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For definiteness sake, let a Doppler 
frequency generated by remote sensi & 
surface with a  heterodyne-reception 
infrared coherent laser radar be the 
parameter to be estimated. Segmentation 
will be considered to be aimed at 
discerning patterns of moving objects of 
the scene. 
PROBLEM FORMALIZATION 
Given: the Doppler image specified in the 
form of a M«N frequenoy matrix F=f js a 
similar intensity matrix A={a  } and 
image segment types numbered from O to 
R-1. Assume that each pixel (T,y) can 
take an arbitrary state Boy" 
corresponding to one of the segment type 
Nos. Segmentation is aimed at generating 
the image Q consisting of the subset Q, 
Uu Q,- Q and Q, n Q, = at V t £ J, (2) 
where Q,7C(7,9):8,, 7 L,3,L, 4(0,...,B-1). 
Ihe segmentation is implemented according 
to a postertort probability maximum 
criterion 
p(FIQ,,~,Q)P(Q,,-,Q) 6) 
P(Q,,,Q, |F)= ^ max, 
p(F) 
where P(Q,,...,Q, |F) - is the probability 
of Q,,....0Q, regions presence in image on 
condition that F image is observed; 
p(F|Q,,...,Q,) - is joint probability 
density of all pixels Doppler frequenoies 
on condition that image is partitioned 
into regions Q, SQ; P(Q,,...,0,) - is 
a probability of ::Q 
presence in : p(F) - is 
unconditional j probability density 
of all pixels Doppler frequencies. 
  
regions 
Consider the cofactor P(Q,,...,Q,) in 
(3). To desoribe laser radar images, use 
can be made of Markovian random-field 
models  (Kelly,1988; Besag,1974; Derin, 
1986; Hanson, 1982; Therrien, 1986) where 
each region is desoribed by iis own 
stationary random process and the 
transition from one image region to 
another is modeled by a Markovian 
process. 
Let us use 3, to designate a set of 
imu) 
states of eight pixels adjacent to  (r,y) 
and N to symbolize a set of states of 
(zy) 
all the pixels without (I,y). Now the 
Markovian model satisfies 
Pre POS, 
CN 
(zy) FE 
eu) 
— Te t 1 B 
where PS 19 (ay)? is the (r,y) pixel 
S state probability on condition that 
885 
neighbouring pixels have S ay) states, 
corresponding to specified image 
partitioning. 
It is known that the Markovian model 
satisfies the Gibbs distribution  (Derin, 
1986), which ean be written as 
1 1 
P(Q ss ell )= — € — V Q 5) 
J i 5 exp { : 5 of } ( 
Q 
where C is the pixel set termed the 
clique which consists either of 
individual pixels or of their Oups, 
satisfying the condition that if  (1,J)ec 
and (k,4)€0 for (1,1)#(h,1), then 11,7) 
and (k,1) are adjacent pixels. C is the 
set of oliques belonging to different 
types. Vo(Q,...,Q,) is the function 
depending only on pixels of type "c" 
cliques, intended for the specified 
fragmentation of the image and termed the 
potential function. T is the constant. Bo 
is the normalization factor. 
To solve the above problems, it is 
expedient to determine clique types in 
accordance with Fig.1. 
  
  
EBB 
# [cul 
| M | Æ | type a type b type c 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
type d type e 
Fig.1. Clique Types for 8-Connection 
Neighbourhood of Pixel (r,y). 
À potential function for the Type 1 
clique consisting of two pixels (r,y,) 
and (TY) can be specified in the form 
; p.f s. y. uv 
(6) 
where - is the parameter corresponding 
to ihe Type I clique. For 
individual-pixel cliques, the potential 
function can be defined as 
V,(æ.w) = à, if Bu (T) 
where a, is the parameter asscoiated with 
the Type 1 clique. Then the potential 
unction for the type "¢" clique, v_(Q), 
specified all over the image Q will be a 
sum of potential functions (6) or (7) for 
the entire image. 
The normalization factor HB shall be 
0 
selected on the basis of the condition