Assuming the probability of the object 
omission is Pr» , it is possible to dof 
no the dimensions of fi =R t - image frag 
ment which includes ith object with 
1-V* probabil jty 
Then for the ith object segmentation it 
is sufficient to process not the full 
image but its fragment bounded by a side 
2R; with a centre in the point (x;,y ; ), 
For k-objects segmentation the number of 
such fragments is equal! to k. If ith 
fragment doesn’t have intersections with 
any other fragment then within this fra 
gment, there are only a background and 
the ith object. Since the fragment di 
mensions are smail then it can be consi 
dered that the background velocity in 
all pixels of a single fragment is con 
stant. Then the segmentation procedure 
can be realized not by the sliding win 
dow but with taking into account all 
fragment pixels, which increases velo 
city calculation accuracy, procedure 
convergence and reduces the computeti- 
onal burden. 
The algorithm allows the general Lzation 
for the object arbitrary motion case. In 
this case the echo frequency on an ob 
ject image element corresponding to the 
ith region of an image is defined as 
follows 
as) 
where g t - is a projection of an object 
translatory motion on to the line of 
sight; are angular rates of an 
object rotation relative to !,he ortho 
gonal axes lying in the plane perpendi 
cular to the line of sight; q is a pro 
portionality factor. Then in accordance 
with the adopted model we get that the 
vector of the observed Doppler frequen 
cies values of the ith region b\ can be 
presented in the form 
07) 
where TjsdjjXjY) is the transformation 
matrix of dimensions n* 3; G,- = (g; ) T 
is the ith region velicity vector; 6i 
is the measurement errors vector; nj is 
the number of pixels in ith region. 
To define the most likely vector esti 
mation It,’s necessary to solve vector- 
matrix equation (17) is relation to Gi 
for the given vector of observable fre 
quencies Fi . In the general case the 
solution of this equation can be obtai 
ned using pseudoinverse matrix method 
(Albert,1972 ). However, for the segmen 
tation of separate image fragments 
containing isolated objects the more 
simple result for Gi vector estimation 
may be obtained, using method of least 
square. In this case we realize the ne 
cessity of recursive solution of the 
following system of the thrird-order 
linear equation with respect to vector 
components g ; , ox , £ c 
The summation is carried out for all 
pixels of ith fragment having a state 
s=1. The system (18) is resolved accor 
ding to the Kramer's rule find is written 
in the form 
where^ and Aj are corresponding system 
determinants. 
In realizing the segmentation pricedure 
the system (18) must be resolved every 
time as soon as any pixel of analysed 
fragment changes, 
8. THE ii/iATHEMATTO MODELING OF THE 
SEGMENTATION ALGORITHM AND CONCLUSIONS 
The jriathematic modeling has shown that 
as a rule the algorithm converges in 5- 
10 iterations and the algorithm with 
a priori given coordinates of regions 
converges in 3-8 iterations. The initial 
segmentstion qua!ity doesn't practically 
affect the processing results and does 
affect only the number of iterations. 
In modeling of algorithm implementation 
for a plane-parallel objects motion an 
acceptable result was obtained using a 
window of 3x3 pixels size. But the esti 
mation of the velocity vector G for ob 
jects arbitrary motion such dimensions 
provide unsatisfactory results. The sa 
tisfactory quality of the segmentation 
was obtained when the frequency was es 
timated with a window of 9x l 3 pixels 
size and the pixels connection was based 
on the analysis of the window of 3x3 
pixels size. Even better result was ob 
tained in modeling the segmentation al 
gorithm with a priori given coordinates 
of regions. 
When implementing the segmentation algo 
rithm for arbitrary moving objects using 
a mainframe digital computer the total 
number of computer operations for pictu 
ring of 912x128 pixels will amount to 
10-12 million for one iteration. Using 
a fragment of 40x10 pixels size this va 
lue will be about 200 thousand operati 
ons for one iteration. 
Fig.1-10 illustrate the segmentation of 
the proposed algorithm. Elf.1 shous the 
reference image for DOT computer genera 
l-ion in case of plane-parallel objects 
motion. Moving objects have the forms of 
simple geometric figures. Fig.2 presents 
720