Precision Agriculture
An International Journal on Advances in
Precision Agriculture

© Springer Science+Business Media, LLC 2010

10.1007/s11119-010-9208-z

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

L. Journaux1 ,
J.-C. Simon1, M. F. Destain2,
F. Cointault3, J. Miteran4 and
A. Piron2

(1)

AgroSupDijon, Engineering Sciences, 26 Bd Dr
Petitjean, BP 87999, 21079 Dijon Cedex,
France

(2)

FUSAGX, Unité de Mécanique et Construction, 2
passage des déportés, 5030 Gembloux,
Belgium

(3)

AgroSupDijon, Agroengineering Sciences, 26 Bd
Dr Petitjean, BP 87999, 21079 Dijon Cedex,
France

(4)

Université de Bourgogne, Le2i, Avenue Alain
Savary, BP 47870, 21078 Dijon Cedex,
France

L. Journaux
Email:
[email-masked]

Published online:
14 December 2010

Abstract

In the context of plant leaf roughness analysis for precision
spraying, this study explores the capability and the performance of some
combinations of pattern recognition and computer vision techniques to extract
the roughness feature. The techniques merge feature extraction, linear and
nonlinear dimensionality reduction techniques, and several kinds of methods of
classification. The performance of the methods is evaluated and compared in
terms of the error of classification. The results for the characterization of
leaf roughness by generalized Fourier descriptors for feature extraction,
kernel-based methods such as support vector machines for classification and
kernel discriminant analysis for dimensionality reduction were encouraging.
These results pave the way to a better understanding of the adhesion mechanisms
of droplets on leaves that will help to reduce and improve the application of
phytosanitary products and lead to possible modifications of sprayer
configurations.

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

Introduction

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

Fig. 1 Representation of the ‘lotus effect’
(photograph by William Thielicke, http://wthielicke.gmxhome.de/bionik/indexuk.htm)

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

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

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

Fig. 3 Illustration
of the Hughes’ phenomenon

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

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

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

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

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

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

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

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

Generalized Fourier descriptors (GFD) and methods of
classification

Texture characterization using generalized Fourier
descriptors (GFD)

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

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

(1)

If (λ, θ) are the polar coordinates of
point ξ we denote
as the Fourier transform of f at (λ, θ). Gauthier et
al. (Gauthier et al. 1991)
defined the mapping of D f from
into
by

(2)

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

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

This GFD vector will be used as an input to the supervised
classification method and will be reduced by DR methods. The GFD features,
calculated according to Eq. 2,
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
et al. 2001)
and many approaches to solve it have been proposed such as the connectionist
approach (Bishop 1995)
or metrics based methods, k-nearest neighbours (k-nn) and
kernel-based methods such as support vector machines (SVM) (Vapnik 1998).
In our experiments, the average performances of the dimensionality reduction
methods and of one basic feature selection method applied to the GFD features
have to be evaluated. In this context, we have chosen and evaluated six
efficient classification approaches from four families of classification: the
boosting (adaboost) family (Schapire 1990)
using three weak classifiers, (hyperplan, hyperinterval and hyperrectangle), the
hyperrectangle (polytope) method (Miteran et al. 1994),
the SVM method (Vapnik 1998;
Abe 2005)
and the neural network family with a multilayer perceptron (MLP) (Rumelhart and
McClelland 1986).
To validate the classification performance and estimate the average error for
each method, we performed 20 iterative experiments with a 10-fold cross
validation procedure (Witten and Eibe 2005).

Dimensionality reduction methods

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

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

The DR methods can be classified according to three
characteristics:

•

Linearity: This describes the type of
transformation applied to the data matrix, mapping it from
to .

•

Scale analysis (local or global): This
reflects the kind of properties the transformation preserves. In most
nonlinear methods, there is a trade-off between the preservation of local
topological relationships between data points or of the global structure
of X.

•

Metric (Euclidean or geodesic): This
defines the distance function used to estimate whether two data points are
close to each other in ,
and should consequently remain close in
after the DR transformation. It is important to note that we conserved the
metrics of the methods generally used in the literature, but there are
also other metrics in Euclidean space such as Minkowski or Chebyshev
distance (Deza and Deza 2006).

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

Table 1 The 13
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

Linear methods

Principal components analysis

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

Second-order blind identification (SOBI)

Second-order blind identification (Belouchrani et al. 1997)
relies on stationary second-order statistics that are based on a joint
diagonalization of a set of covariance matrices. The set X is considered
as a mixed set of independent signals X i (t), (t correspond
to the time) and the p features of the destination space we are searching
are assimilated to a fixed number of original sources S i (t)
corresponding here to the intrinsic dimensionality. Each X i
(t) is assumed to be a linear mixture of n unknown components
(sources) S i (t), from the unknown ‘mixing’ matrix,
A.

(3)

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

Projection pursuit (PP)

This method of Friedman and Tukey (1974),
linked to the independent component analysis method (ICA) (Comon 1994),
is based on the resolution of a cost function, which finds its optimum by a
gradient descent method. For our experiment, we used the fast-ICA algorithm
(HyvÄarinen 1999)
that allows new components to be estimated one by one by deflation. The
symmetric decorrelation of the vectors at each iteration was replaced by a
Gram-Schmidt orthogonalization procedure. When p components,
w1,…,w p have been estimated, the algorithm
determines w p+1. After each iteration, the projections
of the p previously estimated vectors are subtracted from w
p+1. Then, w p+1 is standardized according to
Eq. 4

(4)

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

Nonlinear methods: global approaches

Sammon’s mapping (Sammon)

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

(5)

where
and
are the distances between the ith and jth points in and
.
This function, allows the distances in the projection space to be conserved
compared to the initial space. Sammon’s mapping is a nonlinear, global and
Euclidean method.

Isometric feature mapping (Isomap)

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

•

Form D m (X), the
all-pairs distance matrix.

•

Create a graph from X (k nearest
neighbours). For a given point X i in ,
a neighbour is either one of the k nearest data points from
X i or one for which .
Form the all-pairs geodesic distance matrix, Δ m
(X), using Dijkstra’s shortest path algorithm.

•

Use classical MDS to find the transformation from to
that
minimizes

(6)

Isomap is nonlinear, global and geodesic.

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

Recently, several well-known algorithms for the reduction of
dimensionality of manifolds have been developed to take the kernel machine
approach (Ham et al. 2004;
Shawe-Taylor and Cristianini 2004).
We retain here the three that are known best: kernel-PCA (K-PCA) (Schölkopf et
al. 1998),
kernel isomap (K-Isomap) (Choi and Choi 2007)
and kernel discriminant analysis (KDA) (Liang et al. 2006).
Non-linearity is introduced by mapping the data from the input space
to a feature space .
The projection methods (PCA, isomap or discriminant analysis) are then applied
to this new feature space, expressed by a kernel, K, in terms of a Mercer
kernel function (Schölkopf et al. 1999).
For our experiment, we used the following classical Gaussian kernel such as for
the SVM classification method:

(7)

All kernel methods are nonlinear and global, but K-PCA and KDA
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)
estimates the local coordinates of each data point on the basis of its nearest
neighbours, then searches for a low-dimensional coordinate system. The 3 steps
are:

(1)

Find the neighbourhood graph (see steps 1 and 2 of
isomap).

(2)

Compute the weights, W ij ,
that reconstruct X i best from its neighbours,
and which minimize the reconstruction error, ,
where ,

(3)

Compute vectors y i in
reconstructed by the weights W ij . Solve for all
y i simultaneously:

(8)

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

Laplacian eigenmaps (LE)

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

•

Create the non-oriented symmetric neighbourhood
graph.

•

Associate a positive weight W ij
to each link of the graph (constant weights (W ij
= 1/k), or exponentially decreasing ()).

•

Obtain the final coordinates y i
of the points in
by minimizing the cost function:

(9)

where D is the diagonal
matrix .
The LE is a nonlinear, local, Euclidean method.

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

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

After DR transformation to ,
we also have:

The CCA aims to find the best suitable transformation by
minimizing

(10)

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

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

(11)

where
measures the geodesic distance between x i and x
j , as in Isomap. The CDA is nonlinear, local and geodesic.

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

Feature selection method

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

Texture image databases

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

•

The main texture grey level images (Fig. 6)
used in this study were provided for our agronomic application. These
images were acquired with a SEM microscope and represent different kinds
of leaf surfaces from six plant species. For each class of leaf texture
150–200 images were acquired. Each image is at a scale of 100 μm,
with a resolution of 512 × 512 pixels; this scale was adapted to
our biological application. There were 1242 texture images in six classes.

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

•

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

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

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

Results and discussion

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Conclusion

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

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

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

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

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Footnotes

1

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