des 
[he 
ity 
3.2.4. Straight line fitting of outline of polygon. For 
each curve between neighbor nodes, fitting a straight line 
is carried out with the correlation coefficient 
r-Ixy/ sqri(Ixx- lyy) 
where 
Ixy- Z0x-X)(yiy) 
Ixx- X(xji-X)Oq-X) 
lyy- Z(y-YYr-3) 
and the maximal distance dmax between edge points and 
the straight line. When r<rt or dmax>dt (rt and dt are 
thresholds),the curve will be divided into two parts 
according lo the golden section, and the procedure will be 
repeated. After that, the polygons are determined. 
3.3 Region decomposition 
Region decomposition means: X is the set represented 
objects(regions). If a group of subsets X1, X2,...,Xn 
satisfies: 
n 
X- U Xi 
i=1 
then (X1,X2,...Xn) is a decomposition of X. Usually the 
decomposition should be 
(1) concise 
(2) invariant in shift, rotation and scale transformation 
(3) represent ative of the object 
(4) unique 
3.31 Algorithm 1 Selecting sole structure element B 
with symmetry such as a squre, rhombus or disk, the 
processing 
Xi= ((X-X'(i-1))niB) 6 niB 
X'()= U Xj 
X'0- $ 
Where ni is the maximum size of niB included in X-X (i- 
1) in step i, is repeated untill (X-X'(i))0B=¢ Then X1 X2, 
… is a decomposition of X. In this way, X is decomposed 
as morc parts unconnected. 
3.32 Algorithm 2. There ara several structure 
elements B1, B2, ... Bg. Supose 
Dp i=(XonB)/[Xo(n+1)B], 0<n<Nj 
where Sn, is the n-skeleton subset of X by Bi. 
Step 1: Remove some Dn.i overlaped by other Dn.i 
Sicp 2: In remained dn,i, find the point p satisficd 
M Ni 
U U U (praBi)-X 
=1 n=0 p£Sni 
according to Dn,i S Sn,i@nBi, and the number of p is the 
least. In this way, the computer load is astonishing. 
3.3.3 Algorithm 3. Given pattern Bi, i=1,2,....m 
75 
(1) For each connected subset X' of X, 
P(n,i)=PS y'(n,Bi)/A(X"), 1<=i<=m, O<=n<=Ni 
R(ni)-H((X'onBiyBi) 
A(n,i)-A(nBi) 
where 
Ni=max{nlX'enBi +0} 
PSy'n,Bi)=A[X'onBi/X'o(n+1)Bi] 
is the pattern spectrum of X' by Bi, A(X^) is the area of 
X, 
H((X'onBi)/Bi) = InA(x'onBi) - (1/A(x'onBi)) - 
X PSx'(n,Bi). In[PSx'(n,Bi)] 
n<j<=N; 
is the average roughness of X'By Bi. 
(2) Selecting the suitable n,i satisfies 
P(n,i)=max 
A(n,i)!'=0 
R(n,i) is small. 
(3) Supose S'n,i is skelton subset corresponding to X', 
pÉS'n,i. Then U (p+nBi) is a decomposition of X. 
pCS'ni 
The running time is less than that in algorithm 2, and the 
result is better than that in algorithm 1. 
4. EXPERIMENTAL RESULTS 
lhe partial resalts of image segmentation are shown in 
Fig.1. a) shows the result with multi-thresholding. b) 
shows the result with clustering. c) shows the result of 
region growing. The thninng results are shown in Fig.2 
where a) is the result of the algorithm 1, b) is the result of 
the algorithm 2 and c) is the result of the algorithm 3 Fig.3 
shows the results of 3-intersection extraction. The 
extracted polygons are shown in Fig.4. 
5. CONCLUSION 
The meaningful region can be separated from image by 
thresholding, clustering and separation-merger algorithm. 
Based on preprocessed image, the variable threshold cna 
be employed in the segmentation. The separation-merger 
is batter labling algorithm. 
The edge can be extracted on binary image or grey level 
image with mathematical morphology. The basic thinning 
method is improved, and aller boundary filing, the 
polygon is obtained. The primitives of object shape are 
acquired from region decomposition. 
The information extracted by mathematical morphology 
can be applied in model discription of object and 
structure matching and image interpretation.