A METHOD FOR HANDWRITTEN CHARACTERS
RECOGNITION BASED ON A VECTOR FIELD
Tetsuya Izumi, Tetsuo Hattori, Hiroyuki Kitajima, Toshinori Yamasaki
Graduate School of Engineering, Kagawa University, 2217-20 Hayashi-Cho, Takamatsu City, 761-0396 Japan
Keywords: Handwritten Characters Recogni
tion, Feature Extraction, Vector Field and Fourier Transform
Abstract: In order to obtain a low computational cost method for automatic handwritten characters recognition, this
paper proposes a combined system of two rough classification methods based on features of a vector field:
one is autocorrelation matrix method, and another is a low frequency Fourier expansion method. In each
method, the representation is expressed as vectors, and the similarity is defined as a weighted sum of the
squared values of the inner product between input pattern and the reference patterns that are normalized
eigenvectors of KL (Karhunen-Loeve) expansion. This paper also describes a way of deciding the weight
coefficients based on linear regression, and shows the effectiveness of the proposed method by illustrating
some experimentation results for 3036 categories of handwritten Japanese characters.
1 INTRODUCTION
Since there are very many kinds of categories (or
pattern classes) in Japanese characters (Hiragana and
Chinese characters) and so there are many similar
patterns in those characters, it needs much
computational cost, i.e., computing time and
memory storage, to automatically recognize those
handwritten character patterns at high correct
recognition rate. For this problem, many researches
have been done in recent years (see References).
However, we consider that they still require
considera
bly high computation cost for the
automated recognition of all Japanese handwritten
characters. Therefore, in order to obtain a low cost
recognition system with high accuracy, we think we
still have to pursue simple and efficient rough
classification method based on more effective
feature extraction and similarity measure.
In this paper, we propose a recognition method
using a
vector field, aiming to effectively obtain the
feature information on directions of character lines
and their juxtaposition situation and so on.
Based on the feature point vector field, we
prese
nt two rough classification methods and the
combined one. The two rough classification methods
depend on different representations for the
distribution of feature point’s vectors: one is an
autocorrelation matrix and another Fourier
expansion on low frequency domain that can be
interpreted as a complex-valued function. In each of
the methods, the representation is expressed as high
dimensional vector, and the similarity is defined as a
weighted sum of the squared values of the inner
product between input pattern and the reference
patterns that are eigenvectors of KL (Karhunen-
Loeve) expansion.
This paper shows the effectiveness of the
pr
oposed combined method by giving the
experimental results that the correct recognition rate
of 92.2% for unknown pattern is obtained in 3036
categories of handwritten Japanese characters.
2 FEATURE EXTRACTION
2.1 Vector Field
After a distance transformation is done for the
binarized input pattern (Figure 1), and two-
dimensional vector field is constructed by (1), where
each vector corresponds to the gradient of the
distance distribution at each point P, as shown in
Figure 2. Let T(P) and V(P) be the value of distance
transformation and two-dimensional vector at the
point P, respectively. The V(P) is defined as follows.
417
Izumi T., Hattori T., Kitajima H. and Yamasaki T. (2004).
A METHOD FOR HANDWRITTEN CHARACTERS RECOGNITION BASED ON A VECTOR FIELD.
In Proceedings of the First International Conference on Informatics in Control, Automation and Robotics, pages 417-420
DOI: 10.5220/0001149004170420
Copyright
c
SciTePress
{}
i
i
i
eQTPTPV
=
=
8
1
)()()(
(1)
where,
i
(1 i 8) shows each point of the
eight neighborhood of point P, and
i
shows a
unit length vector in the direction from the point P to
.
Q
e
i
Q
(a) (b)
Figure 1:(a) Binarized pattern. (b) Distance transformation.
(64x64 pixels.)
Figure 2: Vector Field.
2.2 Normalization and Divergence
The length of each vector on the field is normalized
to be one or zero by a threshold. By divergence
operation on the field, source points and sink points
can be extracted as feature points. Those are called
flow-out point” and “flow-in point”, respectively.
Then at the same time, feature point vectors are
obtained (Figure 3), which are vectors on the source
points and sink points, what we call “flow-out point
vectors” and “flow-in point vectors”, respectively in
the same manner to the above naming.
Figure 3: Feature point's vector field.
As a characteristic property of the feature
point's vector field, flow-out and flow-in point
vectors are located on the character lines (or strokes)
and the background, respectively. They show not
only the directional information on the strokes but
also the juxtaposition situation of those strokes.
3 FEATURE REPRESENTATION
AND SIMILARITY
3.1 Outline
After the construction of the above feature point's
vector field, a combined method of two rough
classifications is performed. The two classifications
are based on different expressions of feature point's
vector field: one is Autocorrelation Matrix
Representation Method (AMRM) and another
Fourier expansion in low frequency domain method
(shortly we call Low Frequency Domain Method
(LFDM)).
3.2 Autocorrelation Matrix
Representation Method (AMRM)
The neighborhood vector pattern X of a feature point
vector, i.e., 2-dimensional vectors on 3x3 points
centering the feature point, can be represented as a
9-dimensional complex vector in which each
complex-valued component means 2-dimensional
vector. So, the X can also be regarded as an 18-
dimensional real vector. In order to express the
neighborhood pattern X effectively, we use an
orthonormal (orthogonal and normalized) system
that can be made from a set of nine typical
neighborhood patterns by well-known Gram-
Schmidt’s Orthogonalization Method (GSOM).
Actually, an orthonormal basis
(i=1,…, 6) is
obtained by the GSOM.
}{
i
µ
Then, we can represent the neighborhood vector
pattern X of a feature point P as the following 8-
dimensional real vector
)(P
χ
, using the coordinate
i, jof the point P and a set of the real-valued
inner products between the neighborhood pattern
and each element of the above orthonormal system,
i.e., {
µ
i
X |
}.
(
)
T
XXjiP =
61
|,,|,,)(
µµχ
L
(2)
So, a set of {
)(P
χ
} is extracted from the feature
point vector field. Then, we express the distribution
of the set of {
)(P
χ
} in the 8-dimensional real
vector space by an autocorrelation matrix in 8x8 size.
ICINCO 2004 - ROBOTICS AND AUTOMATION
418
Because the matrix is symmetric, it can be
corresponded to a 36-dimensional real vector.
3.3 Low Frequency Domain Method
(LFDM)
In this method, as a representation of input pattern,
the Fourier expansion on the low frequency domain
is used after the Fourier transform over the feature
point vector field. The Fourier transform is
described as follows. Let
x
and be two 2-
dimensional real positional vectors on a real plane
and the frequency domain, respectively. The Fourier
transform
of the input pattern or complex-
valued function
is defined in the following (3).
ω
)(ωF
)(xf
)()()(
|
xdexfF
R
xj
µ=ω
ω
2
(3)
where j and
mean an imaginary number unit
and an area element, respectively.
)(xµd
For example of the Fourier transform, a
character pattern and its amplitude spectrum image
on the frequency domain are shown in Figure 4. In
this figure, we can see that much information of the
input pattern is in the low frequency domain (near
the center of the image).
Figure 4: Input pattern (left, the same pattern in Figure
1(a)) and its amplitude Fourier spectrum image (right)
where the original point is the center of the image.
Actually, as a feature representation of input
pattern, we use the information on 10×10 points
around the original point in the frequency domain of
the Fourier transform from the feature point vector
field. Therefore, an input pattern is corresponded to
a 100-dimensional complex vector.
3.4 Reference Pattern and Similarity
As aforementioned, an input pattern is represented
as a correspondent feature vector in each of the two
classification methods. Then, an orthonormal basis
(or orthonormal set) is made from eigenvectors of
KL (Karhunen-Loeve) expansion for learning
samples of each character pattern class (or category).
The elements of the orthonormal basis are used as
reference patterns for the category.
The similarity between input pattern and each
category is defined as a weighted sum of the squared
values of inner product between the feature vector
and the reference patterns belonging to the category,
as in the following (4).
Let f and g be an input pattern (or feature
vector) and a category, respectively. Let
{g
k
i
}(i=1,…,n)(k=1,…,m) be a set of reference
patterns of the category g
k
, and let sim(f, g
k
) be the
similarity between f and g
k
, the definition is given
by (4).
=
×
=
n
i
k
ii
k
f
gfW
gfsim
1
2
2
|
),(
(4)
where
= fff |
, ( , i=1,…,n)
shows one of weight coefficients
i
W 0>
i
W
4 DECISION OF WEIGHT
COEFFICIENT
After the similarity computation, input pattern is
classified into a category that gives the highest
similarity in the above computation. Therefore, the
weight coefficient is very influential in the similarity
evaluation. In many cases, a set of the coefficients is
defined by the eigenvalues of the KL expansion as in
the following (5), what we simply call
Eigenvalue
Similarity
.
1
λ
λ
=
i
i
W
(5)
where
i
λ
(
0>
λ
i
, i=1,…, n) shows the i-th largest
eigenvalue in the KL expansion.
However, from our experiences in this kind of
character recognition, the largest eigenvalue is often
much greater than the other eigenvalues, and so the
similarity is decided by the first term of the inner
product between the input and the first reference
pattern. As a result, the recognition rate is
sometimes worse than the case when
W
=1 for all i.
i
In order to decide the suitable weight
coefficients for good recognition rate, we have
adopted an iteration method based on a linear
regression model, starting the initial condition that
i
=1 for all i. And, substituting the product of old
and new coefficient into
i
W
, (i.e.,
ii
),
the updated coefficients are obtained. Thus, we can
iteratively search the suitable coefficients. The
iteration terminates when no improvement of the
recognition rate can be seen.
W
WWW
*
A METHOD FOR HANDWRITTEN CHARACTERS RECOGNITION BASED ON A VECTOR FIELD
419
5 EXPERIMENTATION
The aforementioned two classification methods are
combined by using a synthesized similarity as
defined in (6). Let
x and y be the similarity value
between the input pattern and each category in the
AMRM and LFDM, respectively. The following
sum of squared similarity (like Euclid norm) is used.
S_Similarity =
(6)
22
yx +
Thus we have experimented the above three
kinds of methods for 3036 categories of Japanese
handwritten characters (total number of character
patterns: 3036 x 20 patterns per category = 60,720)
in ETL9B (Electro Technical Laboratory in Japan)
database. The data used for experimentation includes
not only Chinese characters but also Japanese
Hiraganas.
In the experimentation, 10 samples (or character
pattern) per category were used for learning, i.e.,
decision of reference patterns and the weight
coefficients. Therefore, they are what we call
learning patterns. Actually, we have decided that the
number of the reference patterns (or eigenvectors of
KL expansion) per category is eight, because the
number has been the most effective for recognition
of the learning patterns used in experimentation. The
rest 10 patterns are experimented as
unknown
pattern
.
The specification of the computer, OS, etc. that
we used in this experimentation is as follows.
OSMicrosoft Windows XP Professional.
CPUIntel Pentium(2.4GHz).
Main memory1024Mbytes.
Programming language: Borland C++5.02J.
The experimental results are shown in Table 1
through 3. In order to compare the effects of three
kinds of weight coefficient, i.e., no weight (
i
=1
for all
i ), eigenvalue, and weight coefficient decided
by the linear regression model, the results in the
three cases are also shown in the tables.
W
Table 1: Recognition rate by the AMRM.
Weight
Coefficient
Input Pattern
N
o
Weight Eigenvalue
Linear
Regression
Model (LRM)
Learning Pattern 94.01% 68.13% 94.23%
Unknown Pattern 60.72% 60.10% 71.91%
Execution time in LRM: 48 msec/pattern.
Required storage: 6.6 Mbytes.
Table 2: Recognition rate by the LFDM.
Weight
Coefficient
Input Pattern
N
o
Weight Eigenvalue
Linear
Regression
Model (LRM)
Learning Pattern 99.92% 91.83% 99.61%
Unknown Pattern 85.79% 81.30% 87.24%
Execution time in LRM: 66 msec/pattern.
Required storage: 18.5 Mbytes.
Table 3.: Recognition rate by the combined method.
Weight
Coefficient
Input Pattern
o Weigh
Eigenvalue
Linear
Regression
Model (LRM)
Learning Pattern 99.93% 95.62% 99.81%
Unknown Pattern 90.13% 89.45% 92.20%
Execution time in LRM: 68 msec/pattern.
Required storage: approximately 25 Mbytes.
6 CONCLUSION
We have presented two classification methods and a
combined one for handwritten characters recognition
using features of the vector field. We have also
presented a set of weight coefficients in the
similarity, using the linear regression model (LRM).
Moreover, we have revealed the experimental results.
From the results, we can see that it is very effective
to use the feature of the vector field and the decision
of weight coefficients based on LRM. Therefore,
we consider that the feature point’s vector field
method is promising and worthwhile refining in
order to find more effective and low computational
cost (in the sense of time and storage) method.
REFERENCES
Masato S. et al., 2001. A Discriminant Method of Similar
Characters with Quadratic Compound Function,
IEICE Transactions, Vol.J84-D2, No.8, pp.1557-
1565, Aug. 2001 (in Japanese).
Takashi N. et al., 2000. Accuracy Improvement by
Compound Discriminant Functions for Resembling
Character Recognition, IEICE Transactions, Vol.J83-
D2, No.2, pp.623-633, Feb. 2000 (in Japanese).
Kazuhiro S. et al., 2001. Accuracy Improvement by
Gradient Feature and Variance Absorbing Covariance
Matrix in Handwritten Chinese Character
Recognition, IEICE Transactions, Vol.J84-D2, No.11,
pp.2387-2397, Nov. 2001 (in Japanese).
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