(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