(SCALAR (r ;£)) (i,j)=rXf(i,j) 
unless f(i,j)= x , in which case SCALAR(r;f) is 
also undefined at (i,j). 
The implementation of GROW, which is somewhat 
involved, is presented in Figure 5. 
  
0 
| «(TRAN 
  
N 
Y 
fin=fi? HALT 
  
= 
  
~ POR  LHxTADBI-4BIV] 
  
  
SUB 
. : MULT] 
  
  
  
ALTRAN| 
  
  
  
SUB-—[AVERAG|—{SCALARE 
ADD—ABS— THRES DI OR 
Fig. 5 Block Diagram for Region Growing 
In order to test whether the algorithm is feasible, a 
experiment is performed. As a result, it is imparted in 
figure 6. 
x "e 
vif 
te 
» 
Ü 
a N 
9 
réa PN il 
eso 
  
Fig. 6 The Region Outlined by 
Highlighted Curves Resulted 
from Region Growing 
9. DISCRETE FOURIER TRANSFORM AND 
MATRIX REPRESENTATION 
The discrete Fourier transform is a very useful 
vehicle in the digital signal processing and the digital 
image processing, and its algorithm has widely been 
discussed (Rosenfeld &. Kak 1982, Wang 1990). 
Give the m by n bound matrix 
f = 
f(0,0) f0:0), - i 0, —D 
fa,0 fCH1) vey fü,n-—1) 
lim —1,0 fqmc-—4,1) - fon —1,4 "dur 
The discrete Fourier transform (DFT) of f is the 
image 
Pu 
F(0,0) F(0,1) go F(0,n — 1) 
F(1,0) F(1,1) gee F(1 ‚2 — 1) 
Fon — 1,0 F@m—= 1,D- + Km — In — Dar 
where the gray value F(p,q) in F is given by 
14