n r 
1 
28,3, 7 ay) Semel ACHES 
1-1 oit=7 oe 
(8) 
where N is the number of possible 
segmentations of the image. 
Now we shall make specific the potential 
function type for the above clique types. 
In accordance with (6) and using the 
function sign(r), which takes the values 
sign(r) - 
we can write 
1 ==! 
M 
v= a, (MN - y 
¥= 
M N-1 
V 8, (a-0-25- js: | s, - Serra] 
uz] T7 
N 
Vin BA [CM-1)N-2) s: s,,- Sega) 
ys! mf 
M-1 N 
v, sas (010 00-2) jeten|s us, ui] 
y=/x=2 
M-1N-1 
—2 
a} 
y=iz=] 
t,.i!f z > 5 
OQ irf. r0, 
sul u |) © 
Vv = M-1) (N-1) 
duae aer 
Here k is the number of image area types, 
V, are potential functions for individual 
k 
-pixel coliques (type war) and for 
s = i - 
different area types, Ner] to Y id are 
potential functions for cliques of types 
? ? 
bl na" a". 
In acccordance with (4), the probability 
of the specified segmentation can be 
split into two parts 
1 BY San 3 
P(Q,,...,Q >= — exp] X - Ur y } X 
% D T 
Q iz 
6 
x exp] ) V UNS es y } 
T 
J=1 
Then, in view of (9), we have 
6 
orpf) tl) ems [2-s1gnIk-s |- 
m 1 æ+i.y 
i=] 
-sign|k-s 
eda * 82 |2-518ntis,,, ,I- 
-signik-s, 1] + es [o7 tentes, perl 
-signlks,,, , ,1]8, [2-oten tes, , ul 
-sign lica pul] 2, |t-518nl5., xi] 
(11) 
886 
Provided certain assumptions are made, 
(11) can be further simplified. 
SYNTHESIS OF SEGMENTATION ALGORITHM 
The  sliding-window image processing 
(Therrien, 1986; Pratt, 1978) is an 
acceptable technique which can be 
employed for solving the problem. 
Let some initial Doppler 
partitioning is given and all pixels are 
assigned specific state values. The 
initial segmentation procedure will be 
discussed below. 
image 
After that we choose an arbitrary (7,4) 
pixel and superpose the window center on 
it. Then we vary the central pixel state 
without other pixels state ohange and 
calculate the corresponding values of a 
poateriori probability ( with an acouracy 
of up to 1/p(F) 
PPIOP(OPEIS LS ay ) PG, 7D.) 
Note that 
PS Pa a ey Say)” 
E PF (gy) 185,705 (zy) 
where F 
(ry) 
pixel (r,y). 
is the image F without the 
The second cofactor in the 
right-hand side of the relation does not 
depend on Saut so account can be taken 
only of pP(f, ey) Say Sy)" 
In view of the remarks made and of (3) 
the search for the maximum value of a 
posteriori probability at pixel  (r,y) 
state variation is reduced to maximizing 
the expression 
p{ IF ‘38 :=L,5  JP(S- -LIS )— max 
T (ry) Ty (zu) Ty (xy)varL 
and the assignment of a new state to a 
(X,ÿ) pixel. It is necessary to apply the 
given rule for all pixels to get a more 
precise image partitioning and then to 
iterate all the procedure. As a result we 
get a following rule of Doppler image 
segmentation 
(12) 
n : ni n : t 
Py (uu PG, «Lis va t max 
+1 
where s — is a state of a pixel 
are 
(r,y) 
for a current iteration step; e 
states of the window neighbouring pixels 
at the n previous iteration step; 
PL I pylF )- a conditional probability 
(zy)' 
density of (r,y) pixel on condition that 
(I,y) pixel has a ru L, and the window 
e 
neighbouring pixels which were assigned 
B- L at the previous step, have frequenoy 
values F . 
(zy) 
Now consider the cofactor P(F|Q,,...,Q 
of (331. Since all T are independent, 
p(FIQ,, BD p (IQ. - -*pCF 14) 
x!