A new vision-based approach to differential spraying ... - Caltech Vision

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mated weed coverage and weed patchiness based on digital images, using a fuzzy ... and different sizes of the patches, (2) spectral signature and texture similar to those of ..... Our decision-maker uses a multicriteria decision-making. (MCDM) ...
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A new vision-based approach to differential spraying in precision agriculture Alberto Tellaeche a , Xavier P. BurgosArtizzu b , Gonzalo Pajares c,∗ , d ´ Angela Ribeiro b , C´esar Fernandez-Quintanilla a

´ ´ ´ Dpto. Informatica y Automatica, Escuela T´ecnica Superior de Informatica, UNED, Spain ´ Instituto de Automatica Industrial, CSIC, Arganda del Rey, Madrid, Spain c Dpto. Ingenier´ıa del Software e Inteligencia Artificial, Facultad Informatica, ´ Universidad Complutense, 28040 Madrid, Spain d Centro de Ciencias Medioambientales, CSIC, Madrid, Spain b

a r t i c l e

i n f o

a b s t r a c t

Article history:

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

Received 7 February 2007

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

Received in revised form

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

25 July 2007

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

Accepted 26 July 2007

an automatic computer vision method for detecting Avena sterilis, a noxious weed growing in cereal crops, and differential spraying to control the weed. The proposed method

Keywords:

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

Precision agriculture

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

Machine vision

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

Weed detection

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

Image segmentation

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

Multicriteria decision-making

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. © 2007 Elsevier B.V. All rights reserved.

1.

Introduction

Nowadays, there is a clear preference to reducing the use of chemicals in agriculture. Numerous technologies have been developed to make agricultural products safer and to lower their adverse impacts on the environment, and precision agriculture is a valuable component of the framework to achieve this goal (Kropff et al., 1997; Zhang et al., 2002; Stafford, 2006). Within that general framework, weeds can be managed site-specifically using available geospatial and information technologies (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: [email protected] (G. Pajares). 0168-1699/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.compag.2007.07.008

to detect weed seedlings by machine vision focused on geometrical measurements such as shape factor, aspect ´ ratio, and length/area (Perez et al., 2000). Later, colour images were successfully used to detect weeds and other types of pests (Søgaard and Olsen, 2003). Yang et al. (2003) estimated weed coverage and weed patchiness based on digital images, using a fuzzy algorithm for planning site-specific application of herbicides. Recently, Gerhards and Oebel (2006) used real-time differential images (NIR-VIS) obtained with a set of three digital bispectral cameras to detect small weed seedlings in different crops. Other approaches have used colour indices to distinguish plant material from the

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background (Thorp and Tian, 2004; Ribeiro et al., 2005). Bacher (2001) estimated weed density in a field of spring barley by image binarization and morphology followed by the identification of crop rows using information on distances between rows within the crop to decide on spraying. This process serves to make weed plants appear isolated from the crop. Avena sterilis L. (“winter wild oat”) is one of the most widely distributed and abundant weeds of cereals in Spain and other regions with Mediterranean climate, causing substantial losses in these crops (Barroso et al., 2004a; Radics et al., 2004). Although some A. sterilis plants may be found growing singly or in small patches, the majority of them are aggregated in relatively large patches (Ruiz et al., 2006), and those in early spring, after broad-leaved weeds have been controlled by early postemergence treatments, are practically pure stands (Fernandez-Quintanilla, personal observation). Due to these two features, it is relatively easy for an experienced farmer or a technical consultant to detect patches of A. sterilis visually in the early stages of crop growth. In fields of cereals (barley or wheat), the cereal plants grow along the furrows: the plants growing between furrows can only be weeds. But weeds may also grow mixed with the cereal. We sought to detect weeds by differences in appearances: isolated plants, small or large patches, or mixed with the crop. Three main problems arise during detection, namely (1) irregular shapes and different sizes of the patches, (2) spectral signature and texture similar to those of the cereal plants, and (3) irregular distribution of the weeds in the field. This means that methods using only absolute sizes, shapes, textures, or spectral signatures are not applicable to our experiments (Aitkenhead et al., 2003; Onyango and Marchant, 2003; Granitto et al., 2005). The total proportion of weeds in the field is important because it indicates the extent of competition between weeds and the crop (Tian et al., 1999; Ribeiro et al., 2005), but distribution has not been considered in vision-based systems to our knowledge. Barroso et al. (2004b) studied the economic benefits of using site-specific weed management systems for large patches and numerous small patches of weeds. The damage from large patches to the crops is clear; they lower the yield substantially in the current year. When numerous small weeds patches appear during the cereal’s growth phase, they tend to compete with the crop aggressively. Moreover, because weeds are more prolific in producing seeds and the seeds persist longer in soil, a failure to control weeds creates serious problems not only in the current year but also for the following 2–3 years (see Appendix A for details of weed density). Hence, we propose a new method with two objectives: (1) to determine the quantity and distribution of weeds present in the crop and (2) to decide, based on that knowledge, whether to undertake selective spraying to control the weeds. The method consists of an image segmentation process and a decision-making approach. The segmentation 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.

2.

Materials and methods

2.1.

Images

145

The images used for this study were those of a 1.7-ha experimental field of barley on La Poveda Research Station, Arganda del Rey, Madrid. The most common weed in the field was A. sterilis, with densities ranging from 10 to 400 plants m−2 . Although other weed species (Papaver rhoeas, Veronica hedaerefolia, Lamium amplexicaule) were also present in the field, at the time of image acquisition most of them had been killed by an early treatment with bromoxinil and mecocrop. Images were taken on two dates in April 2003, when the plants were at the early tillering stage (3–5 leaves). Row spacing was 0.36 m. Although the standard row width in the area is 0.17 m, much wider rows are common in other semi-arid areas of North America 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 approximately 2.1 m × 19 m and the resolution was 1152 × 864 pixels. The images were captured under the perspective projection, which means that areas of identical size in the field appear under different sizes in the image, depending on their distance from the camera. Hence, we must compute those attributes that are independent of the perspective projection. This is achieved by establishing relative measurements between crops and weeds instead of using absolute measurements, as described in the next sections.

2.2.

The proposed method

The proposed method involves two sub-processes: image segmentation and decision-making. The image segmentation process divides the image into cells and extracts those features and attributes from each cell that make it possible to distinguish between weeds and the crop; based on that information, the decision-making process determines whether a cell is to be sprayed. Such decision-making requires a set of samples 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-line process. The decision-making is carried out by computing similarity measures between the samples stored in the KB and the cell being processed; we call this process of decision-making the on-line process. The image segmentation is identical for both processes (Fig. 1).

2.3.

Image segmentation: weed detection

The steps involved in the proposed image segmentation process are acquiring and binarizing images, detecting crop rows, partition the image into a grid of cells, and extracting attributes from the cells.

2.3.1.

Acquiring and binarizing images

As mentioned before, the images were acquired under the perspective projection, which implies that the crop rows tend to converge at the vanishing point out of the field of view. The goal of this first step was to convert the input red–green–blue

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Fig. 1 – Vision-based decision process.

(RGB) image into a binary image in which the vegetation (whether weeds or the crop) in the RGB image is represented as white points and the rest as black ones. Various methods have been proposed for image binarization (Ribeiro et al., 2005; Granitto et al., 2005; Onyango and Marchant, 2003; Bacher, 2001; Tian and Slaughter, 1998). We selected the method described by Ribeiro et al. (2005). The segmentation was based on the three components (R, G, and B) that together describe each image point. The first stage of the segmentation transforms the original RGB image into a onedimensional grey level (monochrome) image by applying the following 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 is achieved with the following parameter values: r = −1, g = 2, and b = −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 that sets the contrast breakpoint between pixels representing vegetation and rest of the pixels (representing everything else: shadows, stones, straw and other debris, etc.). Finally, the greylevel image was transformed into a black-and-white image to obtain a binary image. According to an earlier evaluation of approaches based on different thresholds for detecting changes in an image (Rosin and Ioannidis, 2003), the best performance was achieved using the entropy of the histogram, following the method described by Kapur et al. (1985). Therefore, we used this approach in our work. To remove spurious white pixels and to smooth the white contours from the binarized image, we applied a morphological opening (erosion followed by dilation) operation (Onyango and Marchant, 2003; Bacher, 2001). However, because of the perspective projection, we had to apply three different structuring elements for performing the morphological opening operation because the central rows of the crop were nearvertical whereas the rows to the left and to the right had different slopes. We divided the image into three strips of identical width: left (L), central (C), and right (R). We used the SL ,

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



0

0

0

1

1



⎢0 0 1 1 1⎥ ⎢ ⎥ ⎢ ⎥ SL = ⎢ 0 1 1 1 0 ⎥ ⎢ ⎥ ⎣1 1 1 0 0⎦ ⎡

1

1

0

0

0

1

1

0

0

0



0

1

1

1

0



⎢0 1 1 1 0⎥ ⎢ ⎥ ⎢ ⎥ SC = ⎢ 0 1 1 1 0 ⎥ ⎢ ⎥ ⎣0 1 1 1 0⎦ 0

1

1

1

0



⎢1 1 1 0 0⎥ ⎢ ⎥ ⎢ ⎥ SR = ⎢ 0 1 1 1 0 ⎥ ⎢ ⎥ ⎣0 0 1 1 1⎦ 0

0

0

1

(2)

1

2.3.2. Detecting crop rows and partitioning the image into a grid of cells In the resulting binary image, all vegetation – whether weeds or the crop – was white and the rest was black. For detecting the crop rows in the image, we used a Hough transform, which is a well-known and robust method, especially if the rows cover the whole image (Astrand and Baerveldt, 2002; Billingsley and Schoenfisch, 1997). The Hough transform obtains 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 cells A(,) indexed by  and , where high values in a cell of the accumulator determine a line with the indexed parameters. Only those values of the accumulator greater than Th , a threshold set to 100 by trial and error, are allowed. Because the orientation of the crop rows was known, we searched only for rows with  and  consistent with this knowledge, i.e. lines that were near-vertical with two slopes (Fig. 2). Finally, and because the crop is not usually a perfect line but has a certain width as well, it is likely that several accumulator cells with similar indices ( and ) will have high accumulated values. This means that several lines are associated to the same crop

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147

Fig. 2 – (a) Original image, (b) segmented image displaying the line of crops and cells.

row. We merged all similar lines into a single line: given two cells A( i , i ) and A( j ,j ), we assumed that they represented the same crop row if | i −  j | ≤ ε1 and |i − j | ≤ ε2 where ε1 and ε2 were set to 5 and 10, respectively. We tested the performance of these values by trial and error. The next step was to partition the image into a grid of cells. This was carried out by tracing horizontal lines, i.e. lines with equation y = kc. Due to the perspective projection, the size of the cells decreases towards the upper part of the image and important details coming from weeds are lost when more cells are used. Therefore, and although we traced horizontal lines in the whole image, we processed the cells only in the lower part of the image. So, k = 1, . . ., n and c = 50, where n is bounded by the height of the image. With n = 13, the details in the cells were retained. Fig. 2(a) shows the original image captured in a barley field and Fig. 2(b) the image after the segmentation process.

undefined weed shapes, similar spectral signatures and textures of the crops and weeds, and so on. Moreover, due to the perspective projection, the cells within a single image differ in size and shape. The attributes chosen for weed detection must be independent of the above factors. In particular, they must be invariant to the size and shape of cells. Therefore, we extracted relative measurements instead of absolute ones. For segmentation, we randomly selected a subset of 30 images from the set of 146 images available to us. From each selected image, we selected 48 cells, i.e. a total of 1440 cells. The number of cells classified as candidates to be sprayed was Fa = 245 (17% of 1440). This relatively small percentage was the focus of interest in deciding upon the differential spraying. For the set of remaining cells (Ha = 1195), we computed the proportion of the white area in the cells:

2.3.3.

Extraction attributes from cells

As mentioned in Section 1, several factors affect weed detection: irregular spatial distribution of weed patches, irregular distribution of crop plants within a row (as a consequence of sowing failures or gaps resulting from various accidents),

1  Wc Ha Ac H

r=

(3)

c=1

where Ac is the total area of a given cell c and Wc the white area in that cell. In this kind of cell, free of weeds, the white area 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 c1 ni = 0 1089

c2 ni = 1

c3 1 < ni ≤ 5

c4 ni > 5

c5 pl = 1

c6 pl = 2

c7 pr = 1

c8 pr = 2

c9 L–R connected

155

105

91

55

44

62

44

21

(R) patches representing the crop areas. We found r ≈ 2/5 and r = rl + rr where rl and rr are the corresponding ratios for the L and 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 taking into account the image-processing procedure, we analysed the distribution of the patches in each cell for both sets Fa and Ha 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 mutually exclusive; a single cell could contain patches of the three types simultaneously. Table 1 shows the number of cells belonging to each of the nine relevant categories found in the cells we analysed. Areas in the lower half of the image below the threshold Ta (measured in pixels), set to 3 in our experiments, were removed beforehand because, upon observation of the above set of cells, it was found that approximately 93% of these small areas represented non-vegetation elements with spectral signatures very similar to those of green plants that had survived the morphological opening operation. However, the number of cells thus removed represents only 5% of the total set of cells. Values of the threshold greater than the above tended to eliminate isolated weed plants, which was undesirable. In the upper half, this was not possible because in the perspective projection weeds could be represented by areas smaller than 3 pixels (see Appendix A where some details are given about Ta ). Each category or case was identified with a condition c1 to c9 and is assigned a separate column in Table 1. We take a condition ci as true when the predicate (defined below for each condition in the table) is true: ni is the number of isolated patches in a cell and pl and pr are the number of patches which appear as protuberances connected to the L and R areas, respectively. The number of cells analysed fulfilling each condition is shown in the second row. Column 1 shows the number of cells containing only the L and R areas, i.e. without isolated patches (ni = 0). Columns 2–4 show the number of cells with ni isolated patches; the predicates are grouped based on the number of cases found. Columns 5–8 show the number of patches pl and pr connected with the L and R areas, respectively. 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 consider more cases with other values for this kind of patches. Finally, column 9 shows the number of cells with the L and R areas interconnected. Based only on the distribution of weed patches, under the conditions c1 to c9 , we could not conclude definitively whether a given cell needed to be sprayed. We therefore searched for area-based attributes because they had been used in some

´ earlier experiments (Granitto et al., 2005; Bacher, 2001; Perez et al., 2000). The area-based attributes take weed densities into account. We observed two important cases where the distribution of patches played an important role in the final decision. (1) There were cells with isolated patches distributed in the cell with a low total density. If area measurements were the only criterion, the decision would have been not to spray such cells. However, as explained in Section 1 and also in the Appendix A, weeds that may be few but distributed widely represent a risk to the current and the following crops, and these cells must be sprayed. (2) On the contrary, there were also patches attached to the L and R areas which represented the crop because it had reached a high density during its growing phase. The high density would have led to the decision to spray—which would have been unnecessary. Thus, decisions based solely on area values could prove incorrect; the method of decision-making therefore justifies the inclusion of the following two kinds of attributes, namely structural-based and area-based. Accordingly, the next step was to define a procedure for computing the values of these attributes. For each cell we conducted the following processes. (1) Extract the connected regions in a cell, identifying each connected region with a unique label and its area (Gonzalez et al., 2004). (2) Identify the L and R labels. Regions that share the same label are connected; those that do not are unconnected; each cell has two regions, RL and RR , each covering 1/5th of 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. L and 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 same labels (either L or R), once L and R are excluded (note that connected regions have the same label). The structural-based attributes were computed as follows. Given a cell i, we built a nine-dimensional structural array Si = {si1 , si2 , . . ., si9 } where each element sij is an attribute defined as follows:

sij =

1 if cj is true 0 otherwise

j = 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

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two elements belonging to the same subset are incompatible. However, this does not affect the performance. Two area-based attributes were computed and embedded as the components of an area-vector ai ; as before, given the cell i, this vector is ai = {ai1 , ai2 }. Let m be the total number of connected regions in the cell i (i.e. the number of labels in the cell) and Aij the area of the jth region. Aic is the total area of the cell and AiL and AiR are the areas for the L and R crop regions, respectively. AiL and AiR are computed taking into account the number of pixels inside of the regions RL and RR as described above in point 2). Based on the area measurements, we computed the following coverage values: • crop coverage: Cic = AiL + AiR

(5)

• weed coverage:

Ciw =

m 

Decision-making process

Given a new image, we apply to it the segmentation process described in Section 2.3, extracting a set of cells i with attributes Si and ai . The goal is to reach a decision on each i with respect to whether it requires spraying, based on a decision-making process that considers the similarity/dissimilarity measures between each cell i and those stored in the KB. This is the on-line process.

2.4.1. Similarity measures: benefit and cost criteria computation Given two structural arrays Si and Sj , we apply the stringmatching concept described in Gonzalez and Woods (2002) and compare them component by component. Let N be the number of elements in the structural arrays (N = 9). Let M be the number of matches between both structural arrays, where a match occurs in the kth element if sik = sjk . A measure of similarity between Si and Sj is defined as the ratio: Rij ≡ R(Si , Sj ) =

Aij − Cic

(6)

j=1

• soil coverage: Cis = Aic − (Cic + Ciw )

(7)

From Eqs. (5)–(7) we computed the components for the areavector ai C ai1 = iw Aic

2.4.

and

C ai2 = iw Cic



C 1 − is Aic

M N

(8)

where ai1 is defined as the weed coverage rate as described in Tian et al. (1999) and Ribeiro et al. (2005) and ai2 can be associated with weed pressure, also as defined in Ribeiro et al. (2005). The area attributes are relative measurements, i.e. they are invariant to the cell’s size (position in the image). The following analysis allowed us to determine the range of variability of these two values. Indeed, when the weed coverage is null, i.e. there are no weeds in the cell, ai1 = 0 but if the weeds cover the full intermediate region (i.e. Ciw = 3/5Aic ), then ai1 = 3/5. Hence, ai1 ranges from [0,3/5]. Also, if the weed coverage is null ai2 = 0. The upper limit of ai2 is achieved when Ciw is maximum (i.e. Ciw = 3/5Aic ) and Cic minimum (i.e. Cic = 0); but if Cic is null, it means the cell has no crops. The minimum value we obtained for Cic was 1/10Aic . Now, assuming that Ciw = 3/5Aic , Cis = 0.3Aic . Finally, the upper limit for ai2 can be fixed from the Eq. (8) as 4.2. Based on these limits, we mapped the component values of the area-vector linearly to the range [0,1]. This was intended so that both components contribute equitably in the computation of a similarity measurement between two area-vectors. The next step was to build a knowledge base (KB) containing KB1 , representing cells that require a spray, and KB2 , representing cells that do not. Each cell j was stored in KB with its associated attributes Sj and aj . This is the off-line process.

(9)

Hence Rij = 1 represents a perfect match – every element in one array matches that in the other array – between both structural arrays (M = N) and 0 a total mismatch – the two arrays do not match even on a single element – between Si and Sj , i.e. M = 0. The largest value of Rij gives the best match. Given two area vectors ai and aj , we obtain the following similarity measure Eij : Eij ≡ E(ai , aj ) = 1 −



149

1 1 + ||ai − aj ||

(10)

where ||·||is the Euclidean norm. As the components of ai and aj 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 ≈ 0.59 √ and ||ai − aj || = 2. Once again, we map Eij to the range [0,1] by applying a linear transformation taking into account these limits. Hence, Eij is null if ai = aj (i.e. a perfect match). The lowest value of Eij gives the best match. From the point of view of the decision-making framework, Rij /Eij are respectively the benefit/cost criteria: the higher/lower the value, the easier it is to arrive at a decision (Wang and Fenton, 2006).

2.4.2.

Decision-making formulation

Our decision-maker uses a multicriteria decision-making (MCDM) framework under a fuzzy context based on the work of Wang and Fenton (2006), Gu and Zhu (2006), and Chen (2000). Given the cell i, the MCDM is expressed as a problem with two mutually exclusive solutions (alternatives) to the spraying of i, namely A1 (yes) and A2 (no), one of which must be chosen. This decision is made based on the following two criteria: C1 ≡ similarity between structural arrays; C2 ≡ similarity between area vectors. We assign a relative weight value for each criterion: w1 for C1 and w2 for C2 . Each criterion is averaged 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), respectively through 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 )

Decision

1 RiM 2 RiM

A1 A2

1

1 1 = Ria 2 /M, Rib2 /M, Ric2 /M ]w1 = Ria /M, Rib /M, Ric /M w1

(Duda et al., 2001). The decision about the cell i is summarized as 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 comprising patterns that indicate that there is no need to spray). For each cell j in KB1 (KB2 ) compute the vectors x1i (resp. x2i ) and y1i (resp. y2i ), k k , Ri2 , . . . , Rijk }, xki ≡ {Ri1

yki ≡ {Eki1 , Eki2 , . . . , Ekij };

k = 1, 2;

j = 1, 2, . . . , Jk

(11)

where J1 /J2 is the number of cells stored in KB1 /KB2 , respectively. (3) For each xki select the three greatest values (they represent k < Rk < Rk where Rk < Rk ; for each the benefit criterion) Ria ib ic ij ia yki select the three smallest values (they represent the cost criterion) Ekia > Ekib > Ekic where Ekij > Ekia and j = a, b, c. (4) Build the normalized performance decision table (Table 2) where R1 , R2 , E1 , and E2 are considered triangular fuzzy numbers. This justifies the choice of three values, the three highest values and the three lowest values, which are fixed by thebenefit and cost respectively:  criteria,  1 , R2 M = max Ric and m = min E1ic , E2ic . ic (5) Choose the best alternative. A distance measurement between two triangular fuzzy numbers a ≡ (a1 ,a2 ,a3 ) and b ≡ (b1 ,b2 ,b3 ) is defined according to the  vertex method defined in Chen (2000) as d(a, b) =

1 3 [(a1

2

2

2

− b1 ) + (a2 − b2 ) + (a3 − b3 ) ]. We define

the ideal positive solution ≡ (1,1,1) and the ideal negative solution p− ≡ (0,0,0). Compute the following sum of distances: p+

1 = d(RiM , p+ ) + d(E1iN , p+ ); d+ i1

2 d+ = d(RiM , p+ ) + d(E2iN , p+ ) i2

(12) 1 = d(RiM , p− ) + d(E1iN , p− ); d− i1

2 d− = d(RiM , p− ) + d(E2iN , p− ) i2

(13) The performance index for each alternative h = 1,2 is: phi =

d− + c − d+ ih ih 2c

3.

C2 (w2 )

E1iN E2iN



= m/E1ia , m/E1ib , m/E1ic w2 2

2 2 = m/Eia , m/Eib , m/Eic w2

Results

To assess the validity and the performance of the proposed approach we used a set of 146 digital images, about half of which were taken on sunny days and the rest on cloudy days. Because the interval between any two members of the two subsets (images taken on sunny days and on cloudy days) was always less than 3 days, we can assume that both samples corresponded to a similar growth stage of weeds and the crop. At this stage, in which the herbicide must be applied, the weeds and the crop plants display similar spectral signatures and textures, which is one of the problems mentioned in the introduction. Under these circumstances, the digital images represented fundamentally different natural lighting conditions.

3.1.

Design of a test strategy

The set of 146 images available was split randomly in three subsets – B1 , B2 , and B3 – of 30, 20, and 96 images, respectively. Each subset was segmented by applying the process described in Section 2.3, obtaining 48 cells for each image. Each cell j is described 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 ). Each cell 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). As before, for each image we extracted 48 cells, hence B2 provided 960 cells. Based on the expertise criterion (Appendix A), 182 (19%) were classified as those that required spraying and the reminder (81%) as those that did not require spraying. For this set B2 we applied the proposed decision-making process (Section 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 combination of weights we computed the decision error by comparing the results of our decision-making strategy with those obtained by applying the expertise criterion. We searched for the minimum error value, which was found to be 17% with w1 = 0.39 and w2 = 0.61. Therefore, these values were then used for testing B3 under the following set of five tests based on the structural and area-based measurements.

(14)

where c is the number of criteria (c = 2 in our approach). The best alternative h for the cell i is that with the phi value closest to 1. So, if |p1i − 1| ≤ |p2i − 1| then select A1 ; otherwise, select A2 .

• 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).

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Fig. 3 – Labelled image with the cells “S” to be sprayed.

• Test 4 uses both the components, ai1 and ai2 , of the areabased vector. • Test 5 uses the structural array and both the components, ai1 and ai2 , of the area-based vector. This is the test for assessing the approach proposed in this paper. Comparing the results obtained by Test 5 with those from the rest of the tests allowed us to establish the performance of the proposed approach. Additionally, through Tests 2 and 3, we compared the effectiveness of our approach with that of the two strategies proposed by Tian et al. (1999) and Ribeiro et al. (2005).

3.2.

Decision-making

Given a cell i belonging to B3 , we made a decision on it (whether to spray) by comparing its attributes with those of all j cells belonging to the sets KB1 and KB2 . Test 5 uses the decision-making process described in this paper based on the fuzzy MCDM. The decision-making process used in rest of the four tests is described below. Test 1: ∀j, j ∈ {KB1 ,KB2 } compute mk = min{Rij }j=k , where Rij is computed according to the Eq. (9); if k ∈ KB1 the cell i is to be sprayed; 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 , and test 4 uses both (ai1 ,aj1 ) and (ai2 ,aj2 ). Obtain Mk = max{Eij }j=k ; if k ∈ KB1 , the cell i is to be treated; otherwise, it should not be sprayed. The decisions for each test were verified against those based on human judgement (Appendix A). Thus, we could compute a measurement for validation.

3.3.

Measurements for validation

The results of comparing the decisions based on expert human judgement with those arrived at by deploying the different tests were analysed based on the following values. True Sprayed (TP, true positive), i.e. the number of cells correctly identified as needing the spray.

True No Sprayed (TN, true negative), i.e. the number of cells correctly identified as not needing the spray. False Sprayed (FP, false positive), i.e. the number of cells that did not need to be sprayed but identified by the method as those that did. False No Sprayed (FN, false negative), i.e. the number of cells that needed to be sprayed but identified by the method as those that did not. Traditionally, from these four quantities, the most used measures for classification are those that combine the four values (Sneath and Sokal, 1973), namely the following. TP+TN (1) The correct classification percentage: CCP = TP+FP+TN+FN  TP  TN   (2) The Yule coefficient: Yule = TP+FP + TN+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 was segmented and processed according to the method described in this paper. The cells labelled with the symbol “S” were to be sprayed based on the decision-making strategy developed as part of this work. Table 3 shows the results in terms of the correct classification from the five tests. We computed the CCP and Yule scores for the set of 96 images; since we processed 48 cells for each image, 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)

CCP Yule % of cells to be sprayed

Test 1

Test 2

Test 3

Test 4

Test 5

73 66 37.6

76 69 32.1

79 71 30.3

86 82 24.2

92 88 20.8

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Table 4 – Categorization of cells with reference into those that need spraying and those that do not, arrived at with different structural and area features Structural features c1

c2

c3

c4

c5

c6

Area features c7

c8

c9

ai1 m1

Number of cells to be sprayed 959 (20.8%) Number of cells not to be sprayed: 3649 (79.2%)

31 2147

89 1215

223 216

indicate better performance. The third row in Table 3 displays the 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 results obtained by using only area-based measurements, as in Test 4. Note that we used the same decision-making process for all tests. (c) Test 4 performed better than Tests 2 and 3; this means that the combination of weed coverage and weed pressure improved the results obtained by using either criterion separately. (d) The worst performance was obtained by using only structural measurements, i.e. Test 1. Table 4 displays the classification of cells – those that need to be sprayed and those that do not – according to the conditions c1 to c9 (shown in Table 1) for the spatial features and the average values for the area features (the standard deviation is also displayed). From Table 4 one cannot determine clear thresholds values in order to make the decision on spraying for use in future experiments. Nevertheless, the following inferences can be drawn. (1) The greatest number of cells to be sprayed fulfil c4 and those not to be sprayed, c1 . (2) The average area values m1 and m2 are above/below a hypothetical threshold fixed at 0.5 for spraying and not spraying, respectively. The number of combinations for all features is high and some of them do not report significant information. Nevertheless, we have found groups of significant combinations, which

616 71

314 436

217 321

41 132

53 98

111 15

ai2 1

0.72 0.0875 0.19 0.0769

m2

2

0.66 0.0912 0.15 0.8260

are reported in Table 5 due to their special relevance. A distinction is made between the two categories of cells: those that need to be sprayed and those that do not. Also displayed is the number and percentage of cells placed in either category by the given combination (so long as the percentage was greater than 80). The symbols ∧ and ∨ denote the logical “and” and “or” operators. The area-feature values ai1 and ai2 are normalized in 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 area features varies with the combination of the structural categories. 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 ), spraying is 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 are relatively small. (c) Combination 4: if the number of isolated patches (c2 , c3 ) is small, with large patches joining crop lines (c9 ), spraying is required although the area-feature values are relatively small. (d) Combinations 5 and 6: if area-feature values are high, irrespective of the number of structural features, spraying is required; if low, spraying is not required. (e) Combination 7: if the number of isolated patches (c1 , c2 ) is small, with patches adjacent to the crops (c5 to c8 ), spraying is not required although the area-feature values are relatively large. One issue to be addressed concerns the weeds occluded under our vision-based system. The weeds are occluded when they appear mixed with the crop and there are no weeds plants within the rows. Because of the similar spectral signatures of weeds and crops plants, possible occlusions can be detected by analysing high densities of crop plants in the crop L and R

Table 5 – Combination of attributes and percentages of cells classified as to be sprayed or not to be sprayed Category

Combination of attributes

Spray

1 2 3 4 5

c1 ∧ (c6 ∨ c8 ) ∧ (ai1 > 0.7) ∧ (ai2 > 0.8) c1 ∧ (c5 ∨ c7 ) ∧ (ai1 > 0.6) ∧ (ai2 > 0.6) c4 ∧ (ai1 > 0.5) ∧ (ai2 > 0.4) (c2 ∨ c3 ) ∧ c9 ∧ (ai1 > 0.4) ∧ (ai2 > 0.3) (ai1 > 0.8) ∧ (ai2 > 0.7)

No spray

6 7

(ai1 < 0.2) ∧ (ai2 > 0.1) (c1 ∨ c2 ) ∧ (c5 ∨ c6 ∨ c7 ∨ c8 ) ∧ (ai1 < 0.6) ∧ (ai2 < 0.5)

No. of cells

% of cells

325 297 524 198 254

95 94 91 85 82

665 1835

90 86

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regions (see discussion in Section 2.3.3). Indeed, if this density tends to cover the entire crop area (AiL or AiR ), it means that gaps within the crop could be filled with weeds. Additionally, the presence of two patches (c6 or c8 ) adjacent to the crops could also be considered a sign of occluded weeds. The above should be accompanied by the absence of isolated patches, i.e. fulfilling c1 . We identified the following two conditions as occlusions, depending on whether the occlusion was associated with the left or right crop line in the cell: Right : |AiR − 15 Aic | < ε ∧ (c6 ∨ c8 ) ∧ c1 ;

(a)

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

(b)

where ε is a tolerance value set to 0.05, it implies that AiL or AiR are considered equal to 1/5Aic so long as the difference is no greater than ε. We found 125 cells fulfilling the above two conditions, where 79 (63%) were placed in the ‘to be sprayed’ category, belonging to the combinations 1 and 2 in Table 4.

4.

Conclusions

We propose a new approach to detecting weeds in row crops for selective spraying in precision agriculture. Although this approach has proved its value for Avena sterilis growing in wide-row cereal crops, it can be used in many other situations as well, e.g. maize. We have designed the method based on two subprocesses: (1) segmentation to separate weeds and crops from the rest and (2) decision-making to determine where the herbicide should be selectively applied. The segmentation is based on a combination of basic processing techniques. The decision-making is carried out by combining both structural and area-based measurements under a fuzzy context through MCDM. Although area-based measurements have been used before, we have established that the use of structural measurements improves the results obtained when area-based attributes are the only attributes used. This is because the distribution of weed patches in this kind of fields must be considered. The occluded weeds must be studied in greater depth in the future to increase the percentage of success. An important issue to be addressed in the future is the robustness of the proposed approach, considering that light conditions outdoors vary a great deal. One approach to account for such variation is to apply homomorphic filtering (Gonzalez et al., 2004), which separates the illumination and the reflectance components, thereby allowing reflectance alone to be considered and illumination effects to be discarded. Thus, only the reflectance of weeds, crops, and soil can be considered. Automatic learning of the weights attached to the benefit and cost criteria used during the decision-making process should also be considered in future research.

Acknowledgements The authors gratefully acknowledge funding from the Spanish Ministry of Education and Science under grant number AGL-2005-06180-C03-03. Alberto Tellaeche is with Tekniker foundation in Eibar, Gipuzkoa, Spain working in Computer

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

Appendix A. Expertise criterion The original images were visually analysed by an expert in order to detect the presence of A. sterilis in patches of sufficient density and distribution to be valid targets for site-specific weed management. The human visual observation was carried out guided by the segmented image through the approach proposed in this paper. The expert identifies the cells to be sprayed by (1) taking into account the density and dispersion of weeds, (2) analysing additional factors affecting the field and 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 a threshold that is considered ‘safe’ from the point of losses in yield of the crop. If the density is above that threshold, the cells must be sprayed. According to experimental studies, A. sterilis at densities above 25 panicles m−2 (5–10 plants m−2 ) can lower the yield of winter barley by 10% (Torner et al., 1991). If the weeds appear dispersed in small or isolated patches, the expert also uses a different threshold. According to Barroso et al. (2005), residual infestations of A. sterilis in the range of 1–10 panicles m−2 (0.2–4 plants m−2 ) represent a risk of yield loss in the current and following 2–3 years (estimated at 15%, particularly in the following years). Based on the perspective projection of our images (Figs. 2 and 3), taking into account the focal length of the camera (about ∼20 mm), and using triangulation between the objects in the field and their images, it was calculated that the cells in the bottom part of the image covered an area of approximately 0.4 m2 , with 8500 pixels. The cells in the 13th row (number of cells processed, n = 13) cover an area of 8 m2 , with approximately 1660 pixels. On average, the size of cells in each row is reduced in the next row at the rate of 6% in terms of the number of pixels and increased at a rate of 15% in real area (m2 ). On average, a weed plant in the first row of cells is represented by approximately 12 pixels. Hence, taking into account the reduction in the number of pixels (∼72%) in the 13th row, this weed plant is represented by 3 or 4 pixels. This justifies the choice of the Ta threshold and the removing of small areas only from the lower half of the image. Additional studies about the dispersion are reported in Barroso et al. (2006).

A.2. Additional factors The expert has available a risk map of the field, drawn up after taking into account the following data: stability of weed patches between different years, latent weeds, biochemical properties of soil, yield in previous years, and weed densities, estimated visually, at harvest in the previous years. The relatively high spatial stability of A. sterilis patches has received special attention in improving the precision of weed detection (Barroso et al., 2004a). Various studies (Walter et al., 1997;

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Christensen and Heisel, 1998) have used stratified weed mapping approaches from historical weed maps (obtained with a low resolution) to divide the field into weed zones. Thereafter, these zones are assessed with a higher resolution using real-time detection technologies.

A.3. Visual observation Visual inspection of the stage of growth of crops and weeds verifies the expert decision based on the above two points. Although such expert assessment is probably reliable enough for practical use, we have to recognize various sources of errors in the estimations. First of all, visual estimations of patch size and density have some degree of uncertainty. Although weed density can be estimated more reliably in areas close to the observer, the degree of reliability decreases rapidly as the distance increases. Furthermore, although it is relatively easy to detect high weed densities visually, it is not so easy to detect low densities (∼1 plant m−2 ). This fact, together with the fact that weed patches often have irregular shapes and poorly defined borders, may introduce some errors in defining the perimeter of the patch. Another potential source of error is the uncertainty in estimating losses in yield. Depending on the weather conditions in a given year, yield losses caused by A. sterilis may vary considerably (Torner et al., 1991). Because of this variability due to weather, the use of economic thresholds for weed control has not received much practical attention in the past—a limitation that can be overcome by using broad infestation categories. In our work with A. sterilis, we used four categories, with infestation levels varying 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 may also contribute to alleviating two major problems inherent in any human assessment, namely inadequate training and the progressive reduction in the quality of assessment due to fatigue, which justifies the use of the automatic machinevision system as a guide because it is free of fatigue.

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