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APPLICATION OF RANDOM DECISION RULES IN LASER LOCATOR IMAGE
OPTIMAL SEGMENTATION ALGORITHMS
V. M. Lisitsyn. N. N. Pasechny. V. A. Stefanov, V. P. Samoilov, D. A. Lukanidin
The State Research Institute of Aviation Systems, Moscow, Russia
Commission III. Working Group 3
KEY WORDS: Mathematics. Algorithms. Image Processing, Radar, Pattern Recognition
ABSTRACT:
The method of speckled laser radar image segmentation based on the criterion of a maximum a posteriori
probability is considered. Laser radar images are described by using the hierarchical two level stochastic
model based on Markov random fields. The higher level of the model is a Gibbs random field which describe
the whole laser image as a composition of the regions of different shapes and types and at the lower level
each region is modelled within its borders by the Gaussian random field with known statistical characteristics.
The grouping of pixels into different regions of image is governed by the new iterative segmentation algo-
rithm. This algorithm has very low sensitivity to initial segmentation quality of the image and has the ability
to achieve the global optimum in sense of probability. As belonging on each step of the iterative segmentation
process the classification of the tested pixel to one of several region classes is made by random decision. The
result of decision making is the value of the specific discrete random variable which distribution is equal to
the a posteriori probabilities of belonging the tested pixel to the different regions. This probabilities are re-
cursively estimated by taking into account only the nearest neighbourhood group of pixels and the results of
the previous decisions. To provide a stochastic algorithm convergence (in probability) to a global maximum it
is necessary to obtain a smooth transition from completely random estimations to deterministic ones. Thus,
during initial iterations the algorithm searches for global maximum regions compensating the low quality of
the initial segmentation and then tends to a deterministic form and provides the optimal image segmentation.
INTRODUCTION
The segmentation is one of steps in pattern recogni-
tion, scene analysis and image description problems
solution which consists in image partitioning into
homogeneous regions by some attribute. The seg-
mentation task. for example. may involve the high-
lighting of objects images in a scene and the sup-
pression of insignificant details (Duda. R.. 1973:
Borisenco 1 1987).
The problem is considered of optimal segmentation
of extended uncertain objects images generated by
10.6 mkm coherent IR laser locator (Dansac, J., 1985
Wang. J.. 1984). By segmentation we mean the parti-
tioning procedure of an image presented in the form
of brightness matrix into a number of mutually dis-
joint regions corresponding to objects patterns and
to the background. The pixels belonging to different
image regions are assigned different states and pixels
belonging to one region are assigned identical states.
The total number of states is equal to a number of
image region types (Therrien, C., 1986; Derin, H.,
1986).
MODELS FOR IMAGE DESCRIPTION
To describe laser locator images a two-level compos-
ite Markov random model is used according to which
the transitions from image region to another (pixel
state change) are described by discrete Markov ran-
dom field with Gibbs distribution and pixel bright-
ness within each region is described by two-
dimensional correlated Gaussian random process
(Derin, H.. 1986: Hanson, F.. 1982: Kelly. P., 1988.
463
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
Lisitsyn, V.. 1995). The probability characteristics of
the processes of both types are assumed to be speci-
fied a priori and to correspond to the characteristics
of observable object and background patterns. Fig.l
showing the two-level composite model illustrates
the description of images.
The segmentation problem under consideration con-
sists in optimal in stochastic sense estimation of
pixels of observable laser locator image based on a
priori specified stochastic characteristics of the two-
level Markov random-field model employed. In this
case the regions of a segmented image coincide in
form with observable objects and background pat-
terns.
The Problems of Image Segmentation
The well-known iterative image segmentation algo-
rithms (Kelly, P.. 1988: Derin. H.. 1986; Lisitsyn, V.,
1991; Lisitsyn, V., 1995) based on sequential pixel
state updating by a posteriori probability maximum
criterion ( probability of current pixel belonging to
different regions with. neighbouring pixels states )
have two grave disadvantages. Firstly, because of
deterministic nature of decision making these algo-
rithms yield the same result under equal initial con-
ditions. Secondly, the algorithms are highly sensitive
to initial conditions: the resulting segmentation
quality heavily depends on initial segmentation
quality especially when signal-to-noise ratio is low.
This is because in pixel-by-pixel optimization, i.e.
when at each step a posteriori probability local
maximum is searched for with a single pixel state
variation, the algorithm provides process conver-
