719 
(x, y) pixel that corresponds to the ine 
quality sign. It is necessary to apply 
the given rule for all pixels to get a 
more precise DOT. partitioning and then 
to .i terate all the procedure. As a re 
sult we get a following rule of binary 
D01 segmentation 
(11) 
where s* 3 is a state of a (x,y) pixel 
for a current iteration step; are 
states of the window neighbouring pixels 
at the previous iteration step; pj(V„ 9 |F<« , ', ) ) 
- a conditional probability density of 
(x,y) pixel on condition that (x,y) pix 
el has a unit state and the window neig 
hbouring pixels which were assigned a 
unit state at the previous step, have 
frequency values; - a conditi 
onal probability density of (x,y) pixel 
on condition that (x,y) pixel has a zero 
state and the window neighbouring pixel.s 
which were assigned a zero state at the 
previous step, have P frequency 
values. Taking into account (1),(6) and 
(8) the decision rule of binary segmen 
tation (11) takes a rather simple and 
physically clear form 
if 02) 
»+i 
then s ra =1, otherwise s wu =0 
*3 
where Q(x,y) is an image region covered 
by the window without a central (x,y) 
pixel; f« 3 is a central pixel frequency 
of the window;6** is a variance of the 
window central pixel frequency estimati 
on which is calculated by (1); n is an 
iteration step number; is the condi 
tional expectation of the (x,y) pixel 
Doppler frequency at the nth iteration 
step provided that the window neighbour 
ing unit pixels have frequencies Fix*) ; 
of*» is a conditional variance of (x,y) 
pixel Doppler frequency under similar 
condition. The Doppler frequency condi 
tional expectation may be estimated by 
(10) which in view of (1) is transformed 
to 
r 5 
M<i(iis) uv 
a ■ s 
’ kv 7 w 
a. 
(13) 
Similarly, it may by shown that Lhe es 
timation of the (x,y) pixel Doppler 
frequency conditional variance will be 
¿r 1 r'' 1 
O -ol +0 
*<i *3 x» 
/ s; v <W 
(14) 
So, the iteration algorithm of the DOI 
binary segmentation maximizing a poste 
riori probability of image partitioning 
into uniform regions is as follows. 
Preliminary we carry out a DOI rough 
segmentation this or other way and as 
sign some initial states to all pixels. 
Then utilizing (13) and (14) we calcu 
late the Doppler frequency conditional 
variance for each pixel. Simultaneously, 
using pixels initial states we calculate 
an exponential curve index for each pix 
el from (5), which assigns the threshold 
shift. Then we apply a decision rule (12) 
to each pixel and successively update 
all pixels states. After that we itera 
te all procedure of calculations until 
the pixel states will not change. 
In the general case the given algorithm 
guarantees some local maximum existence 
which may not coincide with the global 
maximum. However, as mathematical model 
ing has shown even elementary procedures 
of the initial image partitioning provi 
de the Iterative process convergence 
with relatively small number of iterati 
ons (5-10) to the segmentation corres 
ponding to the global maximum of a pos 
teriori probability. The elementary 
procedure of the initial segmentation 
may be a threshold (or two-threshold 
with symmetric thresholds) processing of 
DOI. The threshold value can be automa 
tically determined by hystogram method 
with account of the given number of pix 
els with unit states after the initial 
segmentation. 
7. SOME GENERALIZATION OP THE 
SEGMENTATION ALGORITHM 
Consider a priori given coordinates of 
ith region (x; ,yj- ) centre corresponding 
to a moving object anu coordinates er 
rors have a normal distribution. Let’s 
assume that the conditional probability 
of the availability of 1 belonging to 
the 1th region at distance P from the 
given coordinates (xi,y^) on condition 
of the observable DOI presence,P has 
the same form as the distribution den 
sity of coordinates errors, i.e. 
P(plF)=Ke*p[~fZ26}} 
where , Then (8) may be 
presented as follows 
By carrying out the necessary transfor 
mation and generalizing the result for 
the background motion relative to a sen 
sor we get the following rule of the 
binary segmentation 
if - 
.„ w * 9,/ {r fakA(r,) ' 
then s_. =1 ; otherwise 
(13) 
= 0. 
The last two terms in (15) may be tabu 
lated that facilitates practical reali 
zation