Next: Data model for extracting
Up: Roads Extraction using a
Previous: Road network extraction
Bayesian approach
Notations :
 D : the observed image
 T : finite grid on the image

: the gray level of a pixel
Hypothesis : the line network, S, we want to extract is
composed of a finite number of segments s_{i}

(1) 
We have :

s_{i}=(p_{i},m_{i}) : a segment in the configuration

p_{i}=(x_{i},y_{i}) : the coordinates of its center

: the vector containing the width,
the length and the orientation of the segment
Problem :
to detect the number of the segments, their location and their
parameters
Solution : Bayes rule

(2) 
MAP estimation :

(3) 
Considering we have a Gibbs point process :

(4) 
The estimator of the line network is :

(5) 
Candy model
The parameters of a segment are independent random variables :

: the coordinates of the center of
the segment

: the
width of the segment

: the
length of the segment

: the orientation of
the segment
is a uniform law.
State of segment : a segment has two extremities to be connected with

: no connection

s=s^{tq} : one connected extremity
 s=s^{tq} : two connected extremities
Probability density :

(6) 
State penalties : the short segments and the free segments are penalized

(7) 

(8) 

(9) 
We have :
.
Rejection interactions : we penalize the overlaping segments,
but we enable the crossing segments.
Figure:
Rejection region for a segment

Figure 2:
Rejection interactions btw segments

Attraction interactions : to form a network, the segments
attract each other. We penalize the segments which are not well aligned.
Figure 3:
Attraction region for a segment

Figure 4:
Attraction interactions btw segments

If there is a rejection interaction btw two segments :

(10) 
If there is an attraction interaction btw two segments, the function h is
penalizing the orientation between segments :

(11) 
For each segment, the local prior energy is:

(12) 
hence for the configuration S :
U_{P}(S) 
= 



= 

(13) 
Next: Data model for extracting
Up: Roads Extraction using a
Previous: Road network extraction
Radu Stoica
20000417