n r
1
28,3, 7 ay) Semel ACHES
1-1 oit=7 oe
(8)
where N is the number of possible
segmentations of the image.
Now we shall make specific the potential
function type for the above clique types.
In accordance with (6) and using the
function sign(r), which takes the values
sign(r) -
we can write
1 ==!
M
v= a, (MN - y
¥=
M N-1
V 8, (a-0-25- js: | s, - Serra]
uz] T7
N
Vin BA [CM-1)N-2) s: s,,- Sega)
ys! mf
M-1 N
v, sas (010 00-2) jeten|s us, ui]
y=/x=2
M-1N-1
—2
a}
y=iz=]
t,.i!f z > 5
OQ irf. r0,
sul u |) ©
Vv = M-1) (N-1)
duae aer
Here k is the number of image area types,
V, are potential functions for individual
k
-pixel coliques (type war) and for
s = i -
different area types, Ner] to Y id are
potential functions for cliques of types
? ?
bl na" a".
In acccordance with (4), the probability
of the specified segmentation can be
split into two parts
1 BY San 3
P(Q,,...,Q >= — exp] X - Ur y } X
% D T
Q iz
6
x exp] ) V UNS es y }
T
J=1
Then, in view of (9), we have
6
orpf) tl) ems [2-s1gnIk-s |-
m 1 æ+i.y
i=]
-sign|k-s
eda * 82 |2-518ntis,,, ,I-
-signik-s, 1] + es [o7 tentes, perl
-signlks,,, , ,1]8, [2-oten tes, , ul
-sign lica pul] 2, |t-518nl5., xi]
(11)
886
Provided certain assumptions are made,
(11) can be further simplified.
SYNTHESIS OF SEGMENTATION ALGORITHM
The sliding-window image processing
(Therrien, 1986; Pratt, 1978) is an
acceptable technique which can be
employed for solving the problem.
Let some initial Doppler
partitioning is given and all pixels are
assigned specific state values. The
initial segmentation procedure will be
discussed below.
image
After that we choose an arbitrary (7,4)
pixel and superpose the window center on
it. Then we vary the central pixel state
without other pixels state ohange and
calculate the corresponding values of a
poateriori probability ( with an acouracy
of up to 1/p(F)
PPIOP(OPEIS LS ay ) PG, 7D.)
Note that
PS Pa a ey Say)”
E PF (gy) 185,705 (zy)
where F
(ry)
pixel (r,y).
is the image F without the
The second cofactor in the
right-hand side of the relation does not
depend on Saut so account can be taken
only of pP(f, ey) Say Sy)"
In view of the remarks made and of (3)
the search for the maximum value of a
posteriori probability at pixel (r,y)
state variation is reduced to maximizing
the expression
p{ IF ‘38 :=L,5 JP(S- -LIS )— max
T (ry) Ty (zu) Ty (xy)varL
and the assignment of a new state to a
(X,ÿ) pixel. It is necessary to apply the
given rule for all pixels to get a more
precise image partitioning and then to
iterate all the procedure. As a result we
get a following rule of Doppler image
segmentation
(12)
n : ni n : t
Py (uu PG, «Lis va t max
+1
where s — is a state of a pixel
are
(r,y)
for a current iteration step; e
states of the window neighbouring pixels
at the n previous iteration step;
PL I pylF )- a conditional probability
(zy)'
density of (r,y) pixel on condition that
(I,y) pixel has a ru L, and the window
e
neighbouring pixels which were assigned
B- L at the previous step, have frequenoy
values F .
(zy)
Now consider the cofactor P(F|Q,,...,Q
of (331. Since all T are independent,
p(FIQ,, BD p (IQ. - -*pCF 14)
x!