SUBOPTIMAL PROCEDURE FOR SHIFTING IMAGE DETECTION 
IN COMPLEX SCENES 
N.A.Rosental, V.M.Lisitsyn, K.Y.Obrosov, V.A.Stephanov 
The Research Institute of Aviation Systems, Moscow, Russia 
The paper considers a suboptimal by maximum a posteriori probability 
criterion procedure for finding of patterns moving relative to semifixed 
background in the series of two 
tha 
noise. 
The procedure is based on optimum linear filteri 
Staggered in time frames of 
m ly varying scenes. The procedure is synthesised on the assumption 
an images being analysed contains 
unknoun distortion and additive 
of divergance field of 
previously combined by correlation method fragments of frames as well as 
statistical hypothesis partitioning operation applied to filter output. 
The adopted statistical image model is used for development of methods for 
defining the main statistical character 
istics for the simple detection 
case. The attainable value of total error is presented which arise when the 
synthesised procedure is applied to some characteristic scenes. 
The ability to work for the procedure was proved during simulation. 
KEY WORDS: Algorithm, Change Detection, Image Processing, Classification 
INTRODUCTION 
There is well-known (IhrpMaH, 1986) 
optimum by maximum a posteriori 
probability criterion procedure for 
shifting image detection in complex 
scenes. The procedure is based on 
time-spatial filtering of the series of 
staggered in time frames of scenes are 
formed by any sensor. The procedure is 
highly tradious and is not practicable 
now. Also there are some  heuristic 
methods (Lo, 1979; Holben 1980; Stuller, 
1983; Koskol, 1986) solving this task by 
passing to separate time filtering and 
spatial filtering. All this methods use 
frame subtraction as the simplest form of 
time filtering. The main difference of 
this procedures is compensation of 
geometrical distortion on analised image 
are called by interframe sensor position 
changing. 
For interframe displacements compensation 
the first frame is offered to be 
corrected by a previous researcher 
(Holben, 1980). The correction is 
described by a polinom of the second 
order with parameters estimated by X? = 
oriterion. The correction may be applied 
with the extrapolation not executed in 
any cases. 
Another procedure was B ested in 
previous paper (Lo, 1979). This procedure 
is free from shortcomings of  (Holben, 
1980) and is not SO tradious. In 
accordance with paper (Lo, 1979) the 
image is divided into separate 
fragments. The fragments are 
correlatively combined and for each pair 
divergence fields are oreated and then 
they are analysed. 
Unfortunately the divergence image 
analysis was not given one's attention in 
previous papers. The attainable values of 
428 
alpha and beia errors are lack of too. 
The aim of this artical is the definition 
of mantional characters for the simplest 
interframe deteotor dealing with ideas 
of paper (Lo, 1979) and using linear 
filtering of diverganoe field. 
1. IMAGE AND MOTION MODELS 
We accume that the images available for 
processing consists of a discrete 
homogeneous random fields denoted as bo 
and L, in pattern and background areas 
and additional Gaussian noise denoted as 
T with exponential correlation function 
and average which is equal to zero. Then 
pixel intensity is: 
; à CA) + nf4) + À € Ve Ÿ 
o, (A) = o d A 3 3 
bp tH + NA) 9 A € 2D UT, 
Here A denotes the pixel ooordinates 
veotor, T, denotes the moving object 
pattern area on l-th frame denoted ag P,. 
With accordance to paper (Jesus, 1978) 
we assume that one-variable probability 
density funotions of background B, (x, A) 
and pattern P, (x,À) are Gaussian: 
re. 2 
P,(X,A) = N(a,.0,) 
P_(x,A) = N(a_,0%) 
= Ta (1,1) 
a, >a 
a, #0, 
and their correlation functions are 
double exponential: 
R(L_(A)} = o2+ezpl-(T_,A)]