where Mi is correlation matrix, | M*l - 
matrix determinant, n ; - Pj vector dimen 
sion equal to region pixels number, 
Ij - unit vector of rii dimension. 
Since echo intensity fluctuations in 
neighbouring pixels are statistically 
independent (Sullivan,1980;Wang,1984), 
Pi vector may be presented as f\~sXpo i > 
where o t - is frequency measurement error 
vector in Q t - region pixels, and pixels 
frequency correlation matrix in Q f regi 
on may be presented as follows 
(7) 
where 6t - standart deviation of Qj re 
gion 1th pixel Doppler frequency. 
So far as p(P)= const for a specific 
image, we come to the problem 
.fjwith the proviso 
isl (2) 
Substituting (4),(5) and (6) into (8) 
and taking a logarithm result in 
Mp(FjQ)ffi 
-~>vax (9 ) 
where E xs designates exponential functi 
on index in (9). To determine unknown 
values l&t entering in (9) we utilize 
maximum likelihood estimation and choose 
g t paramètres values which maximize a 
posteriori probability with specific im 
age partitioning into regions. To achi 
eve this goal it is sufficient to calcu 
late the partial derivatives in (9) of 
all g^ paramétrés and equate them to ze 
ro 
This equation differentiation and res 
pective equations solution result in un- 
knoun paramétrés optimal estimates 
o - F 
9r TwTi ", ^ i/5* 
(10) 
(10) follows from (7)« 
Por background DOI regions, combining 
zero state pixels, g- t =0, hence maximum 
likelihood estimation should be applied 
only for unit state pixels regions. 
Proceeding from above observations we 
maximize criterion (9) under condition 
718 
that in Qi unit pixels image regions un 
known parameter g,- is set equal to g t - 
while in zero pixels image regions - eq 
ual to zero. 
6. SEGMENTATION ALGORITHM CONSTRUCTION 
The acceptable problem solution method 
implies the application of sequential 
iteration algorithm of sliding window 
type (Therrien,1986; Pratt,1978). Let 
some initial DOI partitioning is given 
and all pixels are assigned specific 
state values (zero or unit). We set win 
dow size equal to Markovian random field 
model definitional domain according to 
(5). After that we choose an arbitrary 
(x,y) pixel and superpose the window 
centre on it. Then we vary the central 
pixel state without other pixels state 
change and calculate the corresponding 
values of a posteriori probability (with 
an accuracy of up to 1/p(P)) 
p(FlQ}P(Q) z p(Fls x;f =L,S lx;f) ) P(s x:f ~-L, £? 
at L=1 and 0 
where £2 - all pixels states set with 
out (x,y) pixel. Note that 
Since the probability P(S^ i<i() ) doesn’t 
change with a pixel state variation so 
as to determine a posteriori probability 
maximum P(s) which according to 
the adopted Markovian model of pixels 
states relation depends only on S(x,y), 
i.e. it is a conditional probability of 
Markovian field (5) 
P(s^llS ( J=P(s,,-Lin t , 3> ) 
Similary, it may be shown that 
Pft kxi L. S(* s))~p(f x Jff*»), S [x ^j 
where P(x,y) - DOI without (x,y) pixel, 
", ( x,y) frequency. The second factor 
of the left part of the equation doesn't 
depend on s xy , so later on only the 
conditional probability densiti may be 
taken into account 
pfaxvlF«*),s k;j ~L ,¿(*3)) 
Thus the search of a posteriori probabi 
lity maximum for (x,y) pixel state vari 
ation is reduced to the mequality vali 
dity check 
p({«H II&xd) <C 
^ P Q S(xi))P(s v / o 15 (x J 
and the assignment of a new state to a