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

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

 SciTePress

{}

eQTPTPV ⋅

∑

−=

)()()(

(1)

where,

(1≦ i≦ 8) shows each point of the

eight neighborhood of point P, and

shows a

unit length vector in the direction from the point P to

(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.

}{

Then, we can represent the neighborhood vector

pattern X of a feature point P as the following 8-

dimensional real vector

)(P

, using the coordinate

（i, j）of 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., {

〉

〈

X |

(

)

XXjiP 〉〈〉〈=

|,,|,,)(

µµχ

(2)

So, a set of {

)(P

} is extracted from the feature

point vector field. Then, we express the distribution

of the set of {

)(P

} in the 8-dimensional real

vector space by an autocorrelation matrix in 8x8 size.

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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

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).

)(ωF

)(xf

)()()(

xdexfF

µ=ω

∫

〉ω〈−

(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

}(i=1,…,n)(k=1,…,m) be a set of reference

patterns of the category g

, and let sim(f, g

) be the

similarity between f and g

, the definition is given

by (4).

∑

〉〈×

gfW

gfsim

),(

(4)

where

〉〈= fff |

, ( , i=1,…,n)

shows one of weight coefficients．

W 0>

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

(5)

where

(

, 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

=1 for all 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

=1 for all i. And, substituting the product of old

and new coefficient into

, (i.e.,

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.

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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)

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.

OS：Microsoft Windows XP Professional.

CPU：Intel PentiumⅣ(2.4GHz).

Main memory：1024Mbytes.

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 (

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.

Table 1: Recognition rate by the AMRM.

Weight

Coefficient

Input Pattern

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

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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