Image Anal Stereol 2018;37:119-126 doi:10.5566/ias.1821
Original Research Paper
PLANT SPECIE CLASSIFICATION USING SINUOSITY COEFFICIENTS
OF LEAVES
JULES R. KALAB, AND SERESTINA VIRIRI
School of Mathematics, Statistics and Computer Science
University of KwaZulu-Natal, Durban, 4000, South Africa
e-mail: raymondkala1@gmail.com; viriris@ukzn.ac.za
(Received August 11, 2017; revised March 12, 2018; accepted March 12, 2018)
ABSTRACT
Forests are the lungs of our planet. Conserving the plants may require the development of an automated
system that will identify plants using leaf features such as shape, color, and texture. In this paper, a leaf shape
descriptor based on sinuosity coefficients is proposed. The sinuosity coefficients are defined using the sinuosity
measure, which is a measure expressing the degree of meandering of a curve. The initial empirical experiments
performed on the LeafSnap dataset on the usage of four sinuosity coefficients to characterize the leaf images
using the Radial Basis Function Neural Network (RBF) and Multilayer Perceptron (MLP) classifiers achieved
accurate classification rates of 88% and 65%, respectively. The proposed feature extraction technique is further
enhanced through the addition of leaf geometrical features, and the accurate classification rates of 93% and
82% were achieved using RBF and MLP, respectively. The overall results achieved showed that the proposed
feature extraction technique based on the sinuosity coefficients of leaves, complemented with geometrical
features improve the accuracy rate of plant classification using leaf recognition.
Keywords: leaf recognition, plant classification, sinuosity coefficients, sinuosity measure.
INTRODUCTION
Plants are the key elements of life on earth: plants
are source of food for animals, insects, and are source
of energy, and they also help in the process of climate
control. The leaves are one of the most visible and vital
parts of a plant. They have valuable information about
plant environment and can help identify the species to
which a plant belongs to (von Linné, 1788). Botanists
use information from leaves such as the tooth pattern
on the leaf margin to classify plants (Partington, 1837).
The sinuosity of a given curve represents the
degree of meandering of that curve. It has been
extensively used in the domain of medical science for
the analysis of the meandering of a spinal column
(Tanguy and Peuchot, 2002) and in hydrography to
evaluate the degree of meandering of a river (Langbein
and Leopold, 1966). This article is an extension of
a paper presented by Kala et al. (2016), where the
sinuosity coefficients were used to characterize leaf
shapes. In this article, a leaf image is divided into four
sections and the sinuosity coefficients are computed
from each section to construct a model for leaf
classification.
To demonstrate the accuracy of the proposed
model, the LeafSnap data set of more than 1840 leaf
images of 184 species is used. The initial experiment
is used to evaluate the efficacy of the sinuosity
coefficients to characterize a leaf shape. The second
experiment is designed to assess if combining the
sinuosity coefficients to other geometrical features
such as rectangularity, circularity, sphericity and
aspect ratio will improve the classification rate
obtained in the first experiment.
RELATED WORKS
Studies on plant classification using leaves have
been carried out by several researchers with promising
results. In the following subsections, some related
works on plant classification using leaf images and the
use of the sinuosity measure are presented.
PLANT CLASSIFICATION USING
LEAVES
Kalyoncu and Toygar (2015) proposed a method
for plant recognition using leaf images based on the
combination of new and well know feature extraction
techniques and classification algorithms. The proposed
method is based on the Linear Discriminant Classifier
to classify extracted features. The proposed method
achieved a classification rate of 95% on the Flavia
dataset and 70% on the Leafsnap dataset with the Local
Discriminant Classifier (LDC) as a classifier.
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Lei et al. (2014), derived two orthogonal locally
discriminant spline embedding techniques (OLDSE-
I and OLDSE-II) from a Local Spline embedding
(LSE) and a Maximum Margin Criterion (MMC).
The plant leaves are mapped into a leaf subspace
in order to identify the essential leaf manifold. The
proposed approach was applied to a subset of the ICL
leaf image database containing 480 leaf images of 16
different species. It achieved an average classification
rate of 95%. The proposed method was also applied
to the Swedish leaf database and achieved an average
classification rate of 90%.
Cerutti et al. (2014) presented a method for the
analysis of the spatial properties of teeth on the leaf
margin using structured representation. They proposed
a sequential representation of leaf margins where the
teeth are viewed as symbol of a multivariate real
value alphabet. They applied the proposed technique to
design a mobile application for tree identification. The
proposed method achieved an average classification
rate of 90% on leaf images from the Pl@ntLeaves
database.
Yanikoglu et al. (2014) developed a system for
plant identification using leaf images. The proposed
method is based on the combination of shape, color,
and texture features to overcome the difficulties
encountered during the identification process. The
proposed system achieved a classification rate of 81%
on Image-CLEF’12 leaf image dataset with Support
Vector Machine as a classifier.
Wilf et al. (2016) combined shape features to
venation features to construct a system for plant
classification using leaf images. The proposed method
requires a chemical pre-treatment of the leaf to
magnify the venation on the leaf before taking
the image. The proposed method cannot be easily
automated because of the chemical process needed to
expose the venation.
Fu et al. (2004) proposed an ontology based
leaf classification system using leaf shape combined
with leaf venation. The proposed system contained
an algorithm for shape analysis and a neural network
classifier to organize the leaves according to their tooth
pattern. There was a 94% accuracy rate in recognition
of tooth patterns of a set of three plant species.
APPLICATION OF SINUOSITY
MEASURE
The sinuosity measure has been applied in many
fields of science, such as Geography, Biology and
Medical Science as a parameter to explain other natural
phenomena such as the meandering of a river, etc.
In Langbein and Leopold (1966), the sinuosity
measure was used to evaluate the degree of meandering
of a river. It was also explained that the meandering
in the case of a river is the result of an erosion
process tending toward the most stable form in which
the variability of certain essential properties such as
velocity and depth are minimized.
Jaekel and Wake (2007) presented an application
of the sinuosity measure for the characterization of
the webbing on a salamander foot to demonstrate the
morphological changes performed on the animal foot
to adapt to a given surface.
Tanguy and Peuchot (2002) developed a method
for the analysis of spine meandering for the early
detection of spine deformation. Furthermore, Lazarus
and Constantine (2013) used the sinuosity measure to
demonstrate that there were rivers on Mars surface by
analyzing the planet surface to detect deep meandering
shapes.
MATERIALS AND METHOD
The proposed model for plant classification using
leaf recognition is depicted in Fig. 1. The stages of
the model are mainly preprocessing, feature extraction
and classification. The output of the model is the plant
specie or class to which the input leaf image belongs
to.
Thresholding phase on this process is the simplest
segmentation technique used to create a binary
representation of an input image, using Eq. 1.
f (x,y) =
{
0 if f (x,y)> T ,
255 if f (x,y)≤ T .
(1)
The difficulty with using the thresholding method is
determining the threshold (T ) which depends on the
input image.
For the edges detection purpose, Sobel operator is
used, because it can detect edges and their orientation
(Gonzalez and Woods, 1992). A Sobel operator is
obtained from the Prewit operator by increasing
the weight on the central coefficients. Sobel edges
detection is implemented using the masks in Fig. 2.
DATABASE SAMPLING
The sampling method used in our experiment is
based on the formula extracted from (Naing et al.,
2006), to create a sample from a finite population as
defined in Eq. 2,
n′ =
NZ2P(1−P)
d2(N−1)+Z2P(1−P)
, (2)
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Image Anal Stereol 2018;37:119-126
Fig. 1. Proposed model for plant classification
where n′ is the sample size with the finite population;
N is the population size; Z is the Z statistic for a level
of confidence which is usually equal to 1.96; P is the
expect proportion; d is the precision equal to 0.05. For
the LeafSnap dataset the minimum sample obtained
using the formula is equal to 336 leaf images.
DATASET
This study was conducted using LeafSnap created
by Kumar et al. (2012), which is a leaf image database
that contains 23147 Lab images and 7719 Field images
of 185 tree species. For all the experiments 1800
leaves of 100 species were randomly selected from
the LeafSnap database, using the sampling approach
defined in Eq. 2 by considering only the field leaf
images with uniform background to avoid additional
computation cost. Fig. 3 shows some of the randomly
selected leaf images.
IMAGE PREPROCESSING
Let M be a leaf color image, the features for
the characterization of M will be extracted from the
image greyscale. Let I be the binary representation of
the greyscale components of M. Considering a set of
boundary points (xi,yi)i=1,...,n of the binary image. The
following elements are used for the construction of the
Minimum Bounding Rectangle (MBR) in (Kala et al.,
2014; Chaudhuri and Samal, 2007) will be considered:
Fig. 2. 3×3 Sobel masks.
Fig. 3. Sample of the randomly selected leaf images
from LeafSnap
Determination of the boundary centroid. The
centroid, (x̄, ȳ), is the average of the coordinates of the
boundary points, defined as:
(x̄, ȳ) =
(
1
n
n
∑
i=1
xi,
1
n
n
∑
i=1
yi
)
. (3)
Determination of the image orientation and the
image principal axes. The least square method applied
to the coordinates of the boundary points will be used
to determine the orientation of the image shape and
the main axis dividing the object shape into 4 parts.
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The formula given in Eq. 4 is used to obtain the object
orientation, θ (Chaudhuri and Samal, 2007; Kala et al.,
2014).
tan2θ =
2
n
∑
i=1
(xi− x̄)(yi− ȳ)
n
∑
i=1
[(xi− x̄)2− (yi− ȳ)2]
. (4)
This formula is obtained by using the Eq. 5 of the line
passing through the centroid with the angle θ ,
x tanθ − y+ ȳ− x̄ tanθ = 0 , (5)
and the perpendicular distance from that line to an edge
point which is defined as:
pi = (xi− x̄)sinθ − (yi− ȳ)cosθ . (6)
The value of the angle θ defined in Eq. 4 is computed
by minimizing P defined in Eq. 7 with respect to θ
(∂P/∂θ = 0).
P =
n
∑
i=1
[(xi− x̄)sinθ − (yi− ȳ)cosθ ]2. (7)
Sinuosity measure
Let (xi,yi), i = 1,2, ...,n, the coordinates of points
composing the curve l. If l is a continuously derivable
curve having at least one inflexion point, then the
sinuosity of l is equal to the ratio between the length
of l and the length of the straight line joining the two
end points A(x0,y0) and B(xn,yn) of l. The sinuosity
measure of the curve l is expressed by the following
equation:
Sl =
n
∑
i=1
√
(xi− xi−1)2 +(yi− yi−1)2√
(xn− x0)2 +(yn− y0)2
. (8)
The values generated by Eq. 8 are from 1 (for a straight
line) to infinity (closed loop where the shortest path
length is zero) or for an infinitely long curve (Lazarus
and Constantine, 2013). Lets consider a curve formed
by two inverted semicircles located in the same plane.
The sinuosity measure of this curve is equal to: S =
π
2 ≈ 1.5708. In order to evaluate the sinuosity measure
of a curve C, one should make sure that C is continuous
between its two ends. Generally the sinuosity measure
is evaluated in dimension two but it is also valid
in dimension three (Tanguy and Peuchot, 2002). The
basic classification of the sinuosity is either Strong:
1 S or Weak: S ≈ 1). This basic classification is the
point of interest of this paper because the sinuosity
measure will provide the information needed for the
classification of the leaf edge into two groups (smooth
leaf=“Weak” edge and jagged leaf=“Strong” edge).
Sinuosity coefficients
The sinuosity measure of a complete leaf boundary
is infinite because leaf shape is a close contour. In
order to apply the sinuosity measure to a leaf contour,
a leaf shape is divided into four or more different parts
as shown in Fig. 4. In order to obtain the leaf shape
sinuosity coefficients, the sinuosity measure of each of
the following curves (UV,UH), (UV,LH), (LV,UH)
and (LV,LH) (UV : upper vertical point, UH: upper
horizontal point, LV : Lower Vertical point and LH:
Lower horizontal point) was evaluated using Eq. 8.
The sinuosity coefficients of a leaf shape is a vector of
sorted values of the sinuosity measure of each curves
composing the leaf shape. Fig. 5 shows some leaves
with their associated sinuosity coefficients.
Fig. 4. Leaf shape information: LH: Lower Horizontal
point, UH: Upper Horizontal point, UV: Upper
Vertical point, LV: Lower Vertical point, d:distance
between UH and LV.
GEOMETRIC FEATURES
The rectangularity (R) represents the ratio between
the leaf area (Alea f ) and the area of the minimum
bounding rectangle. It evaluate how the leaf shape is
close to a rectangle shape,
R =
Alea f
Dmax×Dmin
. (9)
The aspect ratio (A) is the ratio between
the maximum length(Dmax) and the minimum
length(Dmin) of the minimum bounding rectangle,
A =
Dmax
Dmin
. (10)
The sphericity (S) is expressed by the following
equation:
S =
ri
rc
, (11)
where:
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Image Anal Stereol 2018;37:119-126
Fig. 5. Sinuosity coefficients of four leaf shapes: the sinuosity coefficients of the curves (UV;UH), (UV;LH),
(LV;UH) and (LV;LH) are listed below each leaf image.
ri represents the radius of the incircle of the leaf,
rc the radius of the circumcircle of the leaf.
The ratio between the length of the main inertia
axis and the minor inertia axis of the leaf, determines
the accent of the leaf. It evaluates how much an iconic
section deviates from being circular,
E =
EA
EB
. (12)
The circularity (C) is defined by all the contour
points of the leaf image,
C =
µR
σR
, (13)
where
µR =
1
N
N−1
∑
i=0
||(xi,yi)− (x̄, ȳ)|| ,
and
σR =
1
N
N−1
∑
i=0
(||(xi,yi)− (x̄, ȳ)||−µR)2 .
CLASSIFIERS
In the classification process, two well-known
pattern classifiers will be used, MLP and RBF. They
have been used to solve problems such as pattern
classification and the approximation of functions.
There are strengths and weaknesses associated to each
classifier. Despite the high computational cost of the
MLP and the sensitivity to the over fitting problem,
the MLP has the ability to detect complex nonlinear
relations between related and non-related variables.
The RBF is very easy to design, the capabilities are
very good and it performed robustly even when there
are noises on the input. Depending on the problem
each classifier will perform differently. In all the
experiments the MLP configuration will depend on
the number of inputs. For the first two experiments
the input layer will have 4 or 8 neurons based on
the number of input features. 100 neurons were used
for the output layer because there are 100 species.
There will be 2 hidden layers of 100 neurons each. The
function used in the neurons in the output and hidden
layer was the hyperbolic tangent function. To take
advantage of the differentiability and non-linearity
properties. In addition the following parameters are
used: 500 training epochs with a learning rate of 0.1,
minimum performance gradient of 10−6, a maximum
training time of 120 s, a validation check of 500 and
a performance goal of 0. In the case of RBF the
configuration is based on a Mean Square Error (MSE)
goal of 0, spread of 0.1, 4 and also 8 neurons in the
input layer for the first experiment. The proposed RBF
classifier contains one hidden layer on which some
neurons are added until it meets the specified mean
square error goal. The training step stop when 400
neurons are reached on the hidden layer, as shown
by Adetiba and Olugbara (2015). Both classifiers
were implemented on Matlab using Matlab’s machine
learning packages. For the classification phase 1/2 of
the data set were used for training and 1/4 for testing
and the rest for validation.
RESULTS
For each selected leaf, the associated grey scale
image will be used during the feature extraction
process. A sorted vector of sinuosity measure of
each curve composing the leaf shape was extracted
(sinuosity coefficients), followed by the extraction of
the geometrical features and the 4 Fourier descriptors.
For the first, second, third and fourth experiment
the geometrical features (4 features), 4 sinuosity
(4 features), 8 sinuosity (8 features) and 4 Fourier
descriptors (4 features) and 8 Fourier descriptors (8
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KALA JR ET AL: Plant Specie Classification using Sinuosity Coefficients of Leaves
features) are respectively used to recognized leaf
images. On the fifth, sixth, seventh, height and ninth
experiments, the 4 sinuosity, 8 sinuosity and 4 Fourier
descriptors and 8 Fourier descriptors are combined to
the geometrical features to recognized leaf images. A
total of 8, 12, 8 and 12 features are respectively used
for the classification.
The choice of four Fourier descriptors is because
the sinuosity measure also used four values. The
experimentation is performed using all the species in
LeafSnap database.
Table 1 presents the classification results when
using geometrical features, 4 sinuosity, 8 sinuosity and
4 Fourier descriptors as leaf features on the LeafSnap
dataset. A classification rate of 70% was obtained
using the MLP (Multilayer Perceptron) and 80% when
using the RBF with the geometrical features as input.
A classification rate of 80% was obtained with MLP
and 92% with the RBF when using the 8 sinuosity
coefficients.
Table 1 also presents the results of the
classification when using the geometric features
combined respectively to the 4 sinuosity coefficients,
8 sinuosity coefficients and to the Elliptic Fourier
descriptors to characterize the leaves on the selected
dataset. A classification rate of 82% was obtained
with MLP when using the combination of geometrical
features and 8 sinuosity coefficients and 93% with
the RBF on the database. Finally a classification rate
of 80% was obtained with MLP and 91% with RBF
respectively, using the 4 Elliptic Fourier descriptors
combined to the geometric features. The Elliptic
Fourier descriptors are obtained using a method
describe by Kuhl and Giardina (1982).
DISCUSSION
The classification results of the geometric features
with MLP are shown in the third row, second column
and third column of Table 1. A classification rate of
70% is obtained, with a Mean Square Error (MSE) of
0.0160. A classification rate of 80% with an MSE of
0.015 was also obtained when the geometrical features
were used to characterize the shape of a leaf image
with RBF as a classifier. These results show that the
boundary shape features area able to recognized more
than half of the leaf image. The results of the sinuosity
coefficients and MLP classifier are shown in the third
row, column four and five of Table 1. A classification
rate of 65% was obtained, with an MSE of 0.0274 with
the MLP classifier. A classification rate of 88% with an
MSE of 0.018 was also obtained with RBF classifier.
These results show that the 4 sinuosity coefficients
capture the leaf shape, structure but not with a high
precision. That precision is improved when using the 8
sinuosity coefficients
The classification results when the 4 sinuosity
coefficients are combined with geometrical features
using MLP as the classifier are shown in the third row
and column two of Table 1. A classification rate of 76%
and a MSE of 0.015 were obtained. A classification
rate of 90% and a MSE of 0.0047 were also obtained
with the RBF classifier when using the 4 Sinuosity
Coefficients combined with the geometrical features to
characterize the shape of the leaf images. The results
in Table 1 show that 4 sinuosity coefficients combined
with the geometric features are more efficient than the
4 sinuosity coefficients.
From the results obtained in this study and the
values observed on the subset of the confusion matrix
in Table 2, it is shown that the sinuosity coefficients
are good descriptors of leaf shape. However,
further classification improvement was obtained
by combining the 8 Sinuosity Coefficients with
geometrical features compared to the combination
of the geometrical features to the 4 elliptic Fourier
descriptors.
The MLP performed poorly compared to the RBF
on the overall dataset. The lower results observed are
due to the fact that some leaves look alike and produce
similar feature values. The superior performance of the
RBF over MLP has also been reported in the literature,
as presented by Adetiba and Olugbara (2015).
CONCLUSIONS
This paper has presented a model for leaf
shape analysis based on the sinuosity coefficients
and geometrical features. The proposed features for
leaf shape characterization are translation and scale
invariant. The experiments show that the sinuosity
coefficients combined with geometrical features are
efficient descriptors of leaf shape. A classification
rate of 93% was achieved using the combination of
Geometric features and 8 sinuosity coefficients with
RBF as classifier on LeafSnap dataset. The optimal
number of Sinuosity Coefficients used to describe a
given shape is 8, this constitute one of the limitation
of the Sinuosity Coefficients and the fact that the
rotation invariance remain an issue to investigate.
Further analysis of the sinuosity coefficient for the
characterization of the variations on leaf edges, and
the demonstration of the rotation invariance of the
sinuosity coefficients is envisioned.
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Image Anal Stereol 2018;37:119-126
Table 1. Performance evaluation of all the features.
Geometric Features Sinuosity Coefficients 8 Sinuosity Coefficients 4 Fourier Descriptors 8 Fourier Descriptors
MLP RBF MLP RBF MLP RBF MLP RBF MLP RBF
Sensitivity 0.91 0.92 0.84 0.96 0.894 0.98 0.860 0.878 0.90 0.95
Specificity 0.921 0.93 0.94 0.98 0.974 0.985 0.950 0.965 0.97 0.98
Classification Rate 0.7 0.8 0.65 0.88 0.8 0.92 0.78 0.89 0.90 0.95
4 Sinuosity Coefficients
Geometric Features
8 Sinuosity Coefficients
Geometric Features
4 Fourier Descriptors
Geometric Features
8 Fourier Descriptors
Geometric Features
MLP RBF MLP RBF MLP RBF MLP RBF
0.82 0.92 0.810 0.916 0.83 0.901 0.921 0.930
0.916 0.967 0.955 0.987 0.947 0.970 0.955 0.98
0.76 0.92 0.82 0.93 0.8 0.91 0.88 0.94
Table 2. Subset of the confusion matrix.
Species 1 Species 2 Species 3 Species 4 Species 5 Species 6 Species 7 Species 8 Species 9
Species 1 11 3 0 0 0 0 0 0 0
Species 2 2 16 0 0 0 0 0 0 0
Species 3 0 0 18 0 0 0 0 0 0
Species 4 0 0 0 17 1 0 0 0 0
Species 5 0 0 0 0 17 0 0 0 0
Species 6 0 0 0 0 0 18 0 0 0
Species 7 0 0 0 0 0 0 14 0 0
Species 8 0 0 2 0 0 0 0 13 0
Species 9 0 0 0 0 0 0 0 0 17
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