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