 21

of multispectral data in the visible and near-infrared domain, and 2) to compare the 22

accuracy performance for a spectrum classification into the plant species or group to 23

which it belongs. Six methods were applied: Fisher Linear Discriminant analysis 24

without (FLDA) and with (FLDA-PCA) principal components analysis, Nonparametric 25

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Functional Discriminant Analysis (NPFDA), Feedforward Neural Networks without 1

(FFNN) and with (FFNN-PCA) principal components analysis, and one-Layer Neural 2

Network with principal components analysis (1LNN-PCA). 3

2. Material and methods 4

2.1. Study site and spectral readings 5

The study was conducted in Andalusia, southern Spain, in Santa Cruz (25.6 ha, 6

UTM coordinates 361,076 E, 4,185,313 N) and in Los Palacios (12.3 ha, UTM 7

coordinates 241,290 E, 4,124,063 N). Winter wheat crop was planted mid-November, 8

harvested at the beginning of June. Consistent natural weed infestations were made up 9

of wild oat, canarygrass, ryegrass and rabbit foot in both locations. In mid-May, wheat 10

plants were at an advanced senescent stage, and yellowing, whereas wild oat, 11

canarygrass, ryegrass and rabbit foot were at an advanced seed maturation stage, and 12

still partly green. 13

The spectral signatures of weed-free wheat, grass weed species patches and soil 14

were taken on May 16, 2004 in Santa Cruz and on May 13, 2005 in Los Palacios. Each 15

weed species patch had about 20-25 spikes/ panicles per m2. Twenty measurements 16

were collected for each plant species and soil, respectively, using an ASD HandHeld 17

FieldSpec Spectroradiometer (Analytical Spectral Devices, Inc., 5335 Sterling Drive, 18

Boulder, CO 80301, USA) placed at 60-80 cm above each plant species canopy. The 19

spectral data were converted into reflectance, which is the ratio of energy reflected off 20

the target to the energy incident on the target, with reference to a standard reflectance 21

panel (Spectralon) before and immediately after each measurement. Spectroradiometer 22

readings were taken under sunny conditions between 12 and 14 h (Salisbury, 1999), 23

using a 25º field-of-view optic, measuring an area of about 0.15 to 0.20 m2. Spectral 24

measurements were collected between 325 and 1075 nm with a bandwidth of 1.5 nm, 25

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although the reflectance spectra were very noisy at the extremes of the spectral range 1

and only the measurements between 400 and 900 nm were analyzed. 2

The spectral measurements of wheat, weeds and soil were averaged to express 100-3

nm-wide measurements between 400 and 900 nm to represent similar multispectral 4

broad wavebands (blue, B: 400-500 nm; green, G: 501-600 nm; red, R: 601-700 nm; 5

and near-infrared, NIR: 701-900 nm) available on commercial satellites with high 6

spatial resolution. 7

2.2. Classification techniques 8

A classic discriminant analysis (Anderson, 2003), nonparametric functional 9

discriminant analysis (Ferraty and Vieu, 2006) and neural networks (Bishop, 1995) 10

were applied to construct a classification rule to discriminate between crop, grass weed 11

species or group of weeds, and soil, based on a sample of 120 spectral curves. Four 12

scenarios or classification sets were considered: 1) crop; wild oat; canarygrass; ryegrass; 13

rabbit foot; and soil, 2) crop; grass weeds; and soil, 3) crop; wild oat; the remaining 14

grass weeds; and soil, and 4) crop; wild oat-canarygrass-rabbit foot; ryegrass; and soil. 15

Thus, a spectrum was classified as belonging to the species or group to which it 16

achieved the highest subsequent probability. 17

Fisher linear discrimination analysis was used either without (FLDA) or with 18

PCA (FLDA-PCA) using SPSS software (SPSS 11.0, Inc 2002, Microsoft©). Different 19

numbers of principal components were tried, and the best results were obtained with the 20

first 31. With PCA, the covariance matrix was used to concentrate the variables onto 21

fewer orthogonal latent variables principal components (Borregaard et al. 2000). The 22

NPFDA rule was performed using a functional Nadaraya-Watson estimator with a 23

quartic kernel. The smoothing parameter was selected according to the cross-validation 24

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method (Naya et al. 2004). After a careful examination of the spectral curves in Figure 1

1, the following seminorm was considered for standardizing the data: 2

( ) ( )( )2

( , ) ,b

ad f g f x g x dx= −∫ 3

where a and b were the intervals of wavebands (nm) considered in each classification, 4

these being [400-900], [400-500], [501-600], [601-700], [701-900] and [400-700], 5

and where 6

( ) ( ) ,f x f xα β= + 7

with 8

( ) ( )21b b

a a

b a

f t f s ds dtb a

α −= − − ∫ ∫

9

and 10

( )

( ) ( )2

11

b

a

b b

a a

f t dt

b a f t f s ds dtb a

β = − − − −

∫

∫ ∫ 11

This location-scale transformation is performed in order for the “mean” and the 12

“variance” of the transformed spectral curves to be equal to one, that is, 13

( )11

b

af t dt

b a=

− ∫ and ( ) ( )21 1

1b b

a af t f s ds dt

b a b a − = − − ∫ ∫ . The integrals appearing 14

in the previous discrepancy measures have been approximated numerically over the 25 15

nm equidistant waveband grid. 16

In addition, two neural network approaches were implemented. The first was a 17

feedforward neural network (Bishop, 1995), which was applied with (FFNN-PCA) and 18

without (FFNN) a principal component analysis pre-processing stage. A FFNN is a 19

general framework for representing nonlinear functional mappings between a set of 20

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input and a set of output variables. This is achieved by representing the nonlinear 1

function of many variables in terms of a set of neurons, arranged in a topology 2

composed of several layers, which contain nonlinear functions of a single variable 3

called activation functions. Specifically, in this work, a two-layer neural network was 4

used, containing one hidden and one output layer. More hidden layers could be included 5

in the network, but this was not necessary because several authors demonstrated that 6

that kind of system, with a unique hidden layer and a sufficient number of neurons, can 7

approximate any continuous-differentiable function (Cybenko, 1989; Hornik, 1991). In 8

this research, one hidden layer of 7 neurons and one output layer, containing as many 9

neurons as classes to be detected, were used. The activation function employed was the 10

logistic function for all the neurons in the network. In addition, a Bayesian framework 11

(McKay, 1992) was used as the supervised learning method to train both neural 12

networks. In order to obtain optimum weights, the UCMINF method (Nielsen, 2000), 13

which is based on a Quasi-Newton optimization algorithm with a soft line search and a 14

BFGS (Broyden, Feltcher, Goldfarb, Shanno) updating of the inverse Hessian, was 15

employed, since it performs well in classification problems like the one described in this 16

article. Both, FFNN and FFNN-PCA were subjected to 100 training cycles. 17

The second neural network approach consisted of 1LNN, which is a FFNN with 18

no hidden layers and trained using a linear equation system proposed in Castillo et al. 19

(2002). An important advantage of this second implementation is that it obtains the 20

global optimal solution of the network in only one step, instead of using an iterative 21

learning process. Thus, another achievement is that, consequently, the computational 22

time required was drastically reduced. This last approach was also implemented with a 23

PCA pre-processing stage (1LNN-PCA). Each method was validated through cross-24

validation, which is the technique widely used for the validation of an empirical model. 25

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It works by leaving out one spectrum; then a model is trained with the remaining spectra 1

and, finally, the developed model is used for the classification of the left out spectrum. 2

This is repeated until all the spectra have been left out once (Borregaard et al., 2000). 3

As the data set available contained 120 samples, 119 samples were used for training and 4

1 sample for testing. This process was repeated 120 times, and the percentage of correct 5

classification was calculated. The MATLAB software, developed by The MathWorks 6

(MathWorks, 2007), was used to implement all the algorithms described above. 7

The algorithm called NPFDA-grass weeds implementing the NPFDA method is 8

available at http://www.udc.es/dep/mate/Dpto_Matematicas/Investigacion/ie/ie_eng.htm. 9

The neural network algorithms are available at 10

http://www.dc.fi.udc.es/lidia/downloads/LLM/. 11

3. Results 12

The overall shape of reflectance curves for canarygrass, rabbit foot and ryegrass 13

were similar and exhibited the characteristics peak at 550 nm (G) and the highest 14

reflectance in the range 750 to 900 nm (NIR) of the green vegetation (Figure 2). This 15

demonstrated that three grass species still were in an active living phase. Wild oat 16

showed a spectral signature similar to those of canary grass, rabbit foot and ryegrass in 17

NIR regions, but with reflectance values of 20%, indicating that wild oat was in an 18

intermediate stage of desiccation between and the other three grass weeds. Wheat 19

reflectance curve steadily increased as wavelength increased without the green peak for 20

photosynthetically active vegetation near 550 nm and in NIR spectral window, 21

indicating that wheat plants were at a more advanced desiccation stage. Soil presented 22

its characteristics spectral signature and reflectance increased as wavelengths increased. 23

The correct classification percentage was 100% for FLDA-PCA, FFNN-PCA 24

and 1LNN-PCA, when individual species and soil were included in the classification set 25

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for the interval [400-900 nm] (Table 1a). This was the most difficult, but also 1

challenging approach (Coussans, 1995). Models with no principal component analysis, 2

i.e., FLDA, NPFDA and FFNN did not perform well, showing success rates from 3

77.78% to 86.11%, FLDA being the worst, mis-classifying 42.59% of spectra (57.41% 4

success rate) in the green waveband. Only in 16 of the total classifications there was a 5

correct performance higher than 90%. Generally, the percentage of discriminating wheat 6

from weeds and soil performed better than that for individual species, showing a 7

success percentage of over 75.93% (Table 2a). Thus, in 27 of the total classifications, 8

the classification percentage was higher than 90%; although a 100% classification was 9

only achieved applying FFNN-PCA. According to Yang et al. (2002), this higher 10

classification percentage when the classification set was reduced to three groups, may 11

be due to the fact that, with four weed species grouped in one class, there are many 12

more weed spectra than wheat spectra in the training process. Discrimination between 13

crop, weeds and soil into three groups was also useful, assuming that all these grass 14

weeds were present in the field and could be controlled by a given herbicide treatment 15

(Borregaard et al., 2000). 16

Table 3a shows the classification percentages between wheat, wild oat, the rest 17

of grass weeds and soil, this being of interest in cases in which the precise recognition 18

of wild oat from the rest of grass weeds is important, such as when a selective herbicide 19

only against wild oat has to be applied. Again, FFNN-PCA, and in this case together 20

with FLDA-PCA, exhibited a 100% classification in the interval [400-900 nm].Table 4a 21

shows the successful classification percentage in four groups, i.e., between wheat, wild 22

oat-canarygrass-rabbit foot, ryegrass and soil, of use where the correct recognition of 23

ryegrass from the rest of grass weeds was necessary, so that a selective herbicide against 24

ryegrass, or against herbicide-resistant-ryegrass had to be applied. Highest performance 25

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(higher than 98%) was achieved for FLDA-PCA, FFNN-PCA and 1LNN-PCA 1

methods. 2

The classification matrices for cross-validation corresponding to every 3

classification set with classification percentages lower than 100% in the whole interval 4

[400-900 nm] are shown in Tables 1b, 2b, 3b and 4b. The values in the tables provide 5

the percentage of both correctly classified and misclassified classes for each 6

classification set into the nearest category. Generally speaking, wild oat was usually 7

misclassified as wheat crop, canarygrass as ryegrass, and rabbit foot as wild oat or 8

canarygrass (Table 1b). Soil was correctly classified in any method except for FLDA 9

and FFNN, where soil spectra were classified as grass weeds in Table 2b and 4b, 10

respectively. 11

4. Discussion 12

The classification percentages were higher when the visible and near-infrared 13

wavelengths (400-900 nm) were considered than when only the visible spectral window 14

(400-700 nm) was studied. Smith and Blackshawn (2003) suggested that, regardless of 15

the input samples, wavelengths in the NIR domain are always selected as being 16

important for plant species discrimination. The results of the four classification sets 17

showed that highest correct performance was achieved with a pre-processing stage with 18

a principal components analysis. This is due to the PCA reducing the data set 19

dimensionality to an optimal level, and thus introducing a new set of meaningful 20

variables (Johnson, 1998). The classic FLDA-PCA method gave the best classification 21

in any of the assumptions, followed closely by 1LNN-PCA. Both of them exhibited 22

correct classification percentages in the range of 90%-100% for the different scenarios. 23

The correct classification was typically higher with linear classification techniques 24

(FLDA-PCA and 1LNN-PCA) than with nonparametric ones (NPFDA, FFNN, FFNN-25

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PCA). The main explanation is that the high dimensionality of the data set (each 1

spectral curve was considered as a 101-dimensional vector) implies a poor performance 2

of nonparametric methods (course of dimensionality) and benefits from the dimension 3

reduction. Another factor affecting this performance is the reduced number of samples 4

available on the data set. If more samples or spectra become available in the future, the 5

performance of non-linear methods would probably improve (Bishop, 1995). 6

Our research can not clarify why one method performed better than the other as 7

they are based on different principles. Karimi et al. (2005) tested three classification 8

models for distinguishing weeds at different growth stages and nitrogen treatments, and 9

found that a classic discriminant analysis performed better than ANNs for the earlier 10

phenological stages. They concluded that it was clear that different classification 11

methods should be tried out for a given situation to determine the most accurate method. 12

In our case, it was important to consider both, i.e. that the FLDA-PCA and 1LNN-PCA 13

models showed a nearly similar and high classification performance, and that the 14

additional computational requirements for 1LNN-PCA were not much higher because 15

no iterative learning process was applied. Thus, the criteria for the selection of FLDA-16

PCA or 1LNN-PCA models as the best classification methods compared with the others 17

should be based on the improvement achieved in performance accuracy and decreasing 18

their computational requirements and complexity. 19

Once FLDA-PCA, FFNN-PCA and 1LNN-PCA have shown themselves to 20

successfully classify wheat, wild oat, canarygrass, ryegrass, rabbit foot and soil spectra, 21

the next investigation could address to explore the potential of QuickBird satellite 22

imagery for mapping grass weed patches in large areas (of at least over 64 km²). 23

Barroso et al. (2004a) and Blanco et al. (2006b), applying geostatistical techniques, 24

demonstrated that the extension of wild oat patches and ryegrass in wheat was around 25

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50 m and 20 m, respectively. According to these results, the spectral classification 1

herein presented, and taking into account that QuickBird provides four channels (B, G, 2

R and NIR) of multispectral wavebands with 2.4 m of spatial resolution, it would 3

apparently be possible to successfully map this weed on a large surface. QuickBird has 4

already been seen to be a useful data source which accurately determines ecological, 5

agronomic and forest variables such as salt-marsh vegetation (Belluco et al., 2006), 6

invasive plant species (Tsai et al., 2006), sorghum yield (Yang et al., 2006), rangeland 7

resources (Everitt et al., 2006) or insect attack damage in pine (Coops et al., 2006) . 8

Recent interest in weed remote sensing has increased the need to use 9

documented weed spectral libraries, whose information can provide inputs to canopy 10

radiation models (Verhoef, 1984) and can help to determine which sensors are able to 11

detect a given weed species by maximizing the detection cost according to the spatial 12

and spectral resolutions of each sensor (Hunt et al., 2004). Our study could be a guide 13

for creating a spectral library of wheat and the most important weeds associated with 14

this crop at a late growth stage. The usefulness of the multi-species classification 15

obtained is amply justified because this is usually the real aim of field infestation in 16

many of the cereal crops under our conditions, and because wild oat, canarygrass and 17

ryegrass could require a completely different control action. This strategy would prevent 18

any further spread, especially for hard-to-control herbicide-resistant-ryegrass, and 19

would allow an herbicide selection based on spectral characterization. This would 20

finally improve the decision-making process, which is the ultimate goal of SSWM. 21

5. Conclusions 22

Our results demonstrated that FLDA-PCA, FFNN-PCA and 1LNN-PCA can 23

successfully classify wheat crop, several grass weeds and soil. In addition, classify a 24

spectrum into the specific group or species to which it belongs using spectra sampled 25

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under field conditions in mid-May. Both methods exhibited correct classification 1

percentages in the 90%-100% range for the different classification sets. The 2

classification percentage was higher for linear classification techniques (FLDA-PCA 3

and 1LNN-PCA) than for non-parametric ones (NPFDA, FNN, FFNN-PCA) in any of 4

the scenarios tested. In general, preliminary computation of the most relevant principal 5

components considerably improves the correct classification percentage in all methods. 6

Acknowledgements 7

This research was partially funded by the Spanish Ministry of Education and 8

Science through the projects MTM2005-00429 and AGL2005-06180-CO3-02, and by 9

the Xunta de Galicia by the project PGIDT05TIC10502PR. The research of Dr. M. 10

Jurado-Expósito was supported by the Ramón y Cajal Spanish Program. 11

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10

11

12

13

Table 1a. Percentage of correct classification for Fisher Linear Discriminant Analysis -1

without (FLDA) and with a previous PCA (FLDA-PCA)-, Nonparametric Functional 2

Discriminant Analysis (NPFDA), Feedforward Neural Networks -without (FFNN) and 3

with a previous PCA (FFNN-PCA)-, and One-Layer Neural network with PCA (1LNN-4

PCA) when classifying crop; wild oat; canarygrass; rabbit foot; ryegrass; and soil. 5

6

Methods Wavelengths (nm)

[400-900] [401-500] [501-600] [601-700] [701-900] [400-700]

(visible and NIR) (blue) (green) (red) (NIR) (visible)

FLDA 92.59 80.56 57.41 64.81 70.37 91.67

FLDA-PCA 100 94.44 90.74 92.59 92.59 91.44

NPFDA 77.78 67.59 67.59 64.81 64.81 72.22

FFNN 86.11 88.89 76.85 74.07 74.07 80.56

FFNN-PCA 100 87.96 90.74 91.67 91.67 92.59

1LNN-PCA 100 92.59 89.81 89.81 89.81 92.59

7

8

9

10

11

12

13

14

15

16

Table

Table 1b. Classification matrix (%) obtained for cross-validation using the interval 1

[400-900 nm] for classifying the spectra of crop; wild oat; canarygrass; ryegrass; rabbit 2

foot; and soil. 3

Methods Spectra Predicted Actual Crop Wild

oat Canarygrass Ryegrass Rabbit

foot Soil

FLDA* Crop Wild oat Canarygrass Ryegrass Rabbit foot Soil

90.0 5.6 0.0 4.7 0.0 0.0

10.0 94.4 0.0 4.7 0.0 0.0

0.0 0.0

100.0 14.3 0.0 0.0

0.0 0.0 0.0 76.2 0.0 0.0

0.0 0.0 0.0 0.0

100.0 0.0

0.0 0.0 0.0 0.0 0.0 100.0

NPFDA Crop Wild oat Canarygrass Ryegrass Rabbit foot Soil

85.0 11.1 0.0 0.0 10.5 0.0

15.0 72.2 0.0 4.8 10.5 0.0

0.0 0.0 80.0 28.6 0.0 0.0

0.0 11.1 20.0 66.6 5.3 0.0

0.0 5.6 0.0 0.0 73.7 0.0

0.0 0.0 0.0 0.0 0.0 100.0

FFNN Crop Wild oat Canarygrass Ryegrass Rabbit foot Soil

90.0 16.6 0.0 0.0 5.3 0.0

10.0 77.7 0.0 0.0 0.0 0.0

0.0 0.0 90.0 23.8 0.0 0.0

0.0 0.0 0.0 76.2 5.3 0.0

0.0 5.5

10.0 0.0 89.5 0.0

0.0 0.0 0.0 0.0 0.0 100.0

*See legend in Table 1a 4

5

6

7

8

9

10

11

12

Table 2a. Percentage of correct classification for Fisher Linear Discriminant Analysis -1

without (FLDA) and with a previous PCA (FLDA-PCA)-, Nonparametric Functional 2

Discriminant Analysis (NPFDA), Feedforward Neural Networks -without (FFNN) and 3

with a previous PCA (FFNN-PCA)- and One-Layer Neural network with PCA (1LNN-4

PCA) when classifying crop; grass weeds (wild oat-canarygrass-rabbit foot, ryegrass); 5

and soil. 6

7

Methods Wavelengths (nm)

[400-900] [401-500] [501-600] [601-700] [701-900] [400-700]

(visible and NIR) (blue) (green) (red) (NIR) (visible)

FLDA 94.44 83.33 75.93 79.63 89.81 94.44

FLDA-PCA 97.22 94.44 89.81 91.67 94.44 95.37

NPFDA 96.30 90.74 96.30 92.59 92.59 95.37

FFNN 95.37 93.52 96.30 91.67 93.52 92.59

FFNN-PCA 100 89.81 88.89 89.81 98.15 94.44

1LNN-PCA 98.15 95.37 89.81 92.59 93.52 95.37

8

9

10

11

12

13

14

15

16

17

Table 2b. Classification matrix (%) obtained for cross-validation using the interval 1

[400-900 nm] for classifying the spectra of crop; grass weeds (wild oat-canarygrass-2

rabbit foot-ryegrass); and soil. 3

4

Methods Spectra Predicted Actual Crop Grass weeds Soil FLDA* Crop

Grass weeds Soil

95.0 5.1 0.0

5.0 93.6 0.0

0.0 1.3 100.0

FLDA-PCA Crop Grass weeds Soil

90.0 1.3 0.0

10.0 98.7 0.0

0.0 0.0 100.0

NPFDA Crop Grass weeds Soil

90.0 2.6 0.0

10.0 97.4 0.0

0.0 0.0 100.0

FFNN Crop Grass weeds Soil

90.0 3.8 0.0

10.0 96.2 0.0

0.0 0.0 100.0

1LNN-PCA Crop Grass weeds Soil

95.0 1.3 0.0

5.0 98.7 0.0

0.0 0.0 100.0

5

* See legend in Table 2a. 6

7

8

Table 3a. Percentage of correct classification for Fisher Linear Discriminant Analysis -1

without (FLDA) and with a previous PCA (FLDA-PCA)-, Nonparametric Functional 2

Discriminant Analysis (NPFDA), Feedforward Neural Networks -without (FFNN) and 3

with a previous PCA (FFNN-PCA)- and One-Layer Neural network with PCA (1LNN-4

PCA) when classifying among crop; wild oat; remaining grass weeds (canarygrass- 5

rabbit foot- ryegrass); and soil. 6

7

Methods Wavelengths (nm)

[400-900] [401-500] [501-600] [601-700] [701-900] [400-700]

(visible and NIR) (blue) (green) (red) (NIR) (visible)

FLDA 91.67 90.74 75.00 71.30 87.96 91.67

FLDA-PCA 100 93.52 92.59 94.44 95.37 94.44

NPFDA 88.89 86.11 86.11 87.96 79.63 88.89

FFNN 93.52 90.74 91.67 91.67 93.52 88.89

FFNN-PCA 100 90.74 91.67 91.67 96.30 91.67

1LNN-PCA 99.07 92.59 93.52 91.67 97.22 92.59

8

9

10

11

12

13

14

15

16

17

Table 3b. Classification matrix (%) obtained for cross-validation using the interval 1

[400-900 nm] for classifying the spectra of crop; wild oat; remaining grass weeds 2

(canarygrass-rabbit foot- ryegrass); and soil. 3

Methods Spectra Predicted Actual Crop Wild oat Remaining

grass weeds Soil

FLDA* Crop Wild oat Remaining grass weeds Soil

85.0 11.1 3.3 0.0

15.0 88.9 3.3 0.0

0.0 0.0 93.3 0.0

0.0 0.0 0.0 100.0

NPFDA Crop Wild oat Remaining grass weeds Soil

85.0 11.1 3.3 0.0

15.0 72.2 3.3 0.0

0.0 16.7 93.3 0.0

0.0 0.0 0.0 100.0

FFNN Crop Wild oat Remaining grass weeds Soil

90.0 16.7 0.0 0.0

10.0 77.8 1.7 0.0

0.0 5.5 98.3 0.0

0.0 0.0 0.0 100.0

1LNN-PCA Crop Wild oat Remaining grass weeds Soil

100.0 0.0 1.7 0.0

0.0 100.0 0.0 0.0

0.0 0.0 98.3 0.0

0.0 0.0 0.0 100.0

4

5

*See legend in Table 3a. 6

7

8

9

10

11

12

13

14

Table 4a. Percentage of correct classification for Fisher Linear Discriminant Analysis -1

without (FLDA) and with a previous PCA (FLDA-PCA)-, Nonparametric Functional 2

Discriminant Analysis (NPFDA), Feedforward Neural Networks -without (FFNN) and 3

with a previous PCA (FFNN-PCA)- and One-Layer Neural network with PCA (1LNN-4

PCA) when classifying among crop; wild oat-canarygrass-rabbit foot; ryegrass; and soil. 5

6

Methods Wavelengths (nm)

[400-900] [401-500] [501-600] [601-700] [701-900] [400-700]

(visible and NIR) (blue) (green) (red) (NIR) (visible)

FLDA 82.41 77.78 66.67 68.52 70.37 78.70

FLDA-PCA 98.15 93.52 86.11 90.74 91.67 95.37

NPFDA 81.48 78.70 76.85 75.93 75.93 81.48

FFNN 85.19 76.85 75.93 70.37 73.15 82.41

FFNN-PCA 99.07 90.74 87.04 87.96 89.81 93.52

1LNN-PCA 98.15 94.44 84.26 87.96 88.89 94.44

7

8

9

10

11

12

13

14

15

16

Table 4b. Classification matrix (%) obtained for cross-validation using the interval 1

[400-900 nm] for classifying the spectra of crop; wild oat-canarygrass- rabbit foot; 2

ryegrass; and soil. 3

Methods Spectra Predicted Actual Crop Remaining grass

weeds Ryegrass Soil

FLDA* Crop Remaining grass weeds Ryegrass Soil

65.0 5.3 19.0 0.0

30.0 91.2 14.3 0.0

5.0 3.5 66.7 0.0

0.0 0.0 0.0 100.0

FLDA-PCA Crop Remaining grass weeds Ryegrass Soil

90.0 0.0 0.0 0.0

10.0 100.0 0.0 0.0

0.0 0.0

100.0 0.0

0.0 0.0 0.0 100.0

NPFDA Crop Remaining grass weeds Ryegrass Soil

90.0 7.0 0.0 0.0

10.0 84.2 42.9 0.0

0.0 8.8 57.1 0.0

0.0 0.0 0.0 100.0

FFNN Crop Remaining grass weeds Ryegrass Soil

90.0 7.0 0.0 10.0

10.0 86.0 23.8 0.0

0.0 5.3 76.2 0.0

0.0 1.7 0.0 90.0

FFNN-PCA Crop Remaining grass weeds Ryegrass Soil

100.0 1.8 0.0 0.0

0.0 98.2 0.0 0.0

0.0 0.0

100.0 0.0

0.0 0.0 0.0 100.0

1LNN-PCA Crop Remaining grass weeds Ryegrass Soil

95.0 1.8 0.0 0.0

5.0 98.2 0.0 0.0

0.0 0.0 100.0 0.0

0.0 0.0 0.0 100.0

4

5 6 *See legend in Table 4a. 7 8

9

10

1

Figure 1. Original spectral curves for wheat crop, wild oat, canarygrass, ryegrass, rabbit 2

foot, and soil. 3

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FigureClick here to download Figure: grass weed fig 1 EJA 15 feb 07 Lopez Granados et al.doc

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Figure 2: Mean reflectance curves of wheat crop, wild oat, canarygrass, rabbit foot, 1

ryegrass, and soil. 2

3

4

0%

10%

20%

30%

40%

50%

60%

400 450 500 550 600 650 700 750 800 850 900

Wavelength (nm)

Ref

lect

ance

(%)

wheat crop

wild oat

canary grass

rabbit foot

ryegrass

soil

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FigureClick here to download Figure: grass weed fig 2 EJA 15 feb 07 Lopez Granados et al.doc