3
yeu rng og
a. rl
N =
F-If,l
Fig.l. Two-level composite model.
gence to a maximum which is closer to the states of
pixels corresponding to initial segmentation. Thus,
in case of inadequate initial segmentation the proc-
ess will converge not to a global but to some local
maximum. Another drawback of the algorithms is
the necessity of careful matching of Markov random
field model parameters with really observable image
parameters.
SEGMENTATION ALGORITHM
CONSTRUCTION
To overcome the above-mentioned drawbacks a new
approach to the synthesis of laser locator image
iterative segmentation algorithms is proposed based
on random decision rules.
The pixel-to pixel iterative segmentation of laser
locator images based on stochastic decision rules
represents a step-by-step nondeterministic procedure
of a global maximum search where each pixel state is
randomly update at each iteration step from neigh-
bouring pixels states based on calculated a posteriori
probabilities of a considered (current) pixel belong-
ing to different regions. The algorithm is stochastic
in its nature and can be written in the following form
^
Ss rand{S,,|A(S,,)|
where S, - an update (random) estimation of a cur-
rent ;pixeleástate! (x.)): at /-th. iteration? step
rendi,
AS,)} is the result of a random value gen-
eration (a pixel state estimation) S with a probabil-
ity distribution PAS): (xy) el(00)....(M, N)).
M x N - number of pixels.
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
P(Sy) probability distribution with completely sto-
chastic decision making algorithm is the usual a
posteriori probability distribution of a (x, y) pixel
state at i-th iteration step. In this case the algorithm
gives a random (close to optimal) result of segmen-
tation and does not converge to any state. To pro-
vide a stochastic algorithm convergence (in probabil-
ity) to a global maximum it is necessary to obtain a
smooth transition from completely random estima-
tions to deterministic ones. The above-mentioned
laser locator image segmentation algorithms can be
used as determenistic algorithms (Lisitsyn, V., 1991.
l'isitsyn; V5 1905y.
For considering models the transitions from image
region to another are described by discrete Markov
random field with Gibbs distribution
eta lev b 8
as al =
RA
Int
R total number of pixels; 7; — iteration number;
U(S) - potential function depending on region types;
Zo — normalization factor; A = Umax — Ümin.
where T(t) > 0 at t — 06 and T(t) 2 for 6)
It was shown that in this case the convergence is
provided if
AS, ) = KRIS, IS.)
where RGSO) - a posteriori probability of (x, y)
current pixel state. On condition that B brightness
image is observed and neighbouring pixels at the
previous iteration step had S, states; K - normali-
464
zation
unlimi
TU) €
cilic 5
field.
If the
estime
limite
estime
terion
states
Ils a Ne
with
global
Thus.
for gl
qualit
a dete
segme
Figs:
with 1
in (Li
tic al
laser
noise.
Fig. 4
tion
result
with r
Math:
Case.
and c
equal
menta
tic al
with |
pleme
The p
be ap
tion b
Borise
menta
teleme
Dansa
rangel
compr
