c o m p u t e r s a n d e l e c t r o n i c s i n a g r i c u l t u r e 6 0 ( 2 0 0 8 ) 144–155

avai lab le at www.sc iencedi rec t .com

journa l homepage: www.e lsev ier .com/ locate /compag

A new vision-based approach to differentialspraying in precision agriculture

Alberto Tellaechea, Xavier P. BurgosArtizzub, Gonzalo Pajaresc,∗,Angela Ribeirob, Cesar Fernandez-Quintanillad

a Dpto. Informatica y Automatica, Escuela Tecnica Superior de Informatica, UNED, Spainb Instituto de Automatica Industrial, CSIC, Arganda del Rey, Madrid, Spainc Dpto. Ingenierıa del Software e Inteligencia Artificial, Facultad Informatica, Universidad Complutense, 28040 Madrid, Spaind Centro de Ciencias Medioambientales, CSIC, Madrid, Spain

a r t i c l e i n f o

Article history:

Received 7 February 2007

Received in revised form

25 July 2007

Accepted 26 July 2007

Keywords:

Precision agriculture

Machine vision

a b s t r a c t

One of the objectives of precision agriculture is to minimize the volume of herbicides by

using site-specific weed management systems. To reach this goal, two major factors need

to be considered: (1) the similarity of spectral signatures, shapes, and textures between

weeds and crops and (2) irregular distribution of weeds within the crop. This paper outlines

an automatic computer vision method for detecting Avena sterilis, a noxious weed grow-

ing in cereal crops, and differential spraying to control the weed. The proposed method

determines the quantity and distribution of weeds in the crop fields and applies a decision-

making strategy for selective spraying, which forms the main focus of the paper. The method

consists of two stages: image segmentation and decision-making. The image segmentation

Weed detection

Image segmentation

Multicriteria decision-making

process extracts cells from the image as the low-level units. The quantity and distribution

of weeds in the cell are mapped as area and structural based attributes, respectively. From

these attributes, a multicriteria decision-making approach under a fuzzy context allows us

to decide whether any given cell needs to be sprayed. The method was compared with other

existing strategies.

used real-time differential images (NIR-VIS) obtained with

1. Introduction

Nowadays, there is a clear preference to reducing the use ofchemicals in agriculture. Numerous technologies have beendeveloped to make agricultural products safer and to lowertheir adverse impacts on the environment, and precision agri-culture is a valuable component of the framework to achievethis goal (Kropff et al., 1997; Zhang et al., 2002; Stafford,2006).

Within that general framework, weeds can be managedsite-specifically using available geospatial and informationtechnologies (Gerhards and Christensen, 2006). Initial efforts

∗ Corresponding author. Tel.: +34 1 3 94 75 46; fax: +34 1 3 94 75 47.E-mail address: pajares@fdi.ucm.es (G. Pajares).

0168-1699/$ – see front matter © 2007 Elsevier B.V. All rights reserved.doi:10.1016/j.compag.2007.07.008

© 2007 Elsevier B.V. All rights reserved.

to detect weed seedlings by machine vision focused ongeometrical measurements such as shape factor, aspectratio, and length/area (Perez et al., 2000). Later, colour imageswere successfully used to detect weeds and other typesof pests (Søgaard and Olsen, 2003). Yang et al. (2003) esti-mated weed coverage and weed patchiness based on digitalimages, using a fuzzy algorithm for planning site-specificapplication of herbicides. Recently, Gerhards and Oebel (2006)

a set of three digital bispectral cameras to detect smallweed seedlings in different crops. Other approaches haveused colour indices to distinguish plant material from the

a g r

bBbibpc

wot2sgee(toa(twdspatdut2tittkfipaywtwpofs

tiwTaeqaaft

c o m p u t e r s a n d e l e c t r o n i c s i n

ackground (Thorp and Tian, 2004; Ribeiro et al., 2005).acher (2001) estimated weed density in a field of springarley by image binarization and morphology followed by the

dentification of crop rows using information on distancesetween rows within the crop to decide on spraying. Thisrocess serves to make weed plants appear isolated from therop.

Avena sterilis L. (“winter wild oat”) is one of the mostidely distributed and abundant weeds of cereals in Spain andther regions with Mediterranean climate, causing substan-ial losses in these crops (Barroso et al., 2004a; Radics et al.,004). Although some A. sterilis plants may be found growingingly or in small patches, the majority of them are aggre-ated in relatively large patches (Ruiz et al., 2006), and those inarly spring, after broad-leaved weeds have been controlled byarly postemergence treatments, are practically pure standsFernandez-Quintanilla, personal observation). Due to thesewo features, it is relatively easy for an experienced farmerr a technical consultant to detect patches of A. sterilis visu-lly in the early stages of crop growth. In fields of cerealsbarley or wheat), the cereal plants grow along the furrows:he plants growing between furrows can only be weeds. Buteeds may also grow mixed with the cereal. We sought toetect weeds by differences in appearances: isolated plants,mall or large patches, or mixed with the crop. Three mainroblems arise during detection, namely (1) irregular shapesnd different sizes of the patches, (2) spectral signature andexture similar to those of the cereal plants, and (3) irregularistribution of the weeds in the field. This means that methodssing only absolute sizes, shapes, textures, or spectral signa-ures are not applicable to our experiments (Aitkenhead et al.,003; Onyango and Marchant, 2003; Granitto et al., 2005). Theotal proportion of weeds in the field is important becauset indicates the extent of competition between weeds andhe crop (Tian et al., 1999; Ribeiro et al., 2005), but distribu-ion has not been considered in vision-based systems to ournowledge. Barroso et al. (2004b) studied the economic bene-ts of using site-specific weed management systems for largeatches and numerous small patches of weeds. The dam-ge from large patches to the crops is clear; they lower theield substantially in the current year. When numerous smalleeds patches appear during the cereal’s growth phase, they

end to compete with the crop aggressively. Moreover, becauseeeds are more prolific in producing seeds and the seedsersist longer in soil, a failure to control weeds creates seri-us problems not only in the current year but also for theollowing 2–3 years (see Appendix A for details of weed den-ity).

Hence, we propose a new method with two objectives: (1)o determine the quantity and distribution of weeds presentn the crop and (2) to decide, based on that knowledge,

hether to undertake selective spraying to control the weeds.he method consists of an image segmentation processnd a decision-making approach. The segmentation processxtracts cells from the image as the low-level units. Theuantity and distribution of weeds in the cell are mapped as

rea and structural based attributes, respectively. From thesettributes, a multicriteria decision-making approach under auzzy context allows us to decide whether any given cell needso be sprayed.

i c u l t u r e 6 0 ( 2 0 0 8 ) 144–155 145

2. Materials and methods

2.1. Images

The images used for this study were those of a 1.7-ha experi-mental field of barley on La Poveda Research Station, Argandadel Rey, Madrid. The most common weed in the field wasA. sterilis, with densities ranging from 10 to 400 plants m−2.Although other weed species (Papaver rhoeas, Veronica hedaere-folia, Lamium amplexicaule) were also present in the field, at thetime of image acquisition most of them had been killed by anearly treatment with bromoxinil and mecocrop. Images weretaken on two dates in April 2003, when the plants were atthe early tillering stage (3–5 leaves). Row spacing was 0.36 m.Although the standard row width in the area is 0.17 m, muchwider rows are common in other semi-arid areas of NorthAmerica and Australia. Wider rows simplify weed detection.Digital images were captured with a Sony DCR PC110E camera.The area of each image to be processed was approximately2.1 m × 19 m and the resolution was 1152 × 864 pixels.

The images were captured under the perspective projec-tion, which means that areas of identical size in the fieldappear under different sizes in the image, depending on theirdistance from the camera. Hence, we must compute thoseattributes that are independent of the perspective projec-tion. This is achieved by establishing relative measurementsbetween crops and weeds instead of using absolute measure-ments, as described in the next sections.

2.2. The proposed method

The proposed method involves two sub-processes: image seg-mentation and decision-making. The image segmentationprocess divides the image into cells and extracts those fea-tures and attributes from each cell that make it possible todistinguish between weeds and the crop; based on that infor-mation, the decision-making process determines whether acell is to be sprayed. Such decision-making requires a set ofsamples for the cells of which the decision to spray – or not –was made in the past. Hence, we must build a knowledge base(KB) containing sets of such samples, a stage called the off-lineprocess. The decision-making is carried out by computing sim-ilarity measures between the samples stored in the KB and thecell being processed; we call this process of decision-makingthe on-line process. The image segmentation is identical forboth processes (Fig. 1).

2.3. Image segmentation: weed detection

The steps involved in the proposed image segmentation pro-cess are acquiring and binarizing images, detecting croprows, partition the image into a grid of cells, and extractingattributes from the cells.

2.3.1. Acquiring and binarizing images

As mentioned before, the images were acquired under the per-spective projection, which implies that the crop rows tend toconverge at the vanishing point out of the field of view. Thegoal of this first step was to convert the input red–green–blue

146 c o m p u t e r s a n d e l e c t r o n i c s i n a g r i c u l t u r e 6 0 ( 2 0 0 8 ) 144–155

sed

Fig. 1 – Vision-ba

(RGB) image into a binary image in which the vegetation(whether weeds or the crop) in the RGB image is representedas white points and the rest as black ones.

Various methods have been proposed for image binariza-tion (Ribeiro et al., 2005; Granitto et al., 2005; Onyango andMarchant, 2003; Bacher, 2001; Tian and Slaughter, 1998). Weselected the method described by Ribeiro et al. (2005). The seg-mentation was based on the three components (R, G, and B)that together describe each image point. The first stage of thesegmentation transforms the original RGB image into a one-dimensional grey level (monochrome) image by applying thefollowing expression:

T(i, j) = rR(i, j) + gG(i, j) + bB(i, j) (1)

where r, g, and b are the set of real coefficients to be selected.According to Ribeiro et al. (2005), the best performance isachieved with the following parameter values: r = −1, g = 2, andb = −1; if T(i,j) ≤ 0, then T(i,j) = 0; if T(i,j) ≥ 255, then T(i,j) = 255.The next step was to determine the grey level threshold thatsets the contrast breakpoint between pixels representing veg-etation and rest of the pixels (representing everything else:shadows, stones, straw and other debris, etc.). Finally, the grey-level image was transformed into a black-and-white imageto obtain a binary image. According to an earlier evaluationof approaches based on different thresholds for detectingchanges in an image (Rosin and Ioannidis, 2003), the best per-formance was achieved using the entropy of the histogram,following the method described by Kapur et al. (1985). There-fore, we used this approach in our work.

To remove spurious white pixels and to smooth the whitecontours from the binarized image, we applied a morphologi-cal opening (erosion followed by dilation) operation (Onyangoand Marchant, 2003; Bacher, 2001). However, because of theperspective projection, we had to apply three different struc-turing elements for performing the morphological opening

operation because the central rows of the crop were near-vertical whereas the rows to the left and to the right haddifferent slopes. We divided the image into three strips of iden-tical width: left (L), central (C), and right (R). We used the SL,

decision process.

SC, and SR structuring elements in (2) to be applied to the L, C,and R parts, respectively.

SL =

⎡⎢⎢⎢⎢⎢⎣

0 0 0 1 1

0 0 1 1 1

0 1 1 1 0

1 1 1 0 0

1 1 0 0 0

⎤⎥⎥⎥⎥⎥⎦

SC =

⎡⎢⎢⎢⎢⎢⎣

0 1 1 1 0

0 1 1 1 0

0 1 1 1 0

0 1 1 1 0

0 1 1 1 0

⎤⎥⎥⎥⎥⎥⎦

SR =

⎡⎢⎢⎢⎢⎢⎣

1 1 0 0 0

1 1 1 0 0

0 1 1 1 0

0 0 1 1 1

0 0 0 1 1

⎤⎥⎥⎥⎥⎥⎦

(2)

2.3.2. Detecting crop rows and partitioning the image intoa grid of cellsIn the resulting binary image, all vegetation – whether weedsor the crop – was white and the rest was black. For detect-ing the crop rows in the image, we used a Hough transform,which is a well-known and robust method, especially ifthe rows cover the whole image (Astrand and Baerveldt,2002; Billingsley and Schoenfisch, 1997). The Hough transformobtains line equations in the normal space (Gonzalez et al.,2004; Gonzalez and Woods, 2002), given by x cos � + y sin � = �.The Hough transform also creates an accumulator of cellsA(�,�) indexed by � and �, where high values in a cell ofthe accumulator determine a line with the indexed param-eters. Only those values of the accumulator greater than Th,a threshold set to 100 by trial and error, are allowed. Becausethe orientation of the crop rows was known, we searched onlyfor rows with � and � consistent with this knowledge, i.e. linesthat were near-vertical with two slopes (Fig. 2). Finally, and

because the crop is not usually a perfect line but has a certainwidth as well, it is likely that several accumulator cells withsimilar indices (� and �) will have high accumulated values.This means that several lines are associated to the same crop

c o m p u t e r s a n d e l e c t r o n i c s i n a g r i c u l t u r e 6 0 ( 2 0 0 8 ) 144–155 147

ima

rctε

o

Tetiaipbwap

2Atdo

Fig. 2 – (a) Original image, (b) segmented

ow. We merged all similar lines into a single line: given twoells A(�i, �i) and A(�j,�j), we assumed that they representedhe same crop row if |�i − �j| ≤ ε1 and |�i − �j| ≤ ε2 where ε1 and

2 were set to 5 and 10, respectively. We tested the performancef these values by trial and error.

The next step was to partition the image into a grid of cells.his was carried out by tracing horizontal lines, i.e. lines withquation y = kc. Due to the perspective projection, the size ofhe cells decreases towards the upper part of the image andmportant details coming from weeds are lost when more cellsre used. Therefore, and although we traced horizontal linesn the whole image, we processed the cells only in the lowerart of the image. So, k = 1, . . ., n and c = 50, where n is boundedy the height of the image. With n = 13, the details in the cellsere retained. Fig. 2(a) shows the original image captured inbarley field and Fig. 2(b) the image after the segmentation

rocess.

.3.3. Extraction attributes from cells

s mentioned in Section 1, several factors affect weed detec-

ion: irregular spatial distribution of weed patches, irregularistribution of crop plants within a row (as a consequencef sowing failures or gaps resulting from various accidents),

ge displaying the line of crops and cells.

undefined weed shapes, similar spectral signatures and tex-tures of the crops and weeds, and so on. Moreover, due to theperspective projection, the cells within a single image differin size and shape. The attributes chosen for weed detectionmust be independent of the above factors. In particular, theymust be invariant to the size and shape of cells. Therefore, weextracted relative measurements instead of absolute ones.

For segmentation, we randomly selected a subset of 30images from the set of 146 images available to us. From eachselected image, we selected 48 cells, i.e. a total of 1440 cells.The number of cells classified as candidates to be sprayed wasFa = 245 (17% of 1440). This relatively small percentage was thefocus of interest in deciding upon the differential spraying.For the set of remaining cells (Ha = 1195), we computed theproportion of the white area in the cells:

r = 1Ha

H∑Wc

Ac(3)

c=1

where Ac is the total area of a given cell c and Wc the whitearea in that cell. In this kind of cell, free of weeds, the whitearea represents only crops. Each cell contains left (L) and right

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Table 1 – Number of conditions and predicates according to the distribution of patches in the cell

1

c1 ni = 0 c2 ni = 1 c3 1 < ni ≤ 5 c4 ni > 5 c5 pl =

1089 155 105 91 55

(R) patches representing the crop areas. We found r ≈ 2/5 andr = rl + rr where rl and rr are the corresponding ratios for the Land R crop areas, respectively. This means that rl = rr ≈ 1/5, i.e.each crop area covered 1/5th of the total area of a cell.

Based on the expertise criterion (see Appendix A) and tak-ing into account the image-processing procedure, we analysedthe distribution of the patches in each cell for both sets Fa andHa and found the following observations:

(1) two unique patches identifying the L and R areas,(2) two patches L and R and a number (n) of isolated patches

(small non-connected areas),(3) a number (p) of large patches connected to L or R,(4) L and R interconnected through a patch.

The distribution of patches (1), (2), and (3) was not mutuallyexclusive; a single cell could contain patches of the three typessimultaneously. Table 1 shows the number of cells belong-ing to each of the nine relevant categories found in the cellswe analysed. Areas in the lower half of the image below thethreshold Ta (measured in pixels), set to 3 in our experiments,were removed beforehand because, upon observation of theabove set of cells, it was found that approximately 93% of thesesmall areas represented non-vegetation elements with spec-tral signatures very similar to those of green plants that hadsurvived the morphological opening operation. However, thenumber of cells thus removed represents only 5% of the totalset of cells. Values of the threshold greater than the abovetended to eliminate isolated weed plants, which was undesir-able. In the upper half, this was not possible because in theperspective projection weeds could be represented by areassmaller than 3 pixels (see Appendix A where some details aregiven about Ta). Each category or case was identified with acondition c1 to c9 and is assigned a separate column in Table 1.We take a condition ci as true when the predicate (definedbelow for each condition in the table) is true: ni is the numberof isolated patches in a cell and pl and pr are the number ofpatches which appear as protuberances connected to the L andR areas, respectively. The number of cells analysed fulfillingeach condition is shown in the second row. Column 1 showsthe number of cells containing only the L and R areas, i.e. with-out isolated patches (ni = 0). Columns 2–4 show the number ofcells with ni isolated patches; the predicates are grouped basedon the number of cases found. Columns 5–8 show the numberof patches pl and pr connected with the L and R areas, respec-tively. We found only three cells with pl and pr greater than 2(one each with pl = 3, pr = 3, and pr = 4) and hence did not con-sider more cases with other values for this kind of patches.Finally, column 9 shows the number of cells with the L and Rareas interconnected.

Based only on the distribution of weed patches, under theconditions c1 to c9, we could not conclude definitively whethera given cell needed to be sprayed. We therefore searched forarea-based attributes because they had been used in some

c6 pl = 2 c7 pr = 1 c8 pr = 2 c9 L–R connected

44 62 44 21

earlier experiments (Granitto et al., 2005; Bacher, 2001; Perezet al., 2000). The area-based attributes take weed densitiesinto account. We observed two important cases where thedistribution of patches played an important role in the finaldecision.

(1) There were cells with isolated patches distributed in thecell with a low total density. If area measurements werethe only criterion, the decision would have been not tospray such cells. However, as explained in Section 1 andalso in the Appendix A, weeds that may be few but dis-tributed widely represent a risk to the current and thefollowing crops, and these cells must be sprayed.

(2) On the contrary, there were also patches attached to theL and R areas which represented the crop because it hadreached a high density during its growing phase. The highdensity would have led to the decision to spray—whichwould have been unnecessary.

Thus, decisions based solely on area values could proveincorrect; the method of decision-making therefore justifiesthe inclusion of the following two kinds of attributes, namelystructural-based and area-based.

Accordingly, the next step was to define a procedure forcomputing the values of these attributes. For each cell weconducted the following processes.

(1) Extract the connected regions in a cell, identifying eachconnected region with a unique label and its area(Gonzalez et al., 2004).

(2) Identify the L and R labels. Regions that share the samelabel are connected; those that do not are unconnected;each cell has two regions, RL and RR, each covering 1/5thof the cell’s total area (Ac). (See discussion related to the Eq.(3)). RL covers the left part of the cell and RR the right one. Land R are the white regions inside RL and RR, respectively.

(3) Exclude the L and R regions.(4) Compute the number ni of isolated regions; each region

has a unique label (including the L and R regions).(5) Compute the number of patches pl and pr connected to the

L and R regions; they are the white regions with the samelabels (either L or R), once L and R are excluded (note thatconnected regions have the same label).

The structural-based attributes were computed as follows.Given a cell i, we built a nine-dimensional structural arraySi = {si1, si2, . . ., si9} where each element sij is an attributedefined as follows:

{1 if c is true

sij = j

0 otherwisej = 1, 2, . . . , 9 (4)

The following are subsets of mutually exclusive elements{si1, si2, si3, si4}, {si5, si6}, {si7, si8}, or {si1, si9}. This means that

a g r

tH

accccrna

i

•

•

•

Fv

a

wia(a

oewaeiivCfit[eb

Ksic

c o m p u t e r s a n d e l e c t r o n i c s i n

wo elements belonging to the same subset are incompatible.owever, this does not affect the performance.

Two area-based attributes were computed and embeddeds the components of an area-vector ai; as before, given theell i, this vector is ai = {ai1, ai2}. Let m be the total number ofonnected regions in the cell i (i.e. the number of labels in theell) and Aij the area of the jth region. Aic is the total area of theell and AiL and AiR are the areas for the L and R crop regions,espectively. AiL and AiR are computed taking into account theumber of pixels inside of the regions RL and RR as describedbove in point 2).

Based on the area measurements, we computed the follow-ng coverage values:

crop coverage:

Cic = AiL + AiR (5)

weed coverage:

Ciw =m∑

j=1

Aij − Cic (6)

soil coverage:

Cis = Aic − (Cic + Ciw) (7)

rom Eqs. (5)–(7) we computed the components for the area-ector ai

i1 = Ciw

Aicand ai2 = Ciw

Cic

(1 − Cis

Aic

)(8)

here ai1 is defined as the weed coverage rate as describedn Tian et al. (1999) and Ribeiro et al. (2005) and ai2 can bessociated with weed pressure, also as defined in Ribeiro et al.2005). The area attributes are relative measurements, i.e. theyre invariant to the cell’s size (position in the image).

The following analysis allowed us to determine the rangef variability of these two values. Indeed, when the weed cov-rage is null, i.e. there are no weeds in the cell, ai1 = 0 but if theeeds cover the full intermediate region (i.e. Ciw = 3/5Aic), then

i1 = 3/5. Hence, ai1 ranges from [0,3/5]. Also, if the weed cov-rage is null ai2 = 0. The upper limit of ai2 is achieved when Ciw

s maximum (i.e. Ciw = 3/5Aic) and Cic minimum (i.e. Cic = 0); butf Cic is null, it means the cell has no crops. The minimumalue we obtained for Cic was 1/10Aic. Now, assuming that

iw = 3/5Aic, Cis = 0.3Aic. Finally, the upper limit for ai2 can bexed from the Eq. (8) as 4.2. Based on these limits, we mappedhe component values of the area-vector linearly to the range0,1]. This was intended so that both components contributequitably in the computation of a similarity measurementetween two area-vectors.

The next step was to build a knowledge base (KB) containing

B1, representing cells that require a spray, and KB2, repre-enting cells that do not. Each cell j was stored in KB withts associated attributes Sj and aj. This is the off-line pro-ess.

i c u l t u r e 6 0 ( 2 0 0 8 ) 144–155 149

2.4. Decision-making process

Given a new image, we apply to it the segmentation pro-cess described in Section 2.3, extracting a set of cells i withattributes Si and ai. The goal is to reach a decision oneach i with respect to whether it requires spraying, basedon a decision-making process that considers the similar-ity/dissimilarity measures between each cell i and thosestored in the KB. This is the on-line process.

2.4.1. Similarity measures: benefit and cost criteriacomputationGiven two structural arrays Si and Sj, we apply the string-matching concept described in Gonzalez and Woods (2002) andcompare them component by component. Let N be the numberof elements in the structural arrays (N = 9). Let M be the num-ber of matches between both structural arrays, where a matchoccurs in the kth element if sik = sjk. A measure of similaritybetween Si and Sj is defined as the ratio:

Rij ≡ R(Si, Sj) = M

N(9)

Hence Rij = 1 represents a perfect match – every element inone array matches that in the other array – between both struc-tural arrays (M = N) and 0 a total mismatch – the two arraysdo not match even on a single element – between Si and Sj,i.e. M = 0. The largest value of Rij gives the best match. Giventwo area vectors ai and aj, we obtain the following similaritymeasure Eij:

Eij ≡ E(ai, aj) = 1 − 11 + ||ai − aj||

(10)

where ||·||is the Euclidean norm. As the components of ai andaj range in [0,1], the maximum dissimilarity between ai and aj

is reached when aik = 0 and ajk = 1 or vice versa, i.e. for Eij ≈ 0.59and ||ai − aj|| = √

2. Once again, we map Eij to the range [0,1]by applying a linear transformation taking into account theselimits. Hence, Eij is null if ai = aj (i.e. a perfect match). Thelowest value of Eij gives the best match.

From the point of view of the decision-making frame-work, Rij/Eij are respectively the benefit/cost criteria: thehigher/lower the value, the easier it is to arrive at a decision(Wang and Fenton, 2006).

2.4.2. Decision-making formulationOur decision-maker uses a multicriteria decision-making(MCDM) framework under a fuzzy context based on the workof Wang and Fenton (2006), Gu and Zhu (2006), and Chen (2000).Given the cell i, the MCDM is expressed as a problem with twomutually exclusive solutions (alternatives) to the spraying ofi, namely A1 (yes) and A2 (no), one of which must be chosen.

This decision is made based on the following two crite-ria: C1 ≡ similarity between structural arrays; C2 ≡ similaritybetween area vectors. We assign a relative weight value for

each criterion: w1 for C1 and w2 for C2. Each criterion is aver-aged by assigning it a relative weight: w1 for C1 and w2 for C2.They have been fixed at 0.4 and 0.6 (w1 + w2 = 1), respectivelythrough a cross-validation procedure described in Section 3.1

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Table 2 – Normalized performance decision table according to the criteria and the weights

Criteria (weights)

C1(w1) C2(w2)

Decision A1 R1 =⌊

R1 /M, R1 /M, R1 /M⌋

]w1 E1 =⌊

m/E1 , m/E1 , m/E1⌋

w2

/M, R

iM ia

A2 R2iM

=⌊

R2ia

(Duda et al., 2001). The decision about the cell i is summarizedas follows.

(1) Compute Si and ai according to Eqs. (4) and (8), respectively.(2) Recover the set KB1 (the set comprising patterns that

indicate the need to spray) and KB2 (the set comprisingpatterns that indicate that there is no need to spray). Foreach cell j in KB1 (KB2) compute the vectors x1

i(resp. x2

i)

and y1i

(resp. y2i),

xki ≡ {Rk

i1, Rki2, . . . , Rk

ij},

yki ≡ {Ek

i1, Eki2, . . . , Ek

ij}; k = 1, 2; j = 1, 2, . . . , Jk (11)

where J1/J2 is the number of cells stored in KB1/KB2, respec-tively.

(3) For each xki

select the three greatest values (they representthe benefit criterion) Rk

ia< Rk

ib< Rk

icwhere Rk

ij< Rk

ia; for each

yki

select the three smallest values (they represent the costcriterion) Ek

ia> Ek

ib> Ek

icwhere Ek

ij> Ek

iaand j �= a, b, c.

(4) Build the normalized performance decision table (Table 2)where R1, R2, E1, and E2 are considered triangular fuzzynumbers. This justifies the choice of three values, thethree highest values and the three lowest values, whichare fixed by the benefit and cost criteria, respectively:M = max

{R1

ic, R2

ic

}and m = min

{E1

ic, E2

ic

}.

(5) Choose the best alternative. A distance mea-surement between two triangular fuzzy numbersa ≡ (a1,a2,a3) and b ≡ (b1,b2,b3) is defined accord-ing to the vertex method defined in Chen (2000) as

d(a, b) =√

13 [(a1 − b1)2 + (a2 − b2)2 + (a3 − b3)2]. We define

the ideal positive solution p+ ≡ (1,1,1) and the ideal neg-ative solution p− ≡ (0,0,0). Compute the following sum ofdistances:

d+i1 = d(R1

iM, p+) + d(E1iN, p+); d+

i2 = d(R2iM, p+) + d(E2

iN, p+)

(12)

d−i1 = d(R1

iM, p−) + d(E1iN, p−); d−

i2 = d(R2iM, p−) + d(E2

iN, p−)

(13)

The performance index for each alternative h = 1,2 is:

phi = d−

ih+ c − d+

ih

2c(14)

where c is the number of criteria (c = 2 in our approach). Thebest alternative h for the cell i is that with the ph

ivalue clos-

est to 1. So, if |p1i

− 1| ≤ |p2i

− 1| then select A1; otherwise,select A2.

ib ic iN ia ib ic

2ib

/M, R2ic

/M⌋

w1 E2iN

=⌊

m/E2ia

, m/E2ib

, m/E2ic

⌋w2

3. Results

To assess the validity and the performance of the proposedapproach we used a set of 146 digital images, about half ofwhich were taken on sunny days and the rest on cloudy days.Because the interval between any two members of the twosubsets (images taken on sunny days and on cloudy days)was always less than 3 days, we can assume that both sam-ples corresponded to a similar growth stage of weeds and thecrop. At this stage, in which the herbicide must be applied,the weeds and the crop plants display similar spectral signa-tures and textures, which is one of the problems mentionedin the introduction. Under these circumstances, the digitalimages represented fundamentally different natural lightingconditions.

3.1. Design of a test strategy

The set of 146 images available was split randomly in threesubsets – B1, B2, and B3 – of 30, 20, and 96 images, respectively.Each subset was segmented by applying the process describedin Section 2.3, obtaining 48 cells for each image. Each cell j isdescribed by its attributes Sj and aj, computed using Eqs. (4)and (8), respectively.

B1 is the subset used in Section 2.3.3, with Fa and Ha cells.The KB is loaded with KB1 = 245 (Fa) and KB2 = 1195 (Ha). Eachcell is stored with its attributes. B2 is used for setting the w1

and w2 weights for the benefit and cost criteria (Section 2.4.1)through a cross-validation procedure (Duda et al., 2001). Asbefore, for each image we extracted 48 cells, hence B2 provided960 cells. Based on the expertise criterion (Appendix A), 182(19%) were classified as those that required spraying and thereminder (81%) as those that did not require spraying. For thisset B2 we applied the proposed decision-making process (Sec-tion 2.4) using the KB and varying w1 and w2 from 0.25 to 0.75,taking into account that w1 + w2 = 1. For each combinationof weights we computed the decision error by comparing theresults of our decision-making strategy with those obtainedby applying the expertise criterion. We searched for the min-imum error value, which was found to be 17% with w1 = 0.39and w2 = 0.61. Therefore, these values were then used fortesting B3 under the following set of five tests based on thestructural and area-based measurements.

• Test 1 uses only the structural array.

• Test 2 uses only the component ai1 of the area-based vector,

i.e. weed coverage (Tian et al., 1999).• Test 3 uses only the component ai2 of the area-based vector,

i.e. weed pressure (Ribeiro et al., 2005).

c o m p u t e r s a n d e l e c t r o n i c s i n a g r i c u l t u r e 6 0 ( 2 0 0 8 ) 144–155 151

th th

•

•

to3ta

3

Gtb

pu

is

(tks

bc

3

Tjt

r

Table 3 shows the results in terms of the correct classifica-tion from the five tests. We computed the CCP and Yule scoresfor the set of 96 images; since we processed 48 cells for eachimage, the number of cells tested was 4608. Larger score values

Table 3 – CCP and Yule score values for the tests(percentage of cells to be sprayed)

Test 1 Test 2 Test 3 Test 4 Test 5

Fig. 3 – Labelled image wi

Test 4 uses both the components, ai1 and ai2, of the area-based vector.Test 5 uses the structural array and both the components,ai1 and ai2, of the area-based vector. This is the test forassessing the approach proposed in this paper.

Comparing the results obtained by Test 5 with those fromhe rest of the tests allowed us to establish the performancef the proposed approach. Additionally, through Tests 2 and, we compared the effectiveness of our approach with that ofhe two strategies proposed by Tian et al. (1999) and Ribeiro etl. (2005).

.2. Decision-making

iven a cell i belonging to B3, we made a decision on it (whethero spray) by comparing its attributes with those of all j cellselonging to the sets KB1 and KB2.

Test 5 uses the decision-making process described in thisaper based on the fuzzy MCDM. The decision-making processsed in rest of the four tests is described below.

Test 1: ∀j, j ∈ {KB1,KB2} compute mk = min{Rij}j=k, where Rij

s computed according to the Eq. (9); if k ∈ KB1 the cell i is to beprayed; otherwise, it should not be treated.

Tests 2, 3, 4: ∀j, j ∈ {KB1,KB2} compute Eij according to the Eq.10). Test 2 uses only ai1 and aj1; test 3 uses only ai2 and aj2, andest 4 uses both (ai1,aj1) and (ai2,aj2). Obtain Mk = max{Eij}j=k; if∈ KB1, the cell i is to be treated; otherwise, it should not beprayed.

The decisions for each test were verified against thoseased on human judgement (Appendix A). Thus, we couldompute a measurement for validation.

.3. Measurements for validation

he results of comparing the decisions based on expert human

udgement with those arrived at by deploying the differentests were analysed based on the following values.

True Sprayed (TP, true positive), i.e. the number of cells cor-ectly identified as needing the spray.

e cells “S” to be sprayed.

True No Sprayed (TN, true negative), i.e. the number of cellscorrectly identified as not needing the spray.

False Sprayed (FP, false positive), i.e. the number of cells thatdid not need to be sprayed but identified by the method asthose that did.

False No Sprayed (FN, false negative), i.e. the number of cellsthat needed to be sprayed but identified by the method asthose that did not.

Traditionally, from these four quantities, the most usedmeasures for classification are those that combine the fourvalues (Sneath and Sokal, 1973), namely the following.

(1) The correct classification percentage: CCP = TP+TNTP+FP+TN+FN

(2) The Yule coefficient: Yule =∣∣ TP

TP+FP + TNTN+FN − 1

∣∣CCP is broadly used in computer vision tasks for assessing

a classifier’s performance.

3.4. Analysis of results

Fig. 3 shows an image belonging to the subset B3, which wassegmented and processed according to the method describedin this paper. The cells labelled with the symbol “S” were to besprayed based on the decision-making strategy developed aspart of this work.

CCP 73 76 79 86 92Yule 66 69 71 82 88% of cells to be

sprayed37.6 32.1 30.3 24.2 20.8

152 c o m p u t e r s a n d e l e c t r o n i c s i n a g r i c u l t u r e 6 0 ( 2 0 0 8 ) 144–155

Table 4 – Categorization of cells with reference into those that need spraying and those that do not, arrived at withdifferent structural and area features

Structural features Area features

c1 c2 c3 c4 c5 c6 c7 c8 c9 ai1 ai2

m1 �1 m2 �2

2316

(

Number of cells to be sprayed 959 (20.8%) 31 89 2Number of cells not to be sprayed: 3649 (79.2%) 2147 1215 2

indicate better performance. The third row in Table 3 displaysthe percentage of cells to be sprayed.

The results in Table 3 lead to the following conclusions.

(a) The best performance was achieved by Test 5.(b) Test 5 obtained better results than Test 4; this means

that the structural measurements improved the resultsobtained by using only area-based measurements, as inTest 4. Note that we used the same decision-making pro-cess for all tests.

(c) Test 4 performed better than Tests 2 and 3; this meansthat the combination of weed coverage and weed pressureimproved the results obtained by using either criterionseparately.

(d) The worst performance was obtained by using only struc-tural measurements, i.e. Test 1.

Table 4 displays the classification of cells – those that needto be sprayed and those that do not – according to the condi-tions c1 to c9 (shown in Table 1) for the spatial features and theaverage values for the area features (the standard deviation isalso displayed).

From Table 4 one cannot determine clear thresholds val-ues in order to make the decision on spraying for use in futureexperiments. Nevertheless, the following inferences can bedrawn.

(1) The greatest number of cells to be sprayed fulfil c4 andthose not to be sprayed, c1.

(2) The average area values m1 and m2 are above/below ahypothetical threshold fixed at 0.5 for spraying and notspraying, respectively.

The number of combinations for all features is high andsome of them do not report significant information. Neverthe-less, we have found groups of significant combinations, which

Table 5 – Combination of attributes and percentages of cells cla

Category Combination of attr

Spray 1 c1 ∧ (c6 ∨ c8) ∧ (ai1 > 0.7) ∧ (ai2 > 02 c1 ∧ (c5 ∨ c7) ∧ (ai1 > 0.6) ∧ (ai2 > 03 c4 ∧ (ai1 > 0.5) ∧ (ai2 > 0.4)4 (c2 ∨ c3) ∧ c9 ∧ (ai1 > 0.4) ∧ (ai2 > 05 (ai1 > 0.8) ∧ (ai2 > 0.7)

No spray 6 (ai1 < 0.2) ∧ (ai2 > 0.1)7 (c1 ∨ c2) ∧ (c5 ∨ c6 ∨ c7 ∨ c8) ∧ (ai1

616 314 217 41 53 111 0.72 0.0875 0.66 0.091271 436 321 132 98 15 0.19 0.0769 0.15 0.8260

are reported in Table 5 due to their special relevance. A distinc-tion is made between the two categories of cells: those thatneed to be sprayed and those that do not. Also displayed is thenumber and percentage of cells placed in either category bythe given combination (so long as the percentage was greaterthan 80). The symbols ∧ and ∨ denote the logical “and” and “or”operators. The area-feature values ai1 and ai2 are normalizedin the range [0,1] as explained at the end of Section 2.3.3.

From Table 5, one can see that the threshold for the areafeatures varies with the combination of the structural cate-gories. The following inferences can be drawn.

(a) Combinations 1 and 2: if there are no isolated patches (c1)along with patches adjacent to the crop (c5 to c8), sprayingis required only if the area-feature values are high.

(b) Combination 3: if the patches are widely dispersed (c4),spraying is required even when area-feature values arerelatively small.

(c) Combination 4: if the number of isolated patches (c2, c3) issmall, with large patches joining crop lines (c9), sprayingis required although the area-feature values are relativelysmall.

d) Combinations 5 and 6: if area-feature values are high, irre-spective of the number of structural features, spraying isrequired; if low, spraying is not required.

(e) Combination 7: if the number of isolated patches (c1, c2) issmall, with patches adjacent to the crops (c5 to c8), spray-ing is not required although the area-feature values arerelatively large.

One issue to be addressed concerns the weeds occludedunder our vision-based system. The weeds are occluded when

they appear mixed with the crop and there are no weeds plantswithin the rows. Because of the similar spectral signatures ofweeds and crops plants, possible occlusions can be detectedby analysing high densities of crop plants in the crop L and R

ssified as to be sprayed or not to be sprayed

ibutes No. of cells % of cells

.8) 325 95

.6) 297 94524 91

.3) 198 85254 82

665 90< 0.6) ∧ (ai2 < 0.5) 1835 86

a g r

rtgtcsioa

R

L

wAncc

4

Wfawasfh

pbumtoukbc

rcaiaacbtp

A

TiAf

c o m p u t e r s a n d e l e c t r o n i c s i n

egions (see discussion in Section 2.3.3). Indeed, if this densityends to cover the entire crop area (AiL or AiR), it means thataps within the crop could be filled with weeds. Additionally,he presence of two patches (c6 or c8) adjacent to the cropsould also be considered a sign of occluded weeds. The abovehould be accompanied by the absence of isolated patches,.e. fulfilling c1. We identified the following two conditions ascclusions, depending on whether the occlusion was associ-ted with the left or right crop line in the cell:

ight : |AiR − 15 Aic| < ε ∧ (c6 ∨ c8) ∧ c1; (a)

eft : |AiL − 15 Aic| < ε ∧ (c5 ∨ c7) ∧ c1. (b)

here ε is a tolerance value set to 0.05, it implies that AiL or

iR are considered equal to 1/5Aic so long as the difference iso greater than ε. We found 125 cells fulfilling the above twoonditions, where 79 (63%) were placed in the ‘to be sprayed’ategory, belonging to the combinations 1 and 2 in Table 4.

. Conclusions

e propose a new approach to detecting weeds in row cropsor selective spraying in precision agriculture. Although thispproach has proved its value for Avena sterilis growing inide-row cereal crops, it can be used in many other situations

s well, e.g. maize. We have designed the method based on twoubprocesses: (1) segmentation to separate weeds and cropsrom the rest and (2) decision-making to determine where theerbicide should be selectively applied.

The segmentation is based on a combination of basicrocessing techniques. The decision-making is carried outy combining both structural and area-based measurementsnder a fuzzy context through MCDM. Although area-basedeasurements have been used before, we have established

hat the use of structural measurements improves the resultsbtained when area-based attributes are the only attributessed. This is because the distribution of weed patches in thisind of fields must be considered. The occluded weeds muste studied in greater depth in the future to increase the per-entage of success.

An important issue to be addressed in the future is theobustness of the proposed approach, considering that lightonditions outdoors vary a great deal. One approach toccount for such variation is to apply homomorphic filter-ng (Gonzalez et al., 2004), which separates the illuminationnd the reflectance components, thereby allowing reflectancelone to be considered and illumination effects to be dis-arded. Thus, only the reflectance of weeds, crops, and soil cane considered. Automatic learning of the weights attached tohe benefit and cost criteria used during the decision-makingrocess should also be considered in future research.

cknowledgements

he authors gratefully acknowledge funding from the Span-sh Ministry of Education and Science under grant numberGL-2005-06180-C03-03. Alberto Tellaeche is with Tekniker

oundation in Eibar, Gipuzkoa, Spain working in Computer

i c u l t u r e 6 0 ( 2 0 0 8 ) 144–155 153

Vision tasks and intelligent systems. The authors are gratefulto the referees for their suggestions and constructive criticismof the original version of this paper.

Appendix A. Expertise criterion

The original images were visually analysed by an expert inorder to detect the presence of A. sterilis in patches of sufficientdensity and distribution to be valid targets for site-specificweed management. The human visual observation was car-ried out guided by the segmented image through the approachproposed in this paper. The expert identifies the cells to besprayed by (1) taking into account the density and dispersionof weeds, (2) analysing additional factors affecting the fieldand the crops, and (3) visual inspection.

A.1. Weed density and dispersion

When weeds appear in large patches with a low dispersion,the expert determines visually if the weed density is above athreshold that is considered ‘safe’ from the point of losses inyield of the crop. If the density is above that threshold, thecells must be sprayed. According to experimental studies, A.sterilis at densities above 25 panicles m−2 (5–10 plants m−2) canlower the yield of winter barley by 10% (Torner et al., 1991). Ifthe weeds appear dispersed in small or isolated patches, theexpert also uses a different threshold. According to Barrosoet al. (2005), residual infestations of A. sterilis in the range of1–10 panicles m−2 (0.2–4 plants m−2) represent a risk of yieldloss in the current and following 2–3 years (estimated at 15%,particularly in the following years). Based on the perspectiveprojection of our images (Figs. 2 and 3), taking into accountthe focal length of the camera (about ∼20 mm), and using tri-angulation between the objects in the field and their images,it was calculated that the cells in the bottom part of the imagecovered an area of approximately 0.4 m2, with 8500 pixels. Thecells in the 13th row (number of cells processed, n = 13) coveran area of 8 m2, with approximately 1660 pixels. On average,the size of cells in each row is reduced in the next row at therate of 6% in terms of the number of pixels and increased ata rate of 15% in real area (m2). On average, a weed plant inthe first row of cells is represented by approximately 12 pixels.Hence, taking into account the reduction in the number of pix-els (∼72%) in the 13th row, this weed plant is represented by3 or 4 pixels. This justifies the choice of the Ta threshold andthe removing of small areas only from the lower half of theimage. Additional studies about the dispersion are reported inBarroso et al. (2006).

A.2. Additional factors

The expert has available a risk map of the field, drawn upafter taking into account the following data: stability of weedpatches between different years, latent weeds, biochemicalproperties of soil, yield in previous years, and weed densities,

estimated visually, at harvest in the previous years. The rel-atively high spatial stability of A. sterilis patches has receivedspecial attention in improving the precision of weed detec-tion (Barroso et al., 2004a). Various studies (Walter et al., 1997;

i n a g

r

154 c o m p u t e r s a n d e l e c t r o n i c s

Christensen and Heisel, 1998) have used stratified weed map-ping approaches from historical weed maps (obtained witha low resolution) to divide the field into weed zones. There-after, these zones are assessed with a higher resolution usingreal-time detection technologies.

A.3. Visual observation

Visual inspection of the stage of growth of crops and weedsverifies the expert decision based on the above two points.

Although such expert assessment is probably reliableenough for practical use, we have to recognize various sourcesof errors in the estimations. First of all, visual estimationsof patch size and density have some degree of uncertainty.Although weed density can be estimated more reliably inareas close to the observer, the degree of reliability decreasesrapidly as the distance increases. Furthermore, although itis relatively easy to detect high weed densities visually, it isnot so easy to detect low densities (∼1 plant m−2). This fact,together with the fact that weed patches often have irregu-lar shapes and poorly defined borders, may introduce someerrors in defining the perimeter of the patch. Another potentialsource of error is the uncertainty in estimating losses in yield.Depending on the weather conditions in a given year, yieldlosses caused by A. sterilis may vary considerably (Torner etal., 1991). Because of this variability due to weather, the use ofeconomic thresholds for weed control has not received muchpractical attention in the past—a limitation that can be over-come by using broad infestation categories. In our work with A.sterilis, we used four categories, with infestation levels vary-ing on a logarithmic scale (>0.1 plants m−2, 0.1–1 plants m−2,1–10 plants m−2, and >10 plants m−2). This scoring system mayalso contribute to alleviating two major problems inherentin any human assessment, namely inadequate training andthe progressive reduction in the quality of assessment dueto fatigue, which justifies the use of the automatic machine-vision system as a guide because it is free of fatigue.

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