RESEARCHCONTRIBUTIONS
Image Processing
and Computer
Vision
Robert M. Haralick
Editor
A Fast Parallel Algorithm for
Thinning Digital Patterns
T. Y. ZHANG and C. Y. SUEN
ABSTRACT: A fast parallel thinning algorithm is proposed
in this paper. It consists of two subiterations: one aimed at
deleting the south-east boundary points and the north-west
corner points while the other one is aimed at deleting the
north-west boundary points and the south-east corner
points. End points and pixel connectivity are preserved.
Each pattern is thinned down to a "skeleton" of unitary
thickness. Experimental results show that this method is
very effective.
1. INTRODUCTION
It is well known that the general problem of pattern
recognition lies in the effectiveness and efficiency of
extracting the distinctive features from the patterns.
The stroke analysis method is a powerful approach to
recognizing certain types of digital patterns such as alphanumeric characters and ideographs. It should be
noted that the strokes thinned by hardware or software
are accompanied by different kinds of distortion. Different thinning algorithms produce different degrees of
distortion [1-5, 7-12].
There is no general agreement in the literature on an
exact definition of thinness. Pavlidis [6] describes a
thinning algorithm that determines skeletal pixels by
local operations. At the same time, the pixels are labeled so that the original image can be reconstructed
from its skeleton. The goal of this paper is to find a
© 1984 ACM 0001-0782/84/0300-0236 75¢
236
Communications of the ACM
faster and more efficient parallel thinning algorithm.
The distortion should be as little as possible. Experimental results indicate that this method can be used to
thin a variety of digital patterns.
2. PARALLEL PICTURE PROCESSING
A binary digitized picture is defined by a matrix IT
where each pixel IT(i, j) is either 1 or 0. The pattern
consists of those pixels that have value 1. Each stroke
in the pattern is more than one element thick. Iterative
transformations are applied to matrix IT point by point
according to the values of a small set of neighboring
points. It is assumed that the neighbors of the point (i, j)
are (i - 1, j), (i - 1, j + 1), (i, j + 1), (i + 1, j + 1),
(i + 1, j), (i + 1, j - 1), (i, j - 1), and (i - 1, j - 1), as is
shown in Figure 1. In parallel picture processing, the
new value given to a point at the nth iteration depends
on its own value as well as those of its eight neighbors
at the (n - 1)th iteration, so that all picture points can
P,
(i- 1, j- 1)
P2
(i- 1, j)
P3
(i- 1, j+ 1)
P,
P1
(i, j)
P,
P~
Pe
Ps
(i+ 1 , j - 1)
(i+ 1,j)
(i+ 1,j+ 1)
(i, j -
1)
(i,j+
1)
FIGURE 1. Designations of the nine pixels in a 3 x 3 window.
March 1984
Volume 27
Number 3
Research Contributions
be p r o c e s s e d s i m u l t a n e o u s l y . It is a s s u m e d t h a t a 3 x 3
w i n d o w is used, a n d t h a t e a c h e l e m e n t is c o n n e c t e d
w i t h its e i g h t n e i g h b o r i n g e l e m e n t s . T h e a l g o r i t h m presented in this paper requires only simple computations.
In t h e s e c o n d s u b i t e r a t i o n , o n l y c o n d i t i o n s (c) a n d (d)
are c h a n g e d (Figure 3) as follows:
(c') P2*P4*P8
(d') P2*P6*P8
3. T H I N N I N G A L G O R I T H M
O u r m e t h o d for e x t r a c t i n g t h e s k e l e t o n of a p i c t u r e
consists of r e m o v i n g all t h e c o n t o u r p o i n t s of t h e pict u r e e x c e p t t h o s e p o i n t s t h a t b e l o n g to t h e s k e l e t o n . In
o r d e r to p r e s e r v e t h e c o n n e c t i v i t y of t h e s k e l e t o n , w e
d i v i d e e a c h i t e r a t i o n into t w o s u b i t e r a t i o n s .
In t h e first s u b i t e r a t i o n , t h e c o n t o u r p o i n t P1 is del e t e d from t h e digital p a t t e r n if it satisfies t h e f o l l o w i n g
conditions:
=
=
0
0
a n d t h e rest r e m a i n t h e same.
By c o n d i t i o n s (c) a n d (d) of t h e first s u b i t e r a t i o n , it
will be s h o w n t h a t t h e first s u b i t e r a t i o n r e m o v e s o n l y
t h e s o u t h - e a s t b o u n d a r y p o i n t s a n d t h e n o r t h - w e s t corn e r p o i n t s w h i c h do not b e l o n g to a n ideal s k e l e t o n .
T h e p r o o f for t h e first s u b i t e r a t i o n is given, t h a t is,
t h e p o i n t s to b e d e l e t e d satisfy c o n d i t i o n s :
(a) 2 _< B(P1) -< 6
0
(C) P2*P4*P6 = 0
(d) P4*P6*P8
:
P~
0
1
I
0
0
\2 J
is t h e n u m b e r of n o n z e r o n e i g h b o r s of
FIGURE 2. Counting the 01 patterns in the ordered set P2, P~, P4,
.... P~, P~.
P1,
North
t h a t is,
P2
B(P1) = P2 + P3 + P4 + • • • + P8 + P9.
West
Pa
Pl
If a n y c o n d i t i o n is not satisfied, e.g., t h e v a l u e s of P2,
P3, P4, • • - P9 as s h o w n in Figure 2, t h e n
Pa
FIGURE 3. Pointsunder consideration and their locations•
T h e r e f o r e , P~ is n o t d e l e t e d from t h e p i c t u r e .
.@~.~•
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.
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o . . . . . .
(a)
East
P4
South
A(Pi) = 2
°•o
I
1
0
=
w h e r e A(P1) is t h e n u m b e r of 01 p a t t e r n s i n t h e o r d e r e d
set P2, P3, P4, - • - P8, P9 t h a t are t h e eight n e i g h b o r s of
P1 (Figure 1), a n d
B(Pi)
0
i
(b) A(P~)= 1
. • ° . . . .
.@@@@88@
.8@@8@@@
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• 8@@@8@@
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. . . .
@°
.'.
.°
.@
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~o
.•
• °
o@.,°°
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°°
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..@
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.8@@@@@@@@@~8@@8@#@@@
....
• .@ . . . . . . . . . . . . . . . . . .
@. . . .
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. . . . . . . . . . . . . . . . . .
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8...
..................
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(b)
(c)
FIGURE 4. Resultsof thinning the character 'H' by the subiterations.
March 1984 Volume 27 Number 3
Communications of the ACM
237
Research Contributions
(c)
P2*P4*P6 = 0
(1)
(d)
P4*P6*P8 = 0
(2)
0
O--
0
I
I
I
The solutions to the set of equations (1) and (2) are P4
= 0 or P6 = 0 or (P2 = 0 and Ps = 0). So the point P1,
which has been removed, might be an east or south
boundary point or a north-west corner point. Similarly,
it can be proved that the point P1 deleted in the second
subiteration might be a north-west boundary point or a
south-east corner point. For example, the results of
processing the character "H" by both subiterations are
shown in Figure 4(a) and 4(b). The points marked by
" . " have been removed. The final result is shown in
Figure 4(c).
By condition (a), the endpoints of a skeleton line are
preserved. Also, condition (b) prevents the deletion of
those points that lie between the endpoints of a skeleton line, as shown in Figure 5. The iterations continue
until no more points can be removed.
A flowchart of the proposed thinning algorithm is
shown in Figure 6. Initially, the original picture is
stored in matrix IT and a counter C is set to 0. The
result of the processed picture is stored in matrix IT. To
save m e m o r y space, only two matrices, IT and M, are
used in our computation.
Figures 7(a)-7(c) show the results obtained by our
algorithm for a Chinese character "@," a letter "B,"
and a digital "moving body," respectively. Skeleton
points are marked by "*," or "@," and all those points
that have been deleted in the thinning process are
marked by " - . "
The above algorithm yields very good results with
respect to both connectivity and contour noise immunity. Furthermore, the conditions for searching those
points that should be deleted from the pattern are very
simple. In order to assess the performance of our algorithm, we have chosen one given by Stefanelli and Rosenfeld [11] for comparison. Both algorithms were written in FORTRAN, run on the same CDC Cyber 172
computer, and tested with the same digitized patterns.
The result shows that the execution time of our algorithm is only 50 percent of the one given [11]. As can
be predicted, the execution time depends on the complexity of the pattern and the thickness of the strokes:
0.505 CPU seconds for the Chinese character " ~ " 0.454
CPU seconds for the letter "B" and 1.163 seconds for
the moving body.
0
i
1
I
1
1
0
,0
0
0
0
1
1
I
1
;
0
O.
0
0 ~ 0
I
1
1
I
0 ~ 0
0
FIGURE 5. Preventin9 the deletion of endpoints.
Start
I
l
)
C=O
Search M (satisfied
the conditions of the
first subiteration)
C = C+l, ifM(i,j) = 1
IT = IT - M
Yes
C=O
Search M (satisfied
the conditions of the
second subiteration)
C = C + 1, if M(i,j) = 1
IT = IT - M
TABLE I. Comparison of CPU Time (in seconds) Consumed by
Different Parallel Thinning Algorithms
Pattern
B
•~
Movingbody
238
Method
Yes
Four-Step
Two-Step
Our Algorithm
0.765
1.031
2.713
0.678
0.882
2.221
0.454
0.505
1.163
Communications of the ACM
FIGURE 6. Flowchart of the thinning algorithm.
March 1984 Volume 27 Number 3
Research Contributions
. . •
~
..,.---
...
. .
......
•
.....
,i .......
1,2
~i
*,,;;'.
'~,2
..... ; ............
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•
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iii
.....
ottt
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°
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.
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•
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•
~
~2j,~
~ .... ~
•
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. .@..
.
@..
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. .@@..
222,1
~.2.
"~;;22
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.....
@..........
@@..
..@@@@@@@@@@@@@@@@..
oo•
. . . . . .
(a)
::~;::::
• . • • o ~ o o •
(c)
(b)
FIGURE 7. Thinning of different digital patterns.
4. S U M M A R Y
A parallel algorithm for thinning different types of digital patterns is presented in this paper. Each iteration is
divided into two subiterations that remove the boundary and corner points of the digital patterns. After several iterations, only a skeleton of the pattern remains.
The proposed algorithm appears to be very efficient
in the thinning of digital patterns and it compares favorably with those described in [11]. The results in
Table I indicate that our method is 1.5 to 2.3 times
faster than the four-step and two-step methods described in [11] while the resulting skeletons look very
much the same.
REFERENCES
1. Arcelli, C., Cordelia, L.P. and Levialdi, S. From local maxima to
connected skeletons. IEEE Trans. Pattern Analysis and Machine Intell.
PAMI-3 (March 1981), 134-143.
2. Arcelli, C. A condition for digital points removal. Signal Processing 1,
4 (1979), 283-285.
3. Deutsch, E.S. Thinning algorithms on rectangular, hexagonal, and
triangular arrays. Commun. ACM 15, 9 (Sept. 1972), 827-837.
4. Hilditch, C.J. Linear skeletons from square cupboards. In: Machine
Intelligence IV, B. Mertzer and D. Michie, Eds., University Press,
Edinburgh, 1969, pp. 403-420.
5. Ogawa, H. and Tanguchi, K. Thinning and stroke segmentation for
handwritten Chinese character recognition. Pattern Recognition 15, 4
(1982), 299-308.
6. Pavlidis, T. A Flexible Parallel Thinning Algorithm. Proc. IEEE
Comput. Soc. Conf. on Pattern Recognition and Image Processing. Aug.
1981, pp. 162-167.
March 1984
Volume 27
Number 3
7. Rosenfeld, A. Connectivity in digital picture. J. ACM 17, 1 (Jan.
1971), 146-160.
8. Rosenfeld, A. A characterization of parallel thinning algorithm. Info.
Control 29 (Nov. 1975}, 286-291.
9. Rosenfeld, A. and Davis, L.S. A note on thinning• IEEE Trans. Syst.
Man Cybern. SMC-6, 3 (March 1976), 226-228.
10. Rutovitz, D. Pattern Recognition. Proc. Royal Statists. Soc. 129, Series
A (1966), 504-530.
11. Stefanelli, S. and Rosenfeld, A. Some parallel thinning algorithms for
digital picture• J. ACM 18 (April 1971), 255-264.
12. Tamura, H. A comparison of line thinning algorithms from digital
geometry viewpoint. Proc. 4th Int. Conf. Pattern Recognition, 1978, pp.
715-719.
CR Categories and Subject Descriptors: 1.5.2 [Pattern Recognition[:
Design Methodology--pattern analysis; 1.5.4 [Pattern Recognition[: Applications-computer vision
General Terms: Algorithms, Theory, Applications
Additional Key Words and Phrases: parallel algorithm, thinning of
digital patterns, skeletonization
Received 3/83; accepted 9/83
Authors' Present Addresses: T. Y• Zhang, Department of Computer Science and Automatic Control, Chongqing University, Chongqing, China;
C. Y. Suen, Department of Computer Science, Concordia University,
1455 de Maisonneuve West, Montreal, Quebec H3G 1M8. Canada
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