Nothing Special   »   [go: up one dir, main page]

Handwritten Devanagari Compound Character Recognition Using Legendre Moment An Artificial Neural Network Approach

Download as pdf or txt
Download as pdf or txt
You are on page 1of 5

2013 International Symposium on Computational and Business Intelligence

Handwritten Devanagari Compound Character Recognition using Legendre


Moment an Artificial Neural Network Approach
*1

K.V.Kale, IEEE Senior Member, 2S.V.Chavan, IEEE Student Member,


M.M.Kazi, IEEE Student Member, 1Y.S.Rode, IEEE Student Member
1
Dept. of Computer Science & I.T., Dr. Babasaheb Ambedkar Marathwada Universitiy, Aurangabad (MS) - India
2
Dept. of Computer Science & I.T. MSSs Arts, Commerce & Science College, Ambad Dist. Jalna (MS) - India
kvkale91@gmail.com, shripc@gmail.com, mazhar940@gmail.com, ys.rode@gmail.com
1

Abstract Handwritten Devanagari Compound character


recognition is one of the new challenging task for the
researcher, because Compound character are complex in
structure, they are written by combination two or more
character. Their occurrence in the script is upto 12 to 15%. In
this research paper, a recognition system for handwritten
Devanagari Compound Character is proposed bases on
Legendre moment feature descriptor are used to recognize.
Moment function have been successfully applied to many
pattern recognition problem, due to this they tends to capture
global features which makes them well suited as feature
descriptor. The process image is normalized to 30X30 pixel size
divided into zone, from this structural as well as statistical
feature are extracted from each zone. The proposed system is
trained and tested on 27000 handwritten collected from
different people. For classification we have used Artificial
Neural Network. The overall recognition rate for basic is upto
98.25% and for all compound character is 98.36%.

quality (thick/thin), strokes that substantial extent the


recognition accuracy.
Work on Devanagari was started in 1970. Sinha and
Mahabala[5] presented a syntactic pattern analysis system
for the recognition of Devanagari characters (DC). OCR
work for printed and handwritten characters in various Indian
scripts [6-8] is carried out by researchers but major work is
found for Bangla[9,10]&Devanagari. First research report on
handwritten DC was published in 1977 by Sethi and
Chatterjee[11]. An extensive research work on printed
Devanagari was carried out by Bansal et.al. [12-14]. Work
on Handwritten Numerals of Devanagari is carried out by
researcher is presented in [15-16]. Central, invariant, Zernike
moments use for recognition of character of different
languages reported in [17-25]. In [25-27] research has
proposed Chain Code Histogram and directional information
obtained from the arc tangent of the gradient for feature
extraction. A significant contribution is due to Arora et al. in
which they proposed a multi-feature extraction based
technique in [28]. Pal et al. proposed SVM and MQDF based
scheme for recognition of Devanagari [29]. U. Pal and T.
Wakabayashi [30] proposed a comparative study of different
DC recognizers using features based on curvature and
gradient information. Sushama Shelke et al. [31] presented a
novel approach for recognition of unconstrained handwritten
Marathi characters. Baheti M.J. et. al [32] proposed a method
based on AIM for Gujarati numerals uses KNN and PCA as
classifiers. Recognition of handwritten Bangla compound
character was attempted by U. Pal et al. [33] using gradient
features. Work on handwritten Marathi compound characters
found in [34-35] by S. Shelke and S. Apte. From the above
discussion it is evidence that moment can be considered as
potential features for recognition of character and numerals,
which motivate us to enrich the several orthogonal and
discrete moment features and test the efficacy of the system
for compound characters. While significant advances have
been achieved in recognizing Roman-based scripts like
English, ideographic characters Chinese, Japanese, Korean,
and Arabic to some extent. Only few works on some of the
major Indian scripts like Devanagari, Bangla, Gurumukhi,
Tamil, Telugu, are available in the literature.
The paper is organized as follows: Section 2 deals with
Moments discussion. Database collection & Preprocessing
for the experiment in section 3. Section 4 presents Feature
extraction procedure. Section 5 details of the classifier used
for recognition. The experimental results are discussed in

Keywords- Handwritten Devanagari Compound; Legendre


Moment; ANN; Pattern Recognition;

I.

INTRODUCTION

Handwritten character recognition has always been a


challenging task in image processing and pattern recognition.
There are five major stages in the handwritten character
recognition (HCR) problem: Image preprocessing, feature
extraction, training, testing and post processing. The feature
extraction method is probably the most important stage in
achieving high recognition performance. This field of
research is applicable for application areas i.e. form filling,
job application, bank and postal automation [1-3] and also an
identification of a person of a scanned handwritten script; it
is useful for biometric modality with application in forensic
and historic document analysis (HDA) and represents an
excellent study area within the research field of biometrics.
In the proposed system, we are extracting Legendre moment
features descriptor, from the scanned images of handwritten.
For recognition purpose we have used Artificial Neural
Network.
Recognition of Handwritten in Indian script [4] is also
one of challenging task specially, for several reasons because
of complex structure of character with their modifiers and
presence of compound character. Writing style in
Devanagari script is from left to right. The concept of
upper/lower case is absent in Devanagari script. Compound
characters are those where one half of character is connected
to full character to produce a special character. Thus there
are large variations in shape of character as writing style, pen
978-0-7695-5066-4/13 $26.00 2013 IEEE
DOI 10.1109/ISCBI.2013.62

274

Section 6. Finally, conclusion on the paper is given in


Section 7.
II. MOMENT
The concept of moment in mathematics evolved from the
concept of moment in physics. It is an integrated theory
system. For both contour and region of a shape, one can use
moment's theory to analyze the object.
Moment based techniques have been successfully applied
to several image processing problems and they represent a
fundamental tool for generating feature descriptors. Feature
descriptors built from moment functions capture global
features, and as such they are well suited for shape and
character recognition. Some moment functions exhibit
natural invariance properties, such as invariance to rotation,
translation or scaling. Translation and scale invariance is
usually obtained by normalizing the input image with its
geometric moments. The original image can be reconstructed
from its moments, as an infinite series of moments uniquely
identify a specific distribution. Reconstruction from
orthogonal moment functions can be done.

Fig.1-Sample dataset of handwritten Devanagari


Character
Compound characters can be combinations of two
consonants as well as a consonant and a vowel.
Compounding of three or four characters also exists in the
script. The compound characters are joined in various ways,
by removing vertical line of the character and then join it to
the other character from left side like
, or another way is
join side by side or one above the other
. The e.g.
regarding to the compound is shown in Fig.(2).Split
character is the half character of basic character which get
connected to other character e.g. split is given in Fig.(3).

A. Legendre moments (LM)


The basis function for Legendre moment is nm(x, y) =
Pn(x)Pm(y) where Pp(x) denotes the pth order of Legendre
polynomial. The (n+m)th order of Legendre moment, Lnm, is
defined in Eq. 1 [38].

Fig.2 Example of Compound Character

(2n  1)(2m  1)
Pn( x) Pm( y ) f ( x, y)dxdy.
4
1 1
where Pn(x) is the nth order of Legendre polynomial give by
1 1

Lnm

P ( x)
n

1 n/2
( 2 n  2 k )!
k
x n  2k n
( 1)
n
k
n
k
n
k
!
(

)!
(

2
)!
2 k 0

Fig. (3) Example of Split of Compound Character


A. Database Designing
For the proposed work, the database is prepared by
scanning the images of Handwritten Devanagari Basic &
Compound Character, which are collected on a special
designed sheet, from individuals of various professions.
Source document are scanned at 300 dpi using canon flatbed
scanner and stored in TIFF format images in 1 byte per pixel,
and stored for extraction of isolated character. All output
samples were checked manually and necessary
editing/removal were done. Image samples of the present
databases are also maintained in the original form, the writer
other information is also available for the entire document.
At present no dataset on Devanagari handwritten
compound characters is available. A significant contribution
of present work is the pioneering development of large
database for Handwritten Devanagari Basic and Compound
Character was collected. Details of this database are
provided in Table I. Handwritten Devanagari (Basic &
Compound) character consists of 27000 samples written by
writer from different location, fields, profession.

(2)

Since the Legendre polynomials are orthogonal over the


interval [1, 1], the image f(x, y) can be reconstructed from
its moments. Teague derived a simple approximation to the
inverse transform for a set of moments through order M
given by

M
n
f ( x, y) | L
P
( x) P ( y) (3)
n  m, m n  m
m
n 0m 0
III.

DATA COLLECTION & PREPROCESSING

The basic set of symbols of Devanagari script consists of


12 vowels (or swar), 36 consonants (or vyanjan) as shown in
Fig. 1, which are used for this work, we have also used 45
compound character + 15 split component of compound
character for proposed research which is presented in Fig 2
and Fig 3.

TABLE I.
Script

Devana
gari

275

DATASET OF HANDWRITTEN DEVANAGARI BASIC AND


COMPOUND CHARACTER
Total
Split CompCompCharacte
Basic
onent of
ound
r Set
Charact
Compound
Chara
er
Character
cter
Training
9600
9000
3000

Testing

2400

2250

750

Charact
er

Total

12000

11250

3750

Fig 4: Presence of End Points in partition block of Character


In this paper basic, compound character are written on
a plain paper. The characters are scanned, pre-processed by
the above discussion and store automatically for database
creation. The character is processed, normalized into the
required size and transfer for structural classification and
further features are extracted which are used for training and
testing.

27000

B. Preprocessing
The preprocessing plays important role in handwritten
character recognition as in pattern recognition task.
Preprocessing is an important step of applying a number of
procedures for smoothing, enhancing, filtering for making a
digital image usable by subsequent algorithm in order to
improve their readability. The morphological opening and
closing operators not only remove image noise but also
connect discontinuities. The next step is skeletonization
which reduce the pen width and computation cost.
To achieve the recognition accuracy of Devanagari
Compound character the structural classification is
necessary. There are two methods to recognized compound
character, the one is partitioned of the character and other is
without partition of character. For the first one, two separate
features are extracted and then recognition is done and for
second method without separation the features are extracted.

IV. FEATURE EXTRACTION


Moment based features are extracted from the each
zone of the scaled character bitmapped image. The image is
partitioned into zone and features are extracted from each
zone as shown in Fig 5. In this paper Legendre moments
based feature extraction is proposed for off-line Devanagari
Handwritten Basic and Compound Character. To get the
feature set, at first, the image is segmented to 30 x 30
blocks, and partitioned as feature set as follows.
Feature set 1: Fig 5(a) shows is considered as whole.
Feature set 2: Fig. 5(b) divide the img into four equal zones.
Feature set 3: Fig.5(c) divide the img into 3 vertical equal zones
Feature set 4:Fig.5(d) divide the img into 3 horizontal equal zones

C. Pre-classification
With the help of above processing step, the preclassification of character is done which is based on two
stages global features i.e. presence of vertical line, position
of it in the character and enclosed region in the character
and second is local features i.e. end points and junction in
the character. On the basis of global feature, the character is
classified into three major categories, presence of vertical
bar, at right character and at middle, and absence of vertical
bar.
Vertical bar on right are further classified into two
categories based on whether the vertical bar and rest of the
character are connected or not to the bar. These are show in
the following Table II.
TABLE II.
Sr.
No
1

2
3
4

a
b
c
d
Fig.5 Partition of Devanagari Character into feature set
TABLE III.
Zone set
FS1
FS2
FS3
FS4

Character

Character connected with


vertical bar at right side

K, I, , pe, P, $e, le,


Le, O, ve, He, ye, Y,
c, e, ue, J, m,<e, #,
%e
i, Ce, M

Character not connected with


vertical bar at right side
Character with vertical bar at
middle
Character with absence of
vertical bar

Feature Set
9
36
27
27

In pattern recognition, feature extraction stage in


character recognition plays a major role in improving the
recognition accuracy. Features are extracted from binary
image/characters. Many characters are misclassified due to
their similarity in shape or slight variation in writing style.
So features which are selected should tackle these problems.
Block Diagram of Recognition System

CLASSIFICATION OF DEVANAGARI CHARACTER

Pre-classification

: MOMENT FEATURE SET FOR DEVANAGARI


Moment Feature
Legendre
Legendre
Legendre
Legendre

J, he
[.,, , ", [, {, o, j, n, U

D. Local Structural Classification


The local features are detected on the bases of the end
points of the character. To detect the end points there are
two steps, first partitioned the image into 3x3 i.e. 9
quadrants and secondly detect the end points and junction in
the individual block as shown in Figure 4.

Testing

276

Training

Fig 6: Block Diagram for proposed work

to other FS1, FS3 and FS4. Thus overall recognition rate


for 48 Devanagari Basic Character is 98.25%.

V. CLASSIFICATION & RECOGNITION


For the purpose of training and testing Artificial Neural
Network is used for classification. The network is trained
with a set of handwritten Devanagari Basic and Compound
Character. The network accepts Legendre moment feature
of each character in the form of feature set, 9, 36, 27, 27 as
input. The experimental result obtains by using this feature
to recognized Handwritten Devanagari Basic and
Compound Character is presented in next section. At this
stage the character goes through the pre-classification and
then the Legendre moment features are extracted.
The selected architecture of the network is a two layer
feed forward neural network with 108 neuron each. The
transfer function is log-sig. The network is trained with
Gradient Decent Backpropagation with adaptive learning
rate. The learning rate and momentum term are set to 0.7
and 0.5 respectively. The performance function uses sum
square error. The goal was set to 0.1 The network is trained
with moment feature until the sum squared error is 0.1
After training the network is ready to use for testing.
VI.

TABLE V.
Devanaga
ri Chara

RESULT AND DISCUSSION

FS1

FS2

FS3

FS4

98.75

98.46

98.52

90.25

98.86

98.55

98.54

91.27

98.87

98.64

98.62

90.54
91.25

98.85
98.75

98.57
98.71

98.56
98.52

FS3

FS4

97.57

97.45

94.85

98.76

97.86

98.55

93.55

98.72

97.52

98.54

93.68

98.85

97.64

98.65

94.88

98.75

97.85

98.74

VII. CONCLUSION
In this paper we have proposed handwritten Devanagari
Compound character recognition system from which
Legendre moment based features extracted and using simple
Feed Forward Neural Network the system is trained and
tested. We have obtained better result from the Legendre
moment based feature. It gives better result for basic and
compound character. As the image are partitioned in feature
set FS1,FS2,FS3 and FS4, the feature set FS2 have given
better result to all character as compared to other reference.
Further to get better result we are going to modify the
system with other orthogonal moment features set.
DevanagariBasicCharacterrecognitionin%

: RECOGNITION RATE OF SAMPLE DEVANAGARI BASIC


CHARACTER IN %
Feature Set
90.24

FS2

98.66

100

RecognitionRatein%

Devanaga
ri Char

FS1

94.25

Recognition performance for sample of handwritten


compound character is shown in Table 4. In this, the letter
have got average recognition rate as 97.56% and
from feature set FS2 has maximum 98.75% and minimum
as 94.88% from FS1. Next the character
have
highest average recognition rate i.e. 97.51% and from
feature set FS2 has given maximum 98.76% and minimum
98.55%. The feature set FS2 has gives overall better result
as compared to FS1, FS2 and FS3. Thus it can be conclude
that the recognition rate for all compound character is
98.36%.

The proposed system deals with the Handwritten


Devanagari basic and compound character the preparation
of training and testing set are as discussed in Section 3.1.
Results are shown in Table 2. The database consists of
12000 basic Devanagari characters from which we have
selected 9600 for training and 2400 for testing. The database
also consists of 11250 compound and 3750 split Devanagari
Character First structural pre-classification is done as
discuss in Section 3.2 and then moment based features are
extracted from feature set as discuss in Section 4. The
results are encouraging and average recognition accuracy is
98.25% is obtained.
TABLE IV.

:RECOGNITION RATE OF SAMPLE DEVANAGARI


COMPOUND CHARACTER IN %
Feature Set

95

FS1
FS2

90

From the sample of experiment conducted it can be


seen that the character ie has the average recognition rate
i.e. 96.85 so the highest recognition rate i.e. 98.87% for
feature set FS2, and lower rate is 91.27% for Feature set 1.

85

FS3
FS4
J

ye

ue

DevanagariCharacter

Fig 7. Comparison of Reco. Rate of Basic Character

Secondly from the selected sample the recognition rate for


we have got average recognition rates upto 96.81%
from the feature set the maximum recognition rate for it is
98.75% and minimum is 91.25%. From the feature set FS2
has a highest recognition rate for all character as compared

277

[19] Hamid Reza Boveiri, Persian Printed Numeral Character Recognition using
Geometrical Central Moments and Fuzzy Min Max Neural Network,
International Journal of Signal Processing, 2009, pp. 226 232.
[20] Hamid Reza Boveiri, Persian Printed Numeral Classification using Extended
Moment Invariants, World Academy of Science, Engineering and Technology
63, 2010, pp. 167-174.
[21] S.Arora, D. Bhattacharjee, M. Nasipuri, D.K.Basu, M. Kundu, Application of
Statistical Features in Handwritten Devanagari Character Recognition,
International Journal of Recent Trends in Engineering, Vol 2, No. 2, November
2009, pp. 40 42.
[22] R.Sanjeev Kunte and R.D.Sudhaker Samuel, A Simple and efficient optical
character recognition system for basic symbols in printed Kannada text,
Sadhana, Vol. 32, Part 5, October 2007, pp.21-533.
[23] S.N.Nawaz et. al., An approach to offline Arabic Character Recognition using
Neural Network, IEEE ICECS, 2003, pp. 1325 1331.
[24] S. Kumar, and C. Singh, A Study of Zernike Moments and Its Use in Devnagari
Handwritten Character Recognition. Proc. Intl. Conf. Cognition & Recognition,
Mandya (India), 2005, pp. 514 520.
[25] N. Sharma, U. Pal, F. Kimura, and S. Pal, Recognition of Offline Handwritten
Devnagari Characters Using Quadratic Classifier. Proc. Indian Conf. Computer
Vision Graphics & Image Processing, Madurai (India), 2006, pp. 805 816.
[26] M. Hanmandlu, O.V. Ramana Murthy, and V.K. Madasu, Fuzzy Model Based
Recognition of Handwritten Hindi Characters. Proc. Ninth Biennial Conf.
Australian Pattern Recognition Society on Digital Image Computing
Techniques & Applications, Glenelg (Australia), 2007, pp. 454 461.
[27] U. Pal, N. Sharma, T. Wakabayashi, and F. Kimura, Off-line Handwritten
Character Recognition of Devnagari Script. Proc. Ninth Intl. Conf. Document
Analysis & Recognition, Curitiba (Brazil), 2007, pp. 496 500.
[28] S. Arora, D. Bhattacharjee, M. Nasipuri, D.K. Basu, and M. Kundu, Combining
Multiple Feature Extraction Techniques for Handwritten Devnagari Character
ecognition. Proc. IEEE Region 10 Colloquium and Third Intl. Conf. Industrial &
Information Systems, Kharagpur (India), 2008.
[29] U. Pal, S. Chanda, T. Wakabayashi, and F. Kimura, Accuracy Improvement of
Devnagari Character Recognition Combining SVM and MQDF. Proc. Eleventh
Intl. Conf. Frontiers in Handwriting Recognition, Montreal (Canada), 2008 pp.
367 372.
[30] U. Pal, T. Wakabayashi, and F. Kimura, Comparative Study of Devnagari
Handwritten Character Recognition Using Different Feature and Classifiers.
Proc. Tenth Intl. Conf. Document Analysis & Recognition, Barcelona (Spain),
2009, pp. 1111 1115.
[31] S. Shelke, S. Apte, A Novel Multi-feature Multi-Classifier Scheme for
Unconstrained Handwritten Devanagari Character Recognition, 12th
International Conference on Frontiers in Handwriting Recognition, 2010.
[32] Baheti M. J., Kale K.V. Jadhav M.E. Comparison Of Classifiers For Gujarati
Numeral Recognition, International Journal of Machine Intelligence (IJMI),
Volume 3, Issue 3, 2011, pp-160-163.
[33] U. Pal, T. Wakabayashi, and F. Kimura, Handwritten Bangla Compound
Character Recognition using Gradient Feature, Proc. 10th Int. Conf.
Information Technology, Orissa, India, Dec. 17-20,2007, pp. 208-213.
[34] S. Shelke, S. Apte, A NovelMultistage Classification andWavelet Based
Kernel Generation For Handwritten Marathi Compound Character
Recognition, Proc. Int. Conf. Communications and Signal Processing, Kerala,
India, Feb. 10-12, 2011, pp. 193-197.
[35] S. Shelke, S. Apte, A Multistage Handwritten Marathi Compound Character
Recognition Scheme using Neural Networks and Wavelet Features,
International Journal of Signal Processing, Image Processing and Pattern
Recognition, vol. 4, no. 1, 2011, pp. 81-94.
[36] S. Saharia, P. K. Bora, and D. K. Saikia, .A comparative study on discrete
orthonormal Chebyshev moments and Legendre moments for representation
of printed characters,. in Proc. 4th ICVGIP, 2004, pp.491.496.
[37] Prokop RJ, Reeves AP. A survey of moment-based techniques for unoccluded
object representation and recognition. CVGIP: Graphical Models and Image
Process. 1992;54(5):438460.
[38] Teague MR. Image analysis via the general theory of moments. J Opt Soc Am.
1980;70:920930.

DevanagariCompoundCharacterRecognitionin%

Recognitionin%

100
98

FS1

96

FS2

94

FS3

92
90

kee

le

he

ue

Hee

FS4

DevanagariCompoundCharacter
Fig 8. Comparison of Reco. Rate of Compound Character
Reference
[1]

[2]

[3]
[4]
[5]
[6]
[7]

[8]

[9]

[10]
[11]
[12]
[13]

[14]

[15]

[16]

[17]

[18]

K. Roy, S. Vaidya, U. Pal, B. B. Chaudhuri, A. Belaid, A System for Indian


Postal Automation, Proc. 8th Int. Conf. Document Analysis and Recognition,
Seoul, Korea, Aug. 31-Sep. 1, 2005, pp.1060-1064.
U. Pal,R. K. Roy, K. Roy, F. Kimura, Indian Multi Script Full Pin-code String
Recognition for Postal Automation, Proc. 10th Int. Conf. Document Analysis
and Recognition, Barcelona, Spain, Jul. 26-29, 2009, pp. 456-460.
B. B. Chaudhari, Digital Document Processing - Major Directions and Recent
Advances, London:Springer, 2007.
U. Pal and B. B. Chaudhari, Indian Script Character Recognition: a Survey,
Pattern Recognition,vol. 37, 2004, pp. 1887-1899.
Sinha R.K., Mahabala 1979 Machine Recognition of Devnagari Script, IEEE
Trans. System Man Cyber Pgs 435-441
B. B. Chaudhuri and U. Pal, A complete printed Bangla OCR system, Pattern
Recognition, vol. 31, 1998, pp. 531-549.
K. Roy, T. Pal, U. Pal, and F. Kimura, Oriya Handwritten Numeral Recognition
System, Proc. 8th Int. Conf. Document Analysis and Recognition, vol. 2,
Seoul, Korea, Aug. 31-Sep. 1, 2005, pp. 770 774.
Arun Pujari, C. Dhanunjaya Naidu, M. Sreenivasa Rao, and B. C. Jinaga, An
Intelligent Character Recognizer for Telugu scripts using Multi resolution
Analysis and Associative Memory, Image and Vision Computing, vol. 22,
2004, pp. 1221-1227.
U. Bhattacharya, S. K. Ghosh, and S. K. Parui, A Two Stage Recognition
Scheme for Handwritten Tamil Characters, Proc. 9th Int. Conf. Document
Analysis and Recognition, Parana, Sept. 23-26, 2007, pp. 511 515.
B. B. Chaudhuri, and U. Pal, A Complete Printed Bangla OCR System,
Pattern Recognition, vol. 31, no. 5, 1998, pp. 531-549.
I.K. Sethi, and B. Chatterjee, Machine Recognition of Constrained Hand
Printed Devnagari.Pattern Recognition, vol. 9, no. 2, 1977, pp. 69 75.
V. Bansal, Integrating Knowledge Sources in Devanagari Text Recognition,
Ph.D. Thesis, IIT Kharagpur, 1999.
V. Bansal, R.M.K. Sinha, Partitioning and Searching Dictionary for Correction
of Optically Read Devanagari Character Strings, Proc. 5th Int. Conf.
Document Analysis and Recognition, Bangalore, India, Sept. 20-22, 1999, 6pp.
53-656.
V. Bansal, R. M. K. Sinha, On How to Describe Shapes of Devanagari
Characters and Use them for Recognition, Proc. 5th Int. Conf. Document
Analysis and Recognition, Bangalore, India, Sept. 20-22, 1999, pp. 410-413.
Reena Bajaj, Lipika Dey, and S. Chaudhury, Devnagari numeral recognition
by combining decision of multiple connectionist classifiers, Sadhana, Vol.27,
part. 1, 2002 pp.-59- 72.
P.M. Patil, T. R. Sontakke, Rotation, Scale and Translation Invariant
Handwritten Devanagari Numeral Character Recognition using General Fuzzy
Neural Network, Pattern Recognition, vol. 40, 2007, pp. 2110-2117.
L.C.Barczak,M.J.Johnson,C.H.Messom, Revisiting Moment Invariant: Rapid
Feature Extraction and Classification for Handwritten Digit, Proceeding of
Image and Vision Computing, Hamilton, New Zealand, December, 2007,
pp.137 142.
Duda, R.O.,Hart, P.E., Stork, D.G., Pattern Classification, Second ed. John
Wiley and Sons, Inc. 14, 2001.

278

You might also like