Leaf Identification Based on K means clustering and
Naïve Bayesian Classification
Shilpa Ankalaki
M.Tech Dept. CSE
NMIT
Bangalore-560064 India
[email protected]

Abstract— Recognition of plants has become an active
area of research as most of the plant species are at the
risk of extinction. This paper uses efficient features
including moment invariants features are extracted
during the feature extraction phase. The proposed
system proposes K means clustering method for
clustering the similar images and it also proposed Naïve
Bayesian classification to classify the leaf image into the
one of the cluster. Different distance methods can are be
used to identify the closest match of the leaf. In proposed
system Euclidian distance is used to search similar leaf in
the cluster.
Dr. Jharna Majumdar
Dean R&D, Prof and Head CSE (PG),
Nitte Meenakshi Institute of Technology,
Bangalore,560064,India
digital camera. In this way, we can get an image including
only one leaf.
Key words— Hu moment invariants, K means clustering.
1. INTRODUCTION
The Plant is one of the most important forms of life on earth.
Plants maintain the balance of oxygen and carbon dioxide of
earth’s atmosphere [13]. The relations between plants and
human beings are also very close. In addition, plants are
important means of livelihood and production of human
beings. . Plants are vitally important for environmental
protection. However, it is an important and difficult task to
recognize plant species on earth. Many of them carry
significant information for the development of human
society. The urgent situation is that many plants are at the
risk of extinction [10]. So it is very necessary to set up a
database for plant protection [3-4]. The proposed method
mainly concentrates on leaf shape features regardless of
color features, because the color of the leaf may change due
to the climate change or due to the some disease so color
feature are inefficient.
2. PROPOSED METHODOLOGY
The proposed methodology mainly consists of 2 phases.
i. Learning Phase
ii. Identification phase
Both phases involve four stages which are explained
inconsecutive sub-sections. Fig1 shows the flow diagram of
the learning phase and identification phase.
2.1 Image Acquisition
Leaves are usually clustered so that it is difficult to
automatically extract features of one leaf from the unneeded
background. We created leaf Image plates. Put these leaves
on the light panel, and then take the picture of the leaf with a
Fig.1. Flow diagram of learning and identification phase
2.2 Image Preprocessing
The raw data, depending on the data acquisition type is
subjected to a number of pre processing steps to make it
usable in the descriptive stages of analysis. Pre processing
aims to produce image data that are easy for the Leaf
Identification system and can operate quickly and
accurately.
2.2.1Converting Color leaf image to Gray leaf image
The colors of plant leaves are usually green. Moreover, the
shades and the variety of changes of water, nutrient,
atmosphere and season can cause change of the color, so the
color feature has low reliability. Thus, we decided to
recognize various plants by the grey-level image of plant
leaf. Fig 2 shows the pre processing of leaf image.
An RGB image is firstly converted into a grayscale image.
Eq. (1) is the formula used to convert RGB value of a pixel
into its grayscale value.
Gray = 0.2989 * R + 0.5870 * G + 0.1140 *B
(1)
Where R, G, B correspond to the color of the pixel,
respectively
1
2.2.2 Generation of Binary Image
In the analysis of images, it is essential to separate the
objects of interest from the rest. The techniques used to find
the objects of interest from the rest are referred to as
Thresholding techniques and the cluster of pixels
corresponding to region of interest are known as foreground
pixels and the rest of the pixels are known as background
pixels. The image data is converted to a two level binary
image having pixel values between 0 and 255 this is done
using Thresholding, where all pixels above certain level are
assigned 255 and rest of the pixels 0. The proposed
methodology used statistical mean method and Otsu’s
method for automatic Thresholding.
Roundness =
4π ∗ Area
Perimeter 2
(4)
2.3.5 Sphericity: Spericity [4][5] is the ratio of the radius of
the incircle of the leaf object (ri) and the radius of the excircle
of the leaf object (rc). Incircle and excircle are as shown in
the Fig 3(a).
2.3.6 Principal axes: Principal axes of a given shape can be
uniquely defined as the two segments of lines that cross each
other orthogonally in the centroid of the shape and represent
the directions with zero cross correlation .This way, a contour
is seen as an instance from a statistical distribution. Fig 3 (b)
shows the principal axes.
2.2.3 Generation of Boundary Image
Boundary extraction can be applied to any image containing
only boundary information. Once a single boundary point is
found, the operation seeks to find all other pixels on that
boundary. Boundary can be extracted using chain code
technique. The system defines the boundary of the leaf in
terms of x-y coordinates [11]. From a starting point, the
system traces the boundary coordinates in a clockwise
direction
Fig.2 Pre Processing of leaf image
2.3 Feature Extraction
Feature extraction involves the extraction of efficient leaf
shape features these features are used by the classifier to
classify the leaf image. Different types of features extraction
are discussed below.
2.3.1 Aspect ratio: The aspect ratio[1] is ratio between the
maximum length and the minimum length of the minimum
bounding rectangle or ratio between length and width of the
minimum bounding box of leaf image. It is scale invariant
feature.
Aspect ratio= Length/Width
(2)
2.3.2 Rectangularity: Rectangularity is the measure of how
closely the shape of leaf approaches to rectangle or it can be
defined as the similarity between leaf and rectangle. To
calculate the rectangularity first step is to create bounding
box to the leaf image, and find the ratio of leaf area to the
area of leaf bounding box.
Rectangularity =
Leafarea
(Length∗Width)
(3)
2.3.3. Perimeter: The total number pixels on the leaf
boundary.
2.3.4 Roundness: Roundness [2][8] is the measure of how
closely the shape of leaf approaches that of a circle.
Difference between a leaf and a circle is calculated by using
the Eq. 4
Fig.3 (a) Incircle and Excircle (b) Principal axes
2.3.7 Eccentricity: Eccentricity can be defined as the ratio of
minor principal axes to major principal axes.
2.3.8 Tooth Feature: A tooth point [14] is a pixel on the
contour that has a high curvature, i.e., it is a peak. To
determine whether a point Pi on the contour is a tooth point
or not, we examine the angle  subtended at Pi by its
neighbors Pi-k and Pi+k (where k is a threshold). Fig 4 shows
an example. If the angle is within a particular range, then
Pi is a tooth; otherwise, it is not. It is also possible for two
different types of leaves to have nearly the same number of
teeth at a particular threshold [12]; so we compute the toothbased features at multiple increasing threshold values.
Fig.4 Tooth detection at two different thresholds
2.3.9 Leaf Vein Extraction: Leaf vein extraction [3][6] , is
one of the important features of the leaf. Leaf veins can be
extracted using the greyscale morphological operations.
Algorithm for vein extraction is as follows.
ALGORITHM: To find Veins of leaf
Input
: Grayscale Leaf Image
Output
: Leaf vein structure
Step 1: Read Grayscale Image.
Step 2: Let f be the Grayscale leaf image and b be the disk
shape Structuring element. Structuring element of radius 2,
3, 4 or 5 can be used.
Step 3: Perform the Erosion operation on the grayscale
image using the disk shape structuring element that is find
the minimum neighbor and replace it with origin of the
structuring element.
2
Step 4: Perform the Dilation on the output image of the
erosion using the disk shape structuring element that is find
the maximum neighbor and replace it with origin of the
structuring element. This process is called as Opening
Morphological operation.
Step 5: Subtract the original grayscale image from the result
of opening operation this process is called as Top-hat
Transformation.
Step 6: Convert the result of Top-hat Transformation into
binary image.
Step 7: Perform the Av1/A, where Av1 is the vein area
using structuring element (SE) 2, A is the leaf area.
Step 8: The leaf vein structure can be extracted using
different structuring element like disk shape structuring
element of radius 2,3,4,5 and each vein structure of different
structuring element is stored as feature.
ⱷ4= (Moment30+Moment12)2+(Moment21+Moment03)2
To make the moments invariant to translation the image is
shifted such that its centroid coincides with the origin of the
coordinate system. The centroid of the image in terms of the
moments is given by:
XC=Moment10 /Moment00 , YC=Moment01 /Moment00
Then the central moments are defined as follows
μpq=∑𝑥 ∑𝑦[ (𝑥 − 𝑥c)p,(y - yc)q I(x, y)]
(5)
To compute Hu moments using central moments the ⱷ terms
in equation (5) need to be replaced by μ terms. It can be
verified that μ00 = m00, μ10 = 0 = μ01.
To make the moments invariant to scaling the moments are
normalized by dividing by a power of μ00. The normalized
central moments are defined using Eq. 6:
2.3.10 Moment Invariants: Moment invariants have been
frequently used as features for image processing, remote
Mpq= μpq /( μ00) where p+q)/2
(6)
sensing, shape recognition and classification. Hu (Hu,
1962), proposed the first set out the mathematical
foundation for two-dimensional moment invariants and 2.4 Classification
demonstrated their applications to shape recognition [16]. All the features extracted from all leaves during learning
These moment invariant values are invariant with respect to phase are stored in the database and applied unsupervised
classification method to group the similar leaves that are
translation, scale and rotation of the shape.
For a digital image, [9][15] the moment of a pixel P(x, y) at present in the database. The proposed system introduced K
location (x, y) is defined as the product of the pixel value means clustering method to cluster the similar leaves based
with its coordinate distances i.e. m = x. y. P(x, y). The on the features on the database. K- Means takes the database
moment of the entire image is the summation of the features as the input. User needs to specify the number of
moments of all its pixels. More generally the moment of clusters required. The algorithm for the K-means clustering
is as follows:
order (p, q) of an image I (x, y) is given by
Momentpq=∑𝑥 ∑𝑦[x p yq I(x, y)]
Based on the values of p and q the following are defined:
𝑀𝑜𝑚𝑒𝑛𝑡00 = ∑ ∑[𝑥 0 𝑦 0 𝐼(𝑥, 𝑦)] = ∑ ∑[𝐼(𝑥, 𝑦)]
𝑥
𝑦
𝑥
Algorithm: The k-means algorithm for partitioning, where
each cluster center is represented by the mean value of the
objects in the cluster.
Input:
𝑦
1 0
𝑀𝑜𝑚𝑒𝑛𝑡10 = ∑ ∑[𝑥 𝑦 𝐼(𝑥, 𝑦)] = ∑ ∑[𝑥 ∗ 𝐼(𝑥, 𝑦)]
𝑥
𝑦
𝑥
𝑦
𝑀𝑜𝑚𝑒𝑛𝑡01 = ∑ ∑[𝑥 0 𝑦1 𝐼(𝑥, 𝑦)] = ∑ ∑[𝑦 ∗ 𝐼(𝑥, 𝑦)]
𝑥
𝑦
𝑥
𝑦


K: the number of clusters,
D: a data set containing n objects.
Output: A set of k clusters.
1 1
𝑀𝑜𝑚𝑒𝑛𝑡11 = ∑ ∑[𝑥 𝑦 𝐼(𝑥, 𝑦)] = ∑ ∑[𝑥𝑦 ∗ 𝐼(𝑥, 𝑦)]
𝑥
𝑦
𝑥
Method:
𝑦
2 0
2
𝑀𝑜𝑚𝑒𝑛𝑡20 = ∑ ∑[𝑥 𝑦 𝐼(𝑥, 𝑦)] = ∑ ∑[𝑥 𝐼(𝑥, 𝑦)]
𝑥
𝑦
𝑥
𝑦
𝑀𝑜𝑚𝑒𝑛𝑡02 = ∑ ∑[𝑥 0 𝑦 2 𝐼(𝑥, 𝑦)] = ∑ ∑[𝑦 2 𝐼(𝑥, 𝑦)]
𝑥
𝑦
𝑥
𝑦
2 1
𝑀𝑜𝑚𝑒𝑛𝑡21 = ∑ ∑[𝑥 𝑦 𝐼(𝑥, 𝑦)] = ∑ ∑[𝑥 2 𝑦1 𝐼(𝑥, 𝑦)]
𝑥
𝑦
𝑥
𝑦
1 2
𝑀𝑜𝑚𝑒𝑛𝑡12 = ∑ ∑[𝑥 𝑦 𝐼(𝑥, 𝑦)] = ∑ ∑[𝑥 1 𝑦 2 𝐼(𝑥, 𝑦)]
𝑥
𝑦
𝑥
𝑦
0 3
𝑀𝑜𝑚𝑒𝑛𝑡03 = ∑ ∑[𝑥 𝑦 𝐼(𝑥, 𝑦)] = ∑ ∑[𝑦 3 𝐼(𝑥, 𝑦)]
𝑥
𝑦
𝑥
𝑦
3 0
𝑀𝑜𝑚𝑒𝑛𝑡30 = ∑ ∑[𝑥 𝑦 𝐼(𝑥, 𝑦)] = ∑ ∑[𝑥 3 𝐼(𝑥, 𝑦)]
𝑥
𝑦
𝑥
Step 1: Arbitrarily choose k objects from D as the initial
cluster centers;
Step 2: repeat
Step 3: (re)assign each object to the cluster to which the
object is the most similar, based on the mean value
of the objects in the cluster;
Step 4: update the cluster means, i.e., calculate the mean
value of the objects for each cluster;
Step 5: until no change;
𝑦
At the end of the k-means clustering K number of clusters
will be formed.
The first four Hu invariant moments which are invariant to
rotation are defined as follows:
2.5 Recognition Phase
ⱷ1= Moment20+ Moment02
During the testing, first step is to read the test leaf image.
Second step is preprocessing of given input leaf image, third
ⱷ2= (Moment20-Moment02)2 + (2Moment11)2
2
2
step is feature extraction. Features of given leaf are stored in
ⱷ3= (Moment30- 3Moment12) + (3Moment21 –Moment03)
3
the feature vector. Fourth step is to search the clusters for
given leaf, for this purpose Naïve Bayesian classification is
used.
2.5.1 Naïve Bayesian Classification:
Step 7: To find the P(X/C) for continuous distribution needs
to apply Gaussian distribution, i.e. to find the probability of
the leaf that belongs to the cluster with respect to feature. It
involves following steps.
Naïve Bayesian classification is supervised classification; it  Calculate mean for each cluster with respect to each
feature.
takes the prior knowledge from the clusters. It is possible to
use the Naïve Bayesian classification without using the  Calculate variance for each cluster with respect to each
clustering method, but it is necessary to create the database
feature and the following Gaussian distribution
such that all the similar leaves in one class. So the proposed
formula[17] as shown in Eq.10
system introduced unsupervised classification for clustering
(𝑋−𝜇)2
1
−
and supervised classification to classify the leaf image into
𝑔(𝑥, 𝜇, 𝜎) =
𝑒 2𝜎2
(10)
√2𝜋𝜎
one of the respective class. Algorithm for the Naïve
Finally probability of leaf belong to particular class is given
Bayesian classification is as follows:
in Eq.11
Algorithm: Naive Bayesian classifier
Input: Leaf features of training data set
𝑃(𝑥𝑘 |𝐶𝑖 ) = 𝑔(𝑥𝑘 , 𝜇𝐶𝑖 , 𝜎𝐶𝑖 )
(11)
Output: Classification of Test leaf
The leaf image which is being tested belongs to particular
Step 1: Apply any clustering method on the training data set cluster which has the highest probability.
to form the cluster
Step 2: Store the input leaf feature into feature vector.
Euclidian Distance
Step 3: Find the probability of each cluster that holds the
To recognize the leaf within the cluster the Euclidian distance
given leaf image based features. This probability can be
method [7] [13] is used. To recognize the leaf, find the
called as posterior probability. Posterior probability can be
distance between the input leaf image feature vector to all
calculated using Eq.7
leaves features that are present in particular cluster selected
𝑋
using Naïve Bayesian classifier. The leaf image that has the
𝑃 ( ) 𝑃(𝐶)
𝐶𝑖
𝐶
𝑃( ) =
(7)
minimum distance to the input leaf is selected as recognized
𝑋
𝑃(𝑋)
leaf.
Where
X: feature vector of the given leaf.
EXPERIMENTAL RESULTS
C : Leaf clusters
i: Number of Clusters
The proposed methodology uses the invariant shape features
The calculation of the P(C), P(X/C) and P(X) is given in the
and Hu moment invariants. Hu moment invariants are
further steps
invariant to rotation, scaling and translation. In all the
experiments, a leaf image contains a single leaf on an
uniform background. First, we apply the Otsu or statistical
Step 4: Calculate the class probability P(C) using Eq.8. It is
threshold method to remove the background and keep only
constant value.
the mask corresponding to the leaf. A closed contour is then
|𝐶𝑖,𝐷 |
extracted from the leaf mask. Note that the input of all the
𝑃(𝐶𝑖 ) =
(8)
𝐷
representations described above is a sequence of N boundary
Where
points regardless of other leaf features like texture and color.
The proposed methodology able to identify the correct leaf
D: total number of training tuples in the database.
even though input image is rotated and scaled. The
following table 1 shows the feature of the original image,
|𝐶𝑖,𝐷 | : Number of training tuples of class Ci in D.
same leaf image rotated at 45 degree and features when the
size of the leaf reduced to half of the original image. Fig 5
Step 5: P(x) will be constant, so to maximize the probability
shows the leaf image which is used to compare the results of
its need to maximize the P(X/C)*P(C). P(X) can be
feature under rotation and scaling. Table1 and 2 shows the
calculated using Eq.9 as follows:
features of original, rotated, resized and damaged leaf
P(X)=P(Xk | C1)+…..+P(Xk|Ci)
(9)
image.
Step 6: In order to reduce computation in evaluating
P(X|Ci), the naive assumption of class conditional
independence is made. This presumes that the values of the
attributes are conditionally independent of one another,
given the class label of the tuple. Thus,
𝑃(𝑋|𝐶𝑖 ) = 𝑃(𝑥1 , 𝑥2 … . 𝑥𝑘 |𝐶𝑖 )
= 𝑃(𝑥1 |𝐶𝑖 ) ∗ 𝑃(𝑥2 |𝐶𝑖 ) ∗ … ∗ 𝑃(𝑥𝑛 |𝐶𝑖 )
𝑛
= ∏ 𝑃(𝑥𝑘 |𝐶𝑖 )
𝑘=1
Where X is feature vector with {x1, x2, -----, xk} attributes,
and k is the total number of attributes.
Table1. Features of original image and rotated image
Feature Name
Original
image Features
feature
rotated leaf
Aspect Ratio
0.239521
0.946939
Roundness
0.136196
0.1614271
Spericity
0.056033
0.061743
Rectangularity
0.275299
0.129803
Eccentricity
0.014657
0.014501
Tooth Features at 2
3
angle 30
Tooth Feature at 6
6
of
4
angle 45
Tooth feature at
angle 60
Moment 1
Moment 2
Moment3
Moment 4
Moment 5
Moment 6
Moment 7
8
8
0.844066
0.672120
0.028135
0.025953
0.000701
0.021267
-0.000187
0.847128
0.677481
0.030383
0.026138
0.000823
0.023151
0.000004
Table2 .Features of resized and damaged leaf image
Features
Resized image
Damaged image
Aspect Ratio
0.257485
0.793478
Roundness
0.142336
0.220737
Spericity
0.057785
0.096403
Rectangularity
0.271550
0.262685
Eccentricity
0.017142
0.038267
Tooth Features at 6
2
angle 30
Tooth Feature at 6
4
angle 45
Tooth feature at 10
6
angle 60
Moment 1
0.779586
0.608201
Moment 2
0.567475
0.317910
Moment3
0.019643
0.077895
Moment 4
0.017876
0.055264
Moment 5
0.000335
0.003626
Moment 6
0.013452
0.031154
Moment 7
-0.000100
0.001247
Fig. 6 sample leaves of database one leaf from one species
Precision is defined as the ratio of number of relevant
retrieved images to total number of retrieved images
Precision= Number of relevant retrieved images
Total number of retrieved images
Error rate is defined as ratio of non-relevant images retrieved
to the total number of images retrieved.
Error Rate = Number of irrelevant images
Total number of images retrieved
CONCLUSION
Fig. 5 Original leaf, rotated, resized and damaged leaf image
used to compare the features in Table 1 and 2.
Fig 6 shows the sample leaves of the database some of the
leaves are taken from the flavia dataset. The proposed
methodology identifies the leaf correctly even some part of
the leaf get damaged as shown in the Fig 5. It is important to
measure the effectiveness of the approach. Here recall,
precision and error rate are calculated to measure the
effectiveness of the method [18]. Recall is defined as ratio
of number of relevant retrieved images to number of all
relevant images.
Recall = Number of relevant retrieved images
Number of all relevant images
The work described in this research has been concerned with
the two challenging phases in image analysis applications
which are feature extraction and classification phase. Since
there is no general feature extraction method that is
available for all type of images, an experiment needs to be
conducted in order to determine the suitable methods for
plant leaf images. Therefore, an investigation of some of the
suitable shape features and moment invariants techniques
was presented which were used to be implemented in the
feature extraction of plant leaf images. The proposed
methodology gives the 80 to 85% accuracy even in presence
of damaged leaf. One of the disadvantages in this research is
the use of limited sample of leaf images. So future scope of
this research is the identification of compound with different
background and performance improvement of identification
system.
REFERENCES
1. Chia-Ling Lee and Shu-Yuan Chen, “Classification for Leaf Images”,
16th IPPR Conference on Computer Vision, Graphics and Image
Processing (CVGIP 2003)
5
2. Qingfeng Wu, Changle Zhou and Chaonan Wang, “Feature Extraction
and Automatic Recognition of Plant Leaf Using Artificial Neural
Network”, © A. Gelbukh, S. Torres, I. López (Eds.) Avances en
Ciencias de la Computación, 2006, pp. 5-12.
3. S. G. Wu, F. S. Bao, E. Y Xu, Y-X. Wang, Y-F. Chang, & Q-L.Xiang,
“A Leaf Recognition Algorithm for Plant Classification Using
Probabilistic Neural Network”, IEEE 7th International Symposium on
Signal Processing and Information Technology, Cairo, 2007.
4. J. Du, X. Wang, and G. Zhang, “Leaf shape based plant species
recognition,” Applied Mathematics and Computation, vol. 185-2, pp.
883-893, February 2007.
5. David Knight, James Painte, Matthew Potter, “Automatic Plant Leaf
Classification for a Mobile Field Guide”.
6. Xiaodong Zheng, Xiaojie Wang, “ Leaf Vein Extraction Based on
Gray-scale Morphology”, I.J. Image, Graphics and Signal Processing,
2010, 2, 25-31 Published Online December 2010 in MECS
(http://www.mecs-press.org/)
7. Chomtip Pornpanomchai, Chawin Kuakiatngam ,Pitchayuk
Supapattranon, and Nititat Siriwisesokul, “Leaf and Flower
Recognition System (e-Botanist)”, IACSIT International Journal of
Engineering and Technology, Vol.3, No.4, August 2011
8. Abdul Kadir, Lukito Edi Nugroho, Adhi Susanto and Paulus Insap
Santosa, “Leaf Classification Using Shape, Color, and Texture
Features”, International Journal of Computer Trends and TechnologyJuly to Aug Issue 2011
9. Jyotismita Chaki and Ranjan Parekh, “Plant Leaf Recognition using
Shape based Features and Neural Network classifiers”, (IJACSA)
International Journal of Advanced Computer Science and Applications,
Vol. 2, No. 10, 2011
10. Prof. Meeta Kumar, Mrunali Kamble, Shubhada Pawar, Prajakta Patil,
and Neha Bonde, “ Survey on Techniques for Plant Leaf
Classification”, International Journal of Modern Engineering Research
(IJMER) www.ijmer.com Vol.1, Issue.2, pp-538-544 ISSN: 2249-6645
11. Chomtip Pornpanomchai, Supolgaj Rimdusit, Piyawan Tanasap and
Chutpong Chaiyod, “Thai Herb Leaf Image Recognition System
(THLIRS)”, Kasetsart Journal: Natural Science May 2011 45 : 551 562
12. Akhil Arora, Ankit Gupta, Nitesh Bagmar, Shashwat Mishra, and
Arnab Bhattacharya, “A Plant Identification System using Shape and
Morphological Features on Segmented Leaflets: Team IITK, CLEF
2012”
13. Anant Bhardwaj, Manpreet Kaur, and Anupam Kumar, “Recognition of
plants by Leaf Image using Moment Invariant and Texture Analysis”,
International Journal Of Innovation And Applied Studies ISSN 20289324 Vol. 3 No. 1 May 2013, Pp. 237-248 © 2013 Innovative Space Of
Scientific Research Journals.
14. Vijay Satti and Anshul Satya, “An Automatic Leaf Recognition System
For Plant Identification Using Machine Vision Technology”,
International Journal of Engineering Science and Technology (IJEST)
ISSN : 0975-5462 Vol. 5 No.04 April 2013
15. Jyotismita Chaki and Ranjan Parekh, “Designing an Automated System
for Plant Leaf Recognition”, International Journal of Advances in
Engineering & Technology, Jan 2012. ©IJAET ISSN: 2231-1963
16. Laura Keyes, Adam Winstanley, “USING MOMENT INVARIANTS
FOR CLASSIFYING SHAPES ON LARGE_SCALE MAPS”.
17. George H. John, Pat Langley, “Estimating Continuous Distributions in
Bayesian Classification”, In Proceedings of Conference on uncertainty
in Artificial Intelligence, Morgan Kaufmann Publishers, San
Mateo,1995
18. Komal Asrani, Renu Jain, “Contour Based Retrieval for Plant
Species”, I.J. Image, Graphics and Signal Processing, 2013, 9, 29-35
Published Online July 2013 in MECS (http://www.mecs-press.org/)
6