:d. From EA point 
on. Any fact about 
on about the scene 
as outlined in the 
ity of model-based 
yrocedures are the 
nformation. Based 
itour and intensity 
HT) support the 
ut can not use any 
in images. The 
nís-based image 
ipose the Pytiev's 
odology of Hough 
)st generic model- 
Cart" is connected 
rocedure of image 
a procedure of 
le image, about its 
1 be the evidence, 
le observed is the : 
:d based on these 
ys to provide the 
yroach is the most 
1 outline the EA 
f Bayesian EA. In 
15e extraction is 
\-application for 
  
  
2. EVENTS-BASED IMAGE ANALYSIS: 
DETECTION WITHOUT COMPARISON. 
From the most generic point of view, the set of possible 
object recognition procedures can be separated into two 
principal groups: methods that use the object comparison 
and methods that do not use it. 
This distinction is easy to show for the case of the feature- 
based object classification. Methods of closest neighbors 
based on the comparison of the each new vector that 
characterizes the object with some sample vectors that 
characterize known object classes. A corresponding 
distance or a closeness measure is computed here to be a 
criterion of classification. So, the reliability of object 
recognition (detection) is determined by the comparison of 
the objects in some metric space. On the other hand, the 
statistical classificators immediately use the probability 
distribution functions to estimate the reliability of object 
classification. Some set of samples can be used at the 
training stage but at the stage of decision making any 
comparison with samples is not of use. 
The most important limitation of the comparison-based 
methods is that we can compare only the objects of the 
same type (two images, two contours, two vectors, two wire 
models and so on). So, we can not compare the image and 
the model. 
In our opinion, the most powerful comparison-based 
detection technique is the Pytiev's morphological analysis 
(Stepanov at al, 1994) that really provides the 
invariantness of object detection. Due to this it 
demonstrates the possibilities and disadvantages of 
comparison-based methods with great expression. The 
main idea of Pytiev's morphology is the following. Let the 
images will be the elements of some Hilbert space IM-12. 
So, one can speak about an image norm |Im|| and a 
distance between the images |ml-Im2|. Let also some 
convex and closed image set ZeIM is given. Then for any 
image ImeIM there is the unique image Im'eZ such that 
l[Im'-Im||-min||Im"-Im||, Im" eZ. It is easy to see that this 
mapping v(Im):Im->Z is a projecting operator in the 
(algebraical) sense that v(v(Im))=v(Im). So, we can note 
Im'=Pr7(Im), i.e. Im' is the projection of Im onto the Z. 
Using the image projection notion some special closeness 
measure K(Im,Z) (the morphological correlation 
coefficient) can be defined. It is analogous to the usual 
correlation: 
K(Im,Z)-|[inf(Im,Prz(Im))|/|sup(Im,Prz(Im)|| 
and has the following useful properties: 1) 02K(Im,Z)21, 
ImeIM, ZeIM; 2) (K(Im,Z)=1) <=> (ImeZ). 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996 
The basic advantages of the morphological correlation 
coefficient are connected with the possible full account of 
the registration conditions. Let the registration model is 
described by some transform seS where S is a semigroup 
of transforms and the object model is M={ImM} (object is 
described by its' sample). The Pytiev's morphological 
shape of any image Im will be Zim={Im'=s(Im),seS}. So, 
the morphological correlation coefficient 
Kç(Im',Im)=K(Im',ZTm) provides the correct comparison 
between any test image Im' and the given sample Im=ImM 
under the condition of transformation seS. 
For instance, let consider the generic model of radiometric 
distortions. In the formal way any image is a 2D-function 
of intensity distribution and can be represented as f(x,y)=2 
(a;xx;(<,y)), where x; is an indicator of the i-th region of 
the cadre tesselation and a; is a color (intensity value) of 
this region. So, the set of images "of the same shape" has a 
form: 
Z={f"(x,y)=Z(bjxx;(x.y)), V{b;}}. 
Then the projecting transform is a parametric one and has 
the form: b;=b(a;), where i=0..C-1; C is a number of colors 
in the image. For any image g(x,y) the projection Pry(g) is 
defined by the parameter vector b g 
=. Kid xy) dxdy), i=1..C-1, 
that is easy to compute. Since the parameters of projection 
are computed the morphological correlation coefficient 
K(g.f) is computed immediately. 
So, we see that the Pytiev's morphology decides the 
problem of the invariant object detection in the case of 
object model M={ImM} under the regular registration 
model S. However, when the model M does not satisfy any 
special conditions, computation of the Pry (Im) is too hard 
because we need to compare the test image Im with the 
each element Im' from M to find the closest one. 
Consider this problem applying to non-comparison-based 
techniques. The simple example is a classic pattern 
analysis using Hough Transform (Houle and Malowany, 
1989). 
Let the set of images to be analyzed is a set of planar dot 
patterns and it is required to detect all straight patterns in 
it. The straight pattern here means the sub pattern that 
contains a number of points that lie on the same straight 
line. It is very fuzzy and flexible model M because neither 
the number nor the location of points on the line is not 
defined. So, we can not use any sample here. The 
899 
EE set t LB ss ls