m—1 n—1 
Flog) = > S af pasos 
Tou sz 
This expression equals to F —A f B, where matrax 
A conists of 
— 2airp, 
m 
m eu 
m 
PI SM | 
and matrix B consists of 
— DiS 
en 1) 
boe co) 0Üscs.gee--1 
In fact, 
1 1 1 ... 1 
1 eC 200 /n eC 4/m gU 2mi(m—1))/m 
1 1 eC 4 /m eC 970 /m el 4mi(m—1))/m 
= : 
1 e 20i (m—12/m eC 4i n- D2/m ol 2m(m—1)")/m 
The matrix B is similarly described. 
According to the calculating procedure described 
previously , the block diagram for the discrete Fourier 
transform is denoted by figure 7. 
  
  
PREMLT POSTMLT |—F 
B— 
fo 
  
  
  
  
  
  
where. POSTMLT(f,B) performs 
Ou == SE; pDig 
i=l 
if any fy is a star, so also is ey. 
PREMLT(A,f) performs 
15 
dy = S 
i1 
if any f4 equals to a star, the dy is a star. 
The destinations that we introduce DFT are; 
(1). Since DFT can be indicated by matrix, other 
transforms can also be represented by matrix. 
(2). Though current FFT is faster than the matrix 
method used in serial machines, we say it is 
very effeicient to be run in parallel array 
processors. 
6. CONCLUSIONS 
Digital topology and Matrix structure provide two 
sound mathematical foundations for image 
processing. Our thrust has been in the direction of 
The of this 
introduce underlying digital 
recognition and decision. goal 
investigation is to 
techniques that lead to the formation of quantitative 
knowledge parameters and to quantitative decision 
techniques, the both being central to the development 
of image matching and image understanding, since 
image matching and image understanding must 
employ the topological properties to obtain the 
satisfying results reliably and effectively and Matrix 
structure is a very useful vehicle for dealling with the 
parallel and formative algorithms. Of course, the real 
parallel algorithms to be preformed must have the 
as its premise. 
enough parallel processors 
Nevertheless, it is optimistic for us to see to 
popularize the parallel processors. 
REFERENCES 
Arcelli C., 1979, A Condition for Digital Point 
Removal Signal Process . 1, 283—285. 
Dougherty E. and Giardina C., 1987, Matrix 
Structured Image Processing, Prentice — Hall, 
Ins. 
Hal R. W., 1989, Fast Parallel 
Algorithms ; Parallel Speed and Connectivity 
Preservation , Commn. ACM 32,124— 131. 
Herman G. T. , 1990, On Topology as Applied To 
Image Analysis, CVGIP 52,No. 3,409— 415. 
Kong Y. and Rosenfeld A., 1989, Digital 
Thinning