registration model allows the affin transforms of the image 
plane. 
The Hough Transform (HT) is a well-known technique for 
object detection in the parameter space. It uses the 
parameter space (p,0) of the normal line equation Xcos(0 
)+Ysin(0)=p. The set of parameters (p,0) of all possible 
lines that intersect in some proper point (x,y) of the image 
plane corresponds to a sinusoidal figure in the space (p,9). 
This figure is called the spread function. 
The idea of HT is to accumulate the votes of the pattern 
points in the parameter space through the simple 
summation of their spreads. If two points of the pattern 
belong to some line (p;,0;) then their spreads intersect in 
the point (p;,6;) in the Hough space (p,9). So, the value of 
the resultant accumulator function A(p,0) in the each point 
(pj.0;) is equal to the number of points of the pattern that 
lie on this line (p;,0;). Thus, if the pattern contains m 
straight patterns, it will be m local maxima in the Hough 
space. 
It is very efficient technique that provides the invariant 
detection of the straight patterns without any comparison 
with samples. The Hough Transform does not require any 
sample ImM because it immediately accumulates the votes 
for a model M. So, techniques that do not use the 
comparison can work directly with generic models of 
objects. 
The Events-based image Analysis (EA) approach was 
developed to generalize this important property of Hough 
transform for a common case of object detection. The 
essence of FA is the following. 
Let we have some image Im, and it is required to 
determine a posterior probability of some hypothesis H 
about the scene observed. Then the Bayesian formula takes 
the form: 
P(H/Im)=[P(H)xP(Im/H)}/[P(H)xP(Im/H)+PH"))x 
P(Im/H5)], (1) 
where Hf means "not H". 
Image Im is also considered (in the spirit of Probability 
Theory) as an event, or, in other words, we consider the 
event E(Im) that is connected with this image Im. This 
event E(Im) consists of some different events occurred in 
the process of low-level image analysis. 
While the any essential fact derived from image analysis is 
the event ey, the event E(Im) will be the intersection 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996 
E(Im)=ejneyn..nek, (2) 
where K is the total number of such events. So, we need 
only (1) and (2) to test any hypothesis H about the image 
Im. 
If one supposes that events {ep} are independent in general 
then (1) and (2) supply 
P(H)x [[UXe, / 8) 
P(H / Im) = P(H)x I[t?(e / B) Par?) « [[t2(e, / 8*)' 
.-«(3) 
  
where I Tx 7X1 Xxox...XXk. 
From this point of view the Hough Transform, Generalized 
Hough Transform, Serra morphology, Pytiev's morphology 
and many other popular techniques are the Bayesian EA- 
procedures that differ in events analyzed, hypothesis tested 
and probability models used. 
The most important properties of EA procedures that are 
principally improper for the comparison-based techniques 
are the following: 
e the usage of generic models; 
e the usage of hierarchical models; 
e the usage of non-homogeneous information. 
The first one is provided through the accumulation of 
evidences immediately for the model-based hypothesis. 
The most important result here is that the assumption of 
event's probability independence in general is enough to 
provide the possibility of parallel independent 
accumulation of events' evidences. 
The usage of hierarchical models based on a hierarchical 
application of Bayesian formula. 
The usage of non-homogeneous information is clear 
enough but usually connected with a coarsening of the 
model of real situation. The non-homogeneous image data 
means a set of data from different physical image sources 
or/and from different image processors. Let we have N 
channels of registration and L levels of data abstraction. 
Level of data abstraction is a form of information 
representation (image, contour preparation, dot pattern, 
parameter space, feature vector, etc.). Let the complex 
model of object is described as a set of propositions 
M={ M}}, i=0..N; j=1..C, 1=0..L, that the object must 
satisfy to. The notation M ; means that this proposition 
takes place in i-th channel at 1-th level of abstraction if the 
object of model M is observed. 
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