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i j ixl (13) 
SP) e[S(E), S(£E,.1)] (14) 
Introduction of topological constraint by Equation (14) suppress 
the possibility of distorted mapping by miss matching between 
visible and invisible regions. 
3.2 A Model with Multi-clustering Approach for Abrupt 
Shift Vector Changes 
The model of ANM with edge constraint can improve mapping 
results where edges are detected successfully. However at 
regions with no edges found, it remains the same as original 
ANM, and can be solved by multi-clustering models as follows. 
3.2.1 Principle of Multi-clustering Approach: The multi- 
clustering approach for the control of mapping was originally 
introduced for detecting regional shifts such as dislocation 
caused by earthquake when comparing images before and after 
the quake (Kosugi, 2001). By clustering shifting vectors into 
several groups in the vector space and integrating vectors into 
the nearest class’s center of gravity, the dislocation regions can 
be detected with better precision and less computational time 
(Figure 5). However, since clustering has not put under 
consideration spatial distribution of image regions, the results 
do not always conform to edge lines or valid regions that 
represent ground features. 
  
   
   
   
AY 
^ 
à 2 
Area A d ok“ Shift Vector 
^ 9 Lo 
A Area B ^ SUO Class B 
  
  
  
d AX 
Discontinuity Shift Vector Space (2D) 
Figure 5. Clustering in the shift vector space 
3.2.2 Enhanced Multi-clustering Approach: To enhance 
clustering approach for ANM with consideration of ground 
feature’s distribution, it is necessary to introduce area-based 
concept. On the other hand, in a stereo model with absolute 
orientation, depth information can be extracted by the mapping 
result of ANM process. To enhance the model with edge 
constraint described above, we introduce a process that 
emphasizes on abrupt shifts by approximating or clustering 
similar depth planes owing to region division and merge. The 
details will be discussed in the next chapter. 
4. ENHANCED MULTI-CLUSTER ANM 
4.1 Overview of the Approach 
The general process flow of proposed approach is shown in 
Figure 6. The first stage of pre-processing includes brightness 
adjustment between stereo images, noise reduction, automatic 
pass point detection, calculation of relative orientation 
parameters and image rectification, which have all been 
described in the previous chapter. The following sections will 
describe the remaining processes. 
  
Pre-processing Y 
  
    
  
  
  
  
  
Y Competition Process with 
Edge Constraint Model 
Y 
Consensus Process with 
Multi-cluster Model 
  
  
Region Segmentation 
  
  
  
  
| —— 
  
  
   
S. Converged ? mE 
P E. Yes 
End 
  
  
  
  
Figure 6. Flow of enhanced multi-cluster ANM 
4.2 Model of Enhanced Multi-cluster ANM 
In the enhanced multi-cluster model, improvement of mapping 
at regions where no edge detected are also aimed by realizing 
area-based clustering, which consists of region segmentation 
according to the result of clustering mapping and clustering for 
merge-able adjacent regions. 
4.2.1 Region Segmentation:  Triangulated segments are 
taken as the starting region for clustering. The flow of region 
segmentation process is shown in Figure 7. 
(i) Initial TIN Division 
In the one-sided image of stereo model on which mapping is 
performed, Delaunay triangulation is carried out by using 
matched edge segments and feature points to form initial 
triangulated irregular network (TIN), with edge segments as 
break-lines. There are many operators for extraction of feature 
points, such as famous Moravec’s operator. In this study 
SUSAN operator (Smith, 1997) is being applied, which is stable 
and superior in detection of corner points. 
(ii) Detection of Division Point 
To divide triangular areas into uniform sub-areas that are part of 
the same ground features, further triangulation is necessary. 
Therefore in this step additional area division points are 
detected. For each triangle with area size above predefined 
value, standard deviation of image brightness in triangle area is 
calculated. When deviation value exceeds the threshold, feature 
point that gives maximum value by feature extraction operator 
is selected as a new division point. If the longest length of 
triangle’s section exceeds threshold, a new division point will 
also be inserted at the middle point of the section. 
(iii) Segmentation of TIN 
Delaunay triangulation is again applied with new division 
points detected in the above steps with the edges of previous 
TIN as break-lines. 
  
Initial TIN Division 
Y 
Detection of Division Point 
Y 
Segmentation of TIN 
  
  
    
  
  
  
    
  
  
  
  
= T. 
End 
  
  
  
  
Figure 7. Flow of region segmentation 
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