Te-Wei Chiang

Tienwei Tsai

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A Statistical Mask-Matching Approach for Recognizing 
Handwritten Characters in Chinese Paleography∗
Te-Wei Chiang 
Department of Accounting Information Systems 
Chihlee Institute of Technology 
Taipei, Taiwan, R.O.C. 
ctw@mail.chihlee.edu.tw 
Tienwei Tsai 
Department of Information Management 
Chihlee Institute of Technology 
Taipei, Taiwan, R.O.C. 
twt@mail.chihlee.edu.tw 
                                                          
∗ 0-7803-8566-7/04/$20.00 © 2004 IEEE. 
Abstract - Because most of the characters in the rare 
books transcribed by ancient calligraphers were 
contaminated by noise, to retrieve information from these 
books, we resort to the statistical approach instead of the 
structural approach.  In our approach we generate one 
positive mask and one negative mask for each distinct 
class of characters in the training phase.  The positive 
mask of a class of characters is built by finding the bits of 
the character images that are reliably black.  Likewise, the 
negative mask is built by finding the bits that are reliably 
white.  Then, we can recognize an unknown character by 
finding the prototype character whose masks are best 
fitted for the unknown character.  Experimental results 
show that our approach performs well in this application 
domain. 
Keywords: Handwriting recognition, classification, mask-
matching approach. 
1 Introduction 
In ancient Chinese a lot of significant books were 
transcribed by elite calligraphers.  Even though the 
characters in these rare books were handwritten in regular 
forms, their integrity is greatly damaged by various 
imperfections.  The strokes are of various thicknesses, 
even within the confines of a single character.  
Additionally, characters accompanied by spots and smears 
outside the theoretical limits of the characters and voids 
within them produce enormous variations in their shapes, 
even though they remain legible to human readers. 
In order to retrieve information from these books, 
transforming paper documents into the contents that are 
accessible is inevitable.  One way of digitizing the 
contents of documents is through human typing.  However, 
this kind of labor-intensive approach is not only time 
consuming, but also expensive.  For over the last decade, 
optical character recognition (OCR) technique [10] has 
been introduced as a practical approach for converting 
paper documents into computer codes.  There are two 
distinct philosophies of OCR in general, known as 
“statistical” and “structural”.  In the statistical approach 
the measurements that describe an object are treated only 
formally as statistical objects (variables), neglecting their 
“meaning”.  On the other hand, structural information has 
long been suggested as a useful feature for OCR [1], [11] 
since it contains all the units of characters.  The structural 
approach attempts to recognize characters the same way 
we generate them – as a sequence or at least a combination 
of strokes, straights lines, and curves.  In practice, few 
algorithms can consistently extract structural information 
from characters and most structural matching approaches, 
however, depend largely on the correctness of the 
structural information.  Moreover, most of the characters 
in these rare books were contaminated by various noises.  
It makes the structural approach inapplicable.  Therefore, 
we resort to the statistical approach.   
In the literature, some methods had proposed for 
OCR, such as methods based on neural networks (NNs) 
[2], [6], graph-matching methods [5], and methods based 
on hidden Markov model [9], etc.  Due to the ease of 
realization, neural networks seem to be the most popular 
method; however, its result is not as good as the basic 
nearest neighborhood method [14], especially in the 
recognition of characters with low quality.  Even though 
graph-matching method has strong theoretically 
background, its effect is not satisfactory because of the 
difficulty in combination with feature extraction methods.  
Methods based on hidden Markov model have been 
employed to cope with the recognition of connected 
characters (such as English characters).  However, Chinese 
handwriting recognition is much more difficult than 
alphabetic characters.  The difficulty is due to three factors: 
the character set is very large, the structure of a Chinese 
character is much more complex than that of an alphabetic 
character, and many Chinese characters have similar 
shapes. 
A survey of optical recognition of handwritten 
Chinese characters can be found in [4].  Handwriting 
recognition is divided into online [5] and offline [2], [6], 
[12] categories.  The online recognition takes the 
advantage of capturing the temporal and dynamic 
information of handwriting, such as the number of strokes, 
the order of the strokes, the direction of the writing for 
each stroke, and the speed of the writing within each 
stroke.  As contrasted with online recognition, the offline 
case is much more difficult because it lacks the above 
mentioned knowledge.  In this paper, we focus on offline 
recognition.   
“Mask matching” is the most obvious technique for 
visual pattern recognition.  Imagine the unknown image 
being projected through a cutout (mask) onto a 
photosensor array.  The response will be proportional to 
the degree of matching.  Based on this concept, we can 
store a mask in the computer for each distinct class of 
characters to be recognized, and to compare the unknown 
characters with the stored set to find the best matching.  
Since the scanned characters are supposed to be two-
tone – all black on white backgrounds.  The matching 
degree can be calculated by counting their matching bits, 
which is known as the Hamming distance criterion.  
However, this kind of global Boolean mask is unreliable.  
It is because the bits along the edge of a character image 
are often subject to unpredictable variations and noises.  
Based on above observations, we were motivated to 
devise a statistical mask-matching approach for 
recognizing handwritten characters in Chinese 
paleography.  In our approach we generate one positive 
and one negative mask for each distinct class of characters 
in the training phase.  We superimpose a number of 
images of the “same” character and calculate the fraction 
of time that a given bit is black.  The bits that are reliably 
black are served as the positive mask.  In other words, the 
positive mask is built by finding the core bits of the 
character images.  The core bits are the most central and 
reliable bits, shielded from the edge noise by lying deep 
within the characters.  In contrast, the negative mask is 
built by finding the bits that are reliably white.  Then, we 
can recognize an unknown character by finding the 
prototype character whose masks are best fitted for the 
unknown character.  Experimental results show that our 
approach performs well in this application domain. 
This paper is organized as follows.  The next section 
introduces how we generate positive and negative masks.  
Section 3 describes our statistical mask matching approach.  
Section 4 presents experimental results. Finally, 
conclusions are drawn in Section 5. 
Figure 1. Normalized sample data. 
 
 (a)  (b)  (c) 
Figure 2. Mask generation.  (a) Superimposed characters. 
(b) The positive mask. (c) The negative mask.
2   Mask generation 
Before getting into the main topic, let us consider 
briefly the normalization issue.  The mask matching 
method can be regarded as a variant of the template 
matching method.  In the template matching method, 
usually, normalization of position and size is done prior to 
the matching process [7], [13].  Template matching is 
based on the assumption that the position of each point is 
known, the correspondence of the sampling point is 
already taken, and the similarity is measured only by the 
difference of the sampling “value”.  Therefore, the 
normalization process becomes very important in order to 
fix the sampling position in advance.  Before our 
classification process, we use a simple geometrical 
transformation to “normalize” the circumscribed rectangle 
about a handwritten character to make the shapes of the 
given characters more uniform.  Figure 1 shows four 
normalized sample data extracted from the rare books.  
We can find that the left two characters are clear and the 
others are contaminated.  
We know that the border bits are the most unreliable; 
the bits at the edge of a character image are often subject 
to writing and scanning noise.  We can see this by 
superimposing a number of images of the “same” 
character and calculating the fraction of time that a given 
bit is black.  What we need to find are those bits that are 
reliably black in certain characters and reliably white in 
others.  For example, if we superimpose the same four 
characters (means “Buddha”), we obtain the result of 
Figure 2.  From Figure 2(a) we see that the unreliable bits 
are along the edges.  The darkest bits in the figure 
represent the bits that are the most reliably black, i.e., the 
darker the bits are the more reliably black the bits are.  
Then, the darkest bits form a positive mask of, as shown in 
Figure 2(b), and the pure white bits generate a negative 
mask (see Figure 2(c)). 
In the general case we use thresholds α and β to 
define the meaning of “reliably black” and “reliably 
white”, respectively.  For example, as α = 0.9, a bit is 
regarded as reliably black when the percentage of the 
corresponding bits of the superimposed characters is above 
90%. 
3 Statistical mask-matching approach 
Most commonly used optimization methods in 
statistical approach are based on Bayes’ theorem.  Our 
mask-matching approach is also derived from Bayes’ 
theorem. 
3.1   Bayes classificaton 
In statistical pattern recognition, we recognize that 
features may be measured with error and that some of the 
features are useful for identification of the class while 
others are not.  Our goals are then to obtain useful sets of 
features and to use these features such that the 
identification is as accurate as possible.   If there is an 
object that is to be classified on the basis of a feature x, 
into N possible classes (c1, c2, …, cN), then the probability 
of x in class i when x is observed can be described by 
P(ci|x).  From the “theorem on compound probabilities” 
[3], we obtain 
P(x&y) = P(x|y)•P(y) = P(y|x)•P(x)        (1) 
 In our situation, x is the feature and y represents the 
class variable ci.  Substituting for x and y in Eq. (1), we 
obtain the probability that the class is i when the feature x 
is observed. 
)(
)()|()|(
xP
cPcxPxcP iii =       (2) 
This is Bayes’ theorem, which gives the probability 
of a class i being present when a feature x is observed, 
provided we know the probability of the feature being 
observed when the class is present, the probability of that 
class being present, and the probability of that feature. 
3.2   Measures for mask matching 
        Before the mask-matching process, we have to define 
a measure to indicate the degree of matching between a 
sample character and a mask. 
        Suppose the character images and the masks are of 
the same size ( nn× bitmap).  The black bits are those bits 
with value 1 in the bitmaps, and white bits are those with 
value 0.  Let Nb(p) be the number of black bits in bitmap p, 
and Mb(p, q) be the number of black bits with the same 
positions in both bitmap p and bitmap q.  Then, the degree 
of matching between an unknown character x and the 
positive mask of class i, , can be defined by: im+
            
)(
),(
),( i
b
i
bi
mN
mxM
mxd
+
+
++ =               (3) 
Similarly, let Nw(p) be the number of white bits in 
bitmap p, and Mw(p, q) be the number of white bits with 
the same positions in both bitmap p and bitmap q.  Then, 
the degree of matching between character x and the 
negative mask of class i, , can be defined by: im−
              
)(
),(
),( i
w
i
wi
mN
mxM
mxd
−
−
−− =              (4) 
Definition 1.  If x matches to the positive mask of class i at 
the degree of α, i.e., .  It is 
called x α-match the positive mask of class i, 
and denoted by . 
α=++ ),(
imxd
ix +α
Definition 2.  Similarly, if x matches to the negative mask 
of class i at the degree of β, i.e., 
.  It is called x β-match the 
negative mask of class i, and denoted by 
. 
β=−− ),(
imxd
ix −β
3.3   Statistical mask-matching 
If there is an unknown character x that is to be 
classified on the basis of its matching result into one of N 
possible classes (c1, c2, …, cN), then the probability of x in 
class i when  is observed can be described by 
.  From Bayes’ theorem, we get 
ix +α
)|( ii xcP +α
)(
)()|()|( i
ii
i
i
i xP
cPcxPxcP
+
+
+ =
α
α
α
     (5) 
This equation gives the probability of a class i being 
present when the positive mask of the class is matched, 
provided we know the probability of the mask being 
matched when the class is present, the probability of that 
class being present (called the “prior probability”), and the 
probability of that mask being matched.  Similarly, we get 
)(
)()|(
)|( i
ii
i
i
i xP
cPcxP
xcP
−
−
− =
β
β
β
                (6) 
Finally, to decide the expected class of the input 
pattern x, the following decision rules are used: 
1) Rule PMD (Positive Matching Degree):  
E(x) = arg max1 ≤ i ≤ N { }         (7) ),( imxd ++
2) Rule NMD (Negative Matching Degree):  
E(x) = arg max1 ≤ i ≤ N { }     (8) ),( imxd −−
3) Rule PMP (Positive Matching Probability):  
E(x) = arg max1 ≤ i ≤ N {  }     (9) )|( ii xcP +α
4) Rule NMP (Negative Matching Probability):  
E(x) = arg max1 ≤ i ≤ N {  }   (10) )|( ii xcP −β
5) Rule AMP (Average Matching Probability):  
E(x) = arg max1 ≤ i ≤ N { ( ) 2/)|()|( iiii xcPxcP −+ + βα } (11) 
where  and . ),( imxd ++=α ),(
imxd −−=β
      The concept underlying rules PMD and NMD is very 
intuitively.  The class whose mask matches the input 
pattern most will be regarded as the expected class of the 
input pattern.  On the other hand, rules PMP and NMP 
select the most likely class as the expected class of the 
input pattern according to the probability of the class being 
present when its mask is matched.  As to rule AMP, it 
takes average of the probabilities evolved from the 
positive and negative masks of a class.  Through the 
combination of different viewpoints, we expect AMP will 
outperform the other rules. 
4 Experimental results 
A preliminary experiment has been made to test our 
approach.  There are a total number of 6000 samples 
(about 500 categories) extracted from one of the famous 
handwritten rare books, Kin-Guan bible.  Each character 
pattern was transformed into a bitmap pattern by 
means of simple size normalization.  The positive and the 
negative masks for each character category were generated 
by superimposing the character patterns of the same 
category.  The thresholds α and β used to generate masks 
are equal to 0.8.  1000 of the 6000 samples are used for 
testing.  Table I shows the recognition rate for each 
decision rule.  As we expected, AMP outperforms the 
other rules.  It is worthy of notice that NMD performs 
better than most of the other rules. 
2020×
5 Conclusions 
This paper presents a statistical mask-matching 
approach for recognizing handwritten characters in 
Chinese paleography.  After generating the masks for each 
prototype character
probabilities in advan
class being present w
In our preliminary e
rate is about 88 perc
percent for multichoic
Since only prelim
test our approach, a
improve this system: 
Recognition R
Decision Rule
T
PMD 76
NMD 85
PMP 82
NMP 83
AMP 87
 For accurate 
require at le
Thus in the 
say 4×4mm,
character 40×
current 20×2
 Since feature
another in c
features of 
classification
 In order to 
recognition, 
involved in o
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A Statistical Mask-Matching Approach for Recognizing Handwritten Characters in Chinese Paleography *

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A Statistical Mask-Matching Approach for Recognizing Handwritten Characters in Chinese Paleography *

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