Plant leaf = roughness analysis by texture classification with generalized Fourier = descriptors in a dimensionality reduction context

L. Journaux^1 =,=20 J.-C. Simon¹, M. F. Destain²,=20 F. Cointault³, J. Miteran⁴ and=20 A. Piron²

Keywords Texture=20 classification - Precision spraying - Motion=20 descriptors - Dimensionality reduction - Leaf=20 roughness - Kernel discriminant analysis

Introduction

Since the development of precision agriculture = (Robert=20 1999),=20 much research has been done on the optimization of inputs in the field = to reduce=20 the environmental impact and to increase the yield, which is of benefit = to=20 farmers. Two specific activities have been focused upon especially, the=20 fertilizer application (mineral or organic spreading (Hijazi et al. = 2008;=20 Villette et al. 2008)=20 and spraying for appropriate weed control (Yun et al. 2006).=20 In research on precision spraying, in particular, one objective is to = minimize=20 the volume of phytosanitary products applied to reduce environmental = effects by=20 using more effective plant treatments. The main goal is ensure that the = sprayed=20 products reach their target, to reduce losses that occur at the time of=20 application. The mechanisms of losses by drift are now well known, but = those due=20 to runoff from leaves are still poorly understood. These latter are = related to=20 the adhesion mechanisms of liquids on a surface. Specific models have = been=20 developed (Forster et al. 2005)=20 that showed that the predominant factor is leaf roughness for which = little=20 robust research has been done. For example, with a hydrophobic surface = the=20 =91lotus effect=92 can appear as in the Fig. 1.=20

Fig. 1 Representation of the =91lotus = effect=92=20 (photograph by William Thielicke, http://wthielick= e.gmxhome.de/bionik/indexuk.htm)=20

For natural images, texture in the form of colour = information=20 is a fundamental characteristic usually used in pattern and object = recognition=20 in different domains such as medical and biological imaging, biometry, = earth=20 observation and industrial control by computer vision (Fig. 2).=20

Fig. 2 Different=20 domains in which texture analysis is applied (from left to = right):=20 medical, biological, biometric, earth observation and industrial control =

A successful texture classification or segmentation = requires=20 an efficient method for feature extraction. The major difficulty, = however, is=20 that textures in the real world are often not uniform due to changes in=20 orientation, scale, illumination conditions, or other visual effects. In = our=20 case we consider the invariant features (scale, illumination and = rotation=20 invariant) called generalized Fourier descriptors (GFD) (Smach et al. = 2007),=20 which extract robust but high-dimensional texture features = (high-dimensional=20 vectors) comprising many data. Unfortunately, in a classification = context,=20 high-dimensional vectors are often redundant, strongly correlated and = suffer=20 from the problem of the =91Hughes=92 phenomenon=92 (Hughes 1968),=20 which results in inaccurate classification (Fig. 3).=20

Fig. 3 Illustration=20 of the Hughes=92 phenomenon

To improve classification performance of the original = features=20 we combine the classification steps with a selection of 13 linear and = nonlinear=20 dimensionality reduction (DR) techniques (from classical principal = component=20 analysis (PCA) to more recent methods such as Laplacian eigenmaps (LE) = or kernel=20 discriminant analysis (KDA)), which transform high-dimensional data into = a=20 meaningful representation of reduced dimensionality.

Numerous studies have aimed to compare DR = algorithms, usually=20 using synthetic data such as a swissroll (Lee et al. 2004;=20 Lee and Verleysen 2007),=20 but less so for natural data such as hyperspectral images as in Journaux = et al.=20 (2006)=20 or Niskanen and Silven (2003)=20 (Fig. 4).=20 However, it is important to note that the goal of DR algorithms is to = explore=20 the intrinsic structure of high-dimensional data, for example by = unfolding data=20 in the case of the swissroll or reducing high-dimensional natural signal = data as=20 for hyperspectral images.=20

Fig. 4 a=20 Swissroll manifold frequently used as synthetic data (Lee and Verleysen = 2007)=20 and b natural data from a hyperspectral image (Short 2010)=20

We propose to characterize the leaf roughness of = different plant=20 leaf images (1242 texture images) by taking a computer vision approach = with a=20 combination of spatio-frequency texture feature extraction and six = methods of=20 classification. Previous research into plant leaf identification or = recognition=20 used only one method of classification in general such as in Wu et al. = (2007)=20 or focused on morphological features (Tzionas et al. 2005).=20 However, some studies such as that of Backes and Bruno (2009)=20 explored texture analysis to classify plant leaves.

Our aim is to be able to characterize the hydrophilic = or=20 hydrophobic behavior of a leaf with signal and or image processing so as = to=20 adapt the sprayer settings and application of phytosanitary products to = crops.=20

The advantage in the operational contexts of precision = agriculture or precision spraying relate to two main aspects: for = agricultural=20 equipment manufacturers, knowledge of the optimum characteristics of the = spraying throws necessary to maximize the proportion of the product = deposited on=20 leaves is essential to optimize the equipment to reduce the = environmental=20 impacts and costs tied of phytosanitary products, and secondly so that = the phyto=20 pharmaceutical firms understand the adhesion mechanisms of their = products on the=20 leaves for the development of the sprays, especially of the adjuvant = type=20 (surfactant, oils, humectants).

Finally, within the EcoPhyto 2018 French program this = research=20 could help to optimize previous agronomic models and help landusers, = especially=20 winegrowers, to reduce their input. This work is actually under = investigation=20 with the BIVB¹=20 organization.

This paper describes briefly the GFD used as feature = texture=20 extraction tools, the methods of classification used and the DR methods = that=20 will be cross compared. These methods are combined with a feature = selection=20 approach to complete the comparison. Two texture datasets (one synthetic = and one=20 natural) are compared, and the most efficient combination is highlighted = and=20 discussed. Ideas for future work are included at the end of the results. =

Generalized Fourier descriptors (GFD) and methods = of=20 classification

Texture characterization using generalized Fourier = descriptors (GFD)

The main goal of texture analysis is to formalize the = texture=20 feature by mathematical parameters. Several methods have already been = proposed=20 in the literature to extract the texture features and tested in = practice. There=20 are five main families of methods to extract textural features (Jain and = Tuceryan 1993):=20 structural, statistical and spatio-frequency approaches, and methods = based on=20 form recognition and fractals. To test our protocol, however, we = preferred to=20 use a robust invariant method such as GFD because of the considerable=20 variability in orientation, scale and illumination conditions for the = different=20 textures of leaves.

The GFD are defined as follows. Let f be a = square=20 summable function on the plane. The Fourier transform is then

(1)

If (λ, θ) are the polar = coordinates of=20 point ξ we denote 3D"$$

=20 as the Fourier transform of f at = (λ, θ). Gauthier et=20 al. (Gauthier et al. 1991)=20 defined the mapping of D _ffrom =20 into 3D"$$

=20 by

(2)

where D = _f=20is the GFD feature vector, extracted as in Fig. 5=20 that describes each texture image.=20

Fig. 5 Procedure to=20 find GFD texture vectors (feature vector from the image of centered 2D = Fourier=20 transform of the texture image)

This GFD vector will be used as an input to the = supervised=20 classification method and will be reduced by DR methods. The GFD = features,=20 calculated according to Eq. 2,=20 have several properties that are useful for object recognition: they are = translation-, rotation- and reflection-invariant.

Methods of classification

Classification is a central problem in pattern = recognition (Duda=20 et al. 2001)=20 and many approaches to solve it have been proposed such as the = connectionist=20 approach (Bishop 1995)=20 or metrics based methods, k-nearest neighbours (k-nn) and=20 kernel-based methods such as support vector machines (SVM) (Vapnik = 1998).=20 In our experiments, the average performances of the dimensionality = reduction=20 methods and of one basic feature selection method applied to the GFD = features=20 have to be evaluated. In this context, we have chosen and evaluated six=20 efficient classification approaches from four families of = classification: the=20 boosting (adaboost) family (Schapire 1990)=20 using three weak classifiers, (hyperplan, hyperinterval and = hyperrectangle), the=20 hyperrectangle (polytope) method (Miteran et al. 1994),=20 the SVM method (Vapnik 1998;=20 Abe 2005)=20 and the neural network family with a multilayer perceptron (MLP) = (Rumelhart and=20 McClelland 1986).=20 To validate the classification performance and estimate the average = error for=20 each method, we performed 20 iterative experiments with a 10-fold cross=20 validation procedure (Witten and Eibe 2005).=20

Dimensionality reduction methods

The GFD provide features that have great potential in = pattern=20 recognition, but they result in very high-dimensional data that are = difficult to=20 handle and comprise redundant information. Moreover, the computational = cost of=20 elaborate data processing tasks may be prohibitive. Therefore; = dimensionality=20 reduction (DR) techniques are used to transform high-dimensional data = into a=20 meaningful representation of reduced dimensionality to improve = classification=20 performance.

Let 3D"$$ =20 be an n =D7 m data matrix, where n is the = number of=20 image examples in each texture dataset and m is the dimension of = vector=20 x _i, corresponding to the discrete computation = of 3D"$$ =20 from Eq. 2.=20 Ideally, the reduced representation has a dimensionality that = corresponds to the=20 intrinsic dimensionality of the data (Camastra and Vinciarelli 2002).=20 One of our working hypotheses is that, although the data (all texture = images)=20 are points in 3D"$$ ,=20 there is a p-dimensional manifold M =3D (y = ₁,=20 =85, y _n)^T that can suitably = approximate the=20 space spanned by the data points. The so-called intrinsic dimension (ID) = of=20 X in 3D"$$ =20 is the smallest possible value of p = (p < m)=20 for which the approximation of X by M is reasonable. In other = words, the=20 ID is defined as the number of variables that is sufficient to represent = the=20 signal. To determine the ID of our data, we used a geometric approach = that=20 estimates the equivalent to the fractal dimension (Camastra and = Vinciarelli=20 2002).=20

The DR methods can be classified according to three=20 characteristics:=20

=95	Linearity: This describes the type of=20 transformation applied to the data matrix, mapping it from =20 to .=20
=95	Scale analysis (local or = global): This=20 reflects the kind of properties the transformation preserves. In = most=20 nonlinear methods, there is a trade-off between the preservation = of local=20 topological relationships between data points or of the global = structure=20 of X.
=95	Metric (Euclidean or geodesic): = This=20 defines the distance function used to estimate whether two data = points are=20 close to each other in ,=20 and should consequently remain close in =20 after the DR transformation. It is important to note that we = conserved the=20 metrics of the methods generally used in the literature, but there = are=20 also other metrics in Euclidean space such as Minkowski or = Chebyshev=20 distance (Deza and Deza 2006).=20

Based on these criteria, we retained 13 methods: 4 = linear and=20 9 nonlinear, see Table 1.=20 To complete this review of DR methods, we compared them with one = classical=20 feature selection method to determine which approaches are the most = relevant.

Table 1 The 13=20 dimensionality reduction methods

	Global	Local
Linear	Principal component analysis
Linear discriminant analysis
Second-order blind identification
Projection pursuit
Nonlinear	Sammon mapping	Local linear embedding
Isomap	Laplacian eigenmaps
Kernel isomap	Curvilinear component analysis
Kernel-PCA	Curvilinear distance analysi s =
Kernel discriminant analysis

Metric: Euclidean or Geodesic =

s=20

Linear methods

Principal components analysis

Principal components analysis (PCA) is the best-known = DR method.=20 It finds a linear transformation that retains the subspace with the = largest=20 variance. It can be shown that the reconstruction error, J=20 _PCA, is minimized for the eigenvectors, u = _i=20, of the covariance matrix of X. It is interesting to note = that PCA=20 is close to the classical multidimensional scaling (MDS) introduce by = Shepard=20 (1962)=20 and Kruskal (1964)=20 where Euclidean distance is used as described in Fodor (2002).=20 This relation between MDS and PCA is important because MDS underpins = other=20 nonlinear DR methods such as ISOMAP (Tenenbaum et al. 2000).=20 Principal components analysis is a linear, global and Euclidean = technique.=20

Second-order blind identification (SOBI)

Second-order blind identification (Belouchrani et = al. 1997)=20 relies on stationary second-order statistics that are based on a joint=20 diagonalization of a set of covariance matrices. The set X is = considered=20 as a mixed set of independent signals X_i(t), (t = correspond=20 to the time) and the p features of the destination space we are = searching=20 are assimilated to a fixed number of original sources S_{i =}(t)=20 corresponding here to the intrinsic dimensionality. Each X_{i =}(t) is assumed to be a linear mixture of n unknown = components=20 (sources) S_i(t), from the unknown =91mixing=92 = matrix,=20 A.

(3)

Second-order blind identification is also a linear, = global and=20 Euclidean method.

Projection pursuit (PP)

This method of Friedman and Tukey (1974),=20 linked to the independent component analysis method (ICA) (Comon = 1994),=20 is based on the resolution of a cost function, which finds its optimum = by a=20 gradient descent method. For our experiment, we used the fast-ICA = algorithm=20 (Hyv=C4arinen 1999)=20 that allows new components to be estimated one by one by deflation. The=20 symmetric decorrelation of the vectors at each iteration was replaced by = a=20 Gram-Schmidt orthogonalization procedure. When p components,=20 w₁,=85,w_phave been estimated, the = algorithm=20 determines w_p+1. After each iteration, the = projections 3D"$$

=20 of the p previously estimated vectors are subtracted from w_=20
p+1. Then, w_p+1 is standardized = according to=20 Eq. 4=20

(4)

It is important to note that there is a fundamental = difference=20 between PP and ICA. For the ICA approach, the problem is solved globally = and all=20 components are evaluated at the same time. Conversely, in the PP method = each=20 component is evaluated independently in an iterative procedure. For each = iteration, the algorithm finds a new component and readjusts data in = such a way=20 as to hide the data structure in this new component. Finally, the = difference=20 between these two approaches is based on the iterative =91deflation=92 = approach of=20 PP and the =91global=92 resolution of ICA. The algorithm stops when = p=20 components according to the ID number have been estimated. The = projection=20 pursuit method is also linear, global and Euclidean.

Nonlinear methods: global approaches

Sammon=92s mapping (Sammon)

Sammon=92s mapping (Sammon 1969)=20 is a DR method that tries to preserve the neighbourhood topology of data = by=20 preserving distances between points. To evaluate the preservation = topology, we=20 use the following stress function minimized by a gradient descent

(5)

where =20 and 3D"$$

=20 are the distances between the ith and jth points in 3D"$$

and=20

.=20 This function, allows the distances in the projection space to be = conserved=20 compared to the initial space. Sammon=92s mapping is a nonlinear, global = and=20 Euclidean method.

Isometric feature mapping (Isomap)

Isomap (Tenenbaum et al. 2000)=20 estimates the geodesic distance between data points in a manifold using = the=20 shortest path in the nearest neighbours=92 graph. It then searches for a = low-dimensional representation that approximates those geodesic = distances in the=20 least squares sense. The 3 steps are:=20

=95	Form D _m(X), = the=20 all-pairs distance matrix.
=95	Create a graph from X (k nearest = neighbours). For a given point X _iin ,=20 a neighbour is either one of the k nearest data points from = X _ior one for which .=20 Form the all-pairs geodesic distance matrix, Δ_m=20(X), using Dijkstra=92s shortest path algorithm. =
=95	Use classical MDS to find the transformation = from to=20 that=20 minimizes

(6)

Isomap is nonlinear, global and geodesic.

Kernel methods (K-PCA, K-Isomap, KDA)

Recently, several well-known algorithms for the = reduction of=20 dimensionality of manifolds have been developed to take the kernel = machine=20 approach (Ham et al. 2004;=20 Shawe-Taylor and Cristianini 2004).=20 We retain here the three that are known best: kernel-PCA (K-PCA) = (Sch=F6lkopf et=20 al. 1998),=20 kernel isomap (K-Isomap) (Choi and Choi 2007)=20 and kernel discriminant analysis (KDA) (Liang et al. 2006).=20 Non-linearity is introduced by mapping the data from the input space 3D"$$

=20 to a feature space 3D"$$

.=20 The projection methods (PCA, isomap or discriminant analysis) are then = applied=20 to this new feature space, expressed by a kernel, K, in terms of = a Mercer=20 kernel function (Sch=F6lkopf et al. 1999).=20 For our experiment, we used the following classical Gaussian kernel such = as for=20 the SVM classification method:

(7)

All kernel methods are nonlinear and global, but K-PCA = and KDA=20 use the Euclidean metric and K-isomap uses the geodesic = one.

Nonlinear methods: local approaches

Local linear embedding (LLE)

The LLE algorithm (Roweis and Saul 2000)=20 estimates the local coordinates of each data point on the basis of its = nearest=20 neighbours, then searches for a low-dimensional coordinate system. The 3 = steps=20 are:=20

(1)	Find the neighbourhood graph (see steps 1 and = 2 of=20 isomap).
(2)	Compute the weights, W _{ij =},=20 that reconstruct X _ibest from its = neighbours,=20 and which minimize the reconstruction error, ,=20 where ,=20
(3)	Compute vectors y _{i =}in =20 reconstructed by the weights W _ij. Solve = for all=20 y _isimultaneously:=20

(8)

This algorithm finds the local affine structure of the = data=20 manifold and the best projection of data points in .=20 The LLE is nonlinear, local and Euclidean.

Laplacian eigenmaps (LE)

The Laplacian eigenmaps method finds a = low-dimensional data=20 representation by preserving local properties of the manifold (Belkin = and Niyogi=20 2003).=20 The three steps of the algorithm are:=20

=95	Create the non-oriented symmetric = neighbourhood=20 graph.
=95	Associate a positive weight W = _ij=20to each link of the graph (constant weights (W = _ij=20 =3D 1/k), or exponentially decreasing ()).=20
=95	Obtain the final coordinates y = _i=20of the points in =20 by minimizing the cost function: =

(9)

where D is the = diagonal=20 matrix 3D"$$

.=20 The LE is a nonlinear, local, Euclidean method.

Curvilinear components analysis (CCA) and = curvilinear=20 distances analysis (CDA)

The CCA is an evolution of nonlinear = multidimensional scaling=20 (MDS) and Sammon=92s mapping algorithms (Demartines and H=E9rault = 1997).=20 Instead of the optimization of a reconstruction error, CCA aims to = preserve the=20 distance matrix while projecting data onto a lower dimensional manifold. = Let=20 D _m(X) be the n=20 ² =D7 n ² matrix of distances = between pairs=20 of points in X:

After DR transformation to 3D"$$

,=20 we also have:

The CCA aims to find the best suitable = transformation by=20 minimizing

(10)

where F is a = decreasing, positive=20 weighting function that gives more importance to the preservation of = small=20 distances. The CCA is nonlinear, local and Euclidean.

The CDA is a refinement of CCA (Lee et al. 2004)=20 by minimizing:

(11)

where =20 measures the geodesic distance between x _iand = x=20 _j, as in Isomap. The CDA is nonlinear, local and = geodesic.=20

Although some of the methods are neither completely = global nor=20 local, to simplify their description we have classified them in the way = usually=20 encountered in the literature.

Feature selection method

Feature selection with an exhaustive search is = impractical=20 because of the large number of possible feature subsets. To select the 5 = best=20 features identified by intrinsic dimensionality estimation, we used the=20 sequential forward selection method (SFS) (Kittler 1978)=20 which performs better when the optimal subset has a small number of = features.=20 The criterion function for selection was the average correct rate of=20 classification over all classes, obtained by quadratic discriminant = analysis=20 (QDA) on all observations. The QDA approach was chosen because it does = not=20 depend on features other than the observations and its aim is a measure = of=20 efficiency of the feature subset and not the optimal rate of = classification. At=20 the end of the process, the 5 best features were selected.

Texture image databases

To test our texture classification protocol, the = experiments=20 included images from two different sources:=20

=95

The main texture grey level images = (Fig. 6)=20 used in this study were provided for our agronomic application. = These=20 images were acquired with a SEM microscope and represent different = kinds=20 of leaf surfaces from six plant species. For each class of leaf = texture=20 150=96200 images were acquired. Each image is at a scale of = 100 μm,=20 with a resolution of 512 =D7 512 pixels; this scale was = adapted to=20 our biological application. There were 1242 texture images in six = classes.=20

Fig. 6 The six=20 classes of leaf texture images: a tomato, b rye = grass=20 (Lolium perenne), c mature wheat, d pea, = e=20 young wheat and f horsetail

=95

The well known Brodatz texture dataset = (Brodatz 1966)=20 cited in more than 500 relevant papers over the past 20 years = (Fig. 7).=20

Fig. 7 Samples=20 of the 32 Brodatz textures used in the experiments

The Brodatz dataset comprises 32 different textures. = The=20 original grey level images have a resolution of 256 =D7 256 = pixels, but=20 here they were cropped to 16 disjointed 64 =D7 64 samples. To = evaluate=20 scale and rotation invariance, three additional samples were generated = per=20 original sample (90=B0 rotation, 64 =D7 64 scaling, = combinations of=20 rotation and scaling). Finally, the set contained almost 2048 images = with 64=20 samples per texture.

Results and discussion

From the two datasets described above, we obtained=20 n =3D 2048 vectors in m =3D 32 = dimensions by GFD=20 extraction from the Brodatz texture database and = n =3D 1034=20 vectors in m =3D 254 dimensions from plant leaf texture = database.=20 These datasets represent 32 and 6, respectively, classes of texture = surfaces.=20 According to the geometric approach proposed by Camastra and Vinciarelli = (2002),=20 we estimated and fixed the intrinsic dimensionality of our two datasets = as being=20 p =3D 5.

The classification performance and average error = rate for each=20 classification method were compared. The classification error rate = corresponds=20 to the percentage of misclassification of the signals of test samples in = the=20 cross-validation procedure. For the SVM, we used the classic Gaussian = kernel for=20 which we determined the optimum. For the Brodatz texture dataset = (Table 2),=20 the best results on classification error using the original feature = space (not=20 reduced) were obtained using SVM (e =3D 2.65%).

Table 2 Classification results on the = Brodatz=20 dataset (% error rate)

3DMediaObjects/11119_2010_9208_Tab2_HTML.gif=20

The best combination is in bold and is also = highlighted other=20 combinations in bold correspond to results whose value is better than = those=20 obtained with the original data features

All the other methods gave poorer results (from 12.2 = to=20 22.5%). Their performance is generally improved by DR: the optimum error = is=20 obtained by combining KDA and SVM (e =3D 0.8%, i.e. the = error is=20 divided by a factor of 3 compared to the classification without RD = methods and=20 original high-dimensional features). The combination of LE with SVM = gives=20 similar results. One can note that the use of kernel methods in = combination with=20 DR generally improves performance compared to the standalone DR approach = (isomap=20 vs. K-isomap, PCA vs. K-PCA). In the group of fast methods of decision, = the best=20 result is obtained using Hyperrectangle combined with KDA. These results = are=20 generally confirmed by the experiments with the plant leaf dataset=20 (Table 3),=20 although the dimension of the original space is significantly higher = than in the=20 previous case (254 vs. 32) and the number of classes is fewer (6 vs. = 32). In=20 this case, the gain factor is 3 (comparing SVM classification with = original high=20 dimensional features, and the combination of SVM/KDA).

Table 3 Classification results on the = plant leaf=20 dataset (% error rate)

3DMediaObjects/11119_2010_9208_Tab3_HTML.gif=20

The best combination is in bold and is also = highlighted; other=20 combinations in bold correspond to results whose value is better than = those=20 obtained with the original data features

The combination of GFD and KDA appears to provide = sufficient=20 information to characterize plant leaf roughness. In particular, this = solution=20 to texture classification enables us to separate our six types of = agronomic=20 image into six different clusters as shown in Fig. 8.=20 This is further validated by the small difference detected between two = wheat=20 clusters that differ from one another in terms of growth stage only. In = fact, it=20 is important to note that the difference between young and old wheat is=20 characterized by the loss of water that transforms the structure of the = leaf=20 surface. This transformation results in slightly different features. = This result=20 allows us to consider future applications in order to follow the = evolution of=20 wheat maturity.=20

Fig. 8 3D Projection=20 of the third component of Kernel discriminant analysis for the plant = leaf=20 dataset (each axes corresponds to the reduced coordinates of the = original=20 features by KDA)

The results are acceptable and the proposed method can = be used=20 as a robust tool for roughness analysis. Nevertheless, the experiments = were done=20 on small samples for the agronomic dataset, although the results = obtained on the=20 Brodatz dataset are pertinent. To improve on these results, we will = increase the=20 number of leaf texture surfaces with different leaf species (vines and = other=20 crops) at different growth stages to follow the evolution of the crops. =

From the image processing viewpoint, comparisons are = currently=20 done with other texture features such as spatio-frequential and = statistical=20 parameters (Gabor filters, co-occurence matrices and so on) and = combinations of=20 colour-texture analysis that provide high-dimensional data by the = concatenation=20 of the textural features and the spectral information as in Cointault et = al.=20 (2008).=20

Finally, the combination of KDA and SVM could be used = for the=20 detection of other agronomic properties such as hydrophobic or = hydrophilic=20 surfaces, or monocotyledon and or dicotyledon recognition. Artificial = leaf=20 textures could be modeled to control the hydrophobicity of the surface = for=20 laboratory experiments so that sprays could be developed or adapted = accordingly=20 in future research. For this research, comparisons with spectral tools = will be=20 necessary.

For the same crop we are now able to distinguish = between=20 different growth stages (e.g. wheat, Fig. 8)=20 in order to optimize the inputs, but also to detect diseases earlier. A = disease=20 will modify the structure of the leaf and its texture and these can be=20 identified by our types of analysis.

Finally, we are currently developing some research in = precision=20 viticulture, and the results and methods presented in this paper will = help us to=20 model the evolution of vine leaf roughness. This will be combined with = the use=20 of optical approaches, such as particle tracking velocimetry sizing = (PTVS) to=20 study the behaviour of the droplets on the leaves. This type of research = is of=20 interest to the sprayer manufacturers and also the phyto pharmaceutical = firms.=20

Conclusion

A better understanding of the droplet adhesion = mechanisms on=20 leaves is an essential step to evaluate the amount of phytosanitary = product=20 absorbed by the leaf and the amount of product lost in the environment. = It is a=20 global objective to reduce the effect of sprays in the context of = precision=20 spraying. Discrimination and modeling of leaf surface roughness is a = necessary=20 stage of this. Its evaluation can be done by image or signal processing = tools.=20

Our research has shown that the SVM classifier = outperforms all=20 other classification methods using the original feature space. Moreover, = we have=20 demonstrated experimentally that some DR methods can improve the final=20 classification performance further. The best DR method is KDA combined = with SVM=20 classifiers with an error of classification for the plant leaf dataset = of 0.4%.=20

This study has proved that image processing provides = an accurate=20 way of determining plant leaf roughness, one of the most important = properties=20 for understanding phytosanitary product losses during spraying.

The scientific spin-off can be seen in at least two = different=20 but complementary ways: a better qualitative and quantitative = understanding of=20 fluid spraying on natural surfaces and a better understanding of the=20 microstructure effect on the impact and adhesion phenomenon of droplets = on=20 leaves.

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Footnotes

¹	Bureau Interprofessionnel des Vins de Bourgogne=20 (Interprofessional Bureau of the Burgundy=20 Wines).