image 
  
Gaussian convolution 
  
  
  
  
    
  
    
  
convoluted image 
  
  
edge detection 
  
  
  
  
zero-crossing edges 
  
| 
generation of edge 
segments 
  
  
  
  
  
Y 
  
  
preliminary edge segments 
  
detection of corner 
  
  
  
  
  
  
  
  
  
  
  
points 
M 
updated edge segment data 
generation of RAG 
anlyses of 
edge-support regions 
  
  
  
  
  
edge-segment graph 
  
Fig 1.1. The matching procedure. Generation of a 
neighbourhood graph. 
the left and in the right image, a correspondence graph is 
built. The stereo correspondence problem is therefore 
formulated in form of a search for maximum cliques in a 
graph. Horaud and Skordas perform an exhaustive as 
well as a simplified heuristic search in the 
correspondence graph. 
The approaches reviewed here had to be improved 
concerning the matching of curved lines. An algorithm 
was developed that avoids the use of the epipolar 
constraint and nevertheless provides matches efficiently. 
An overview about the developed stereo method is 
shown in flow diagrams. First, both images are processed 
separately (see Fig. 1.1). When two edge neighbourhood 
graphs have been generated, then the matching is 
conducted (see Fig. 1.2). 
2. Edge Detection 
An edge in a digital image occurs when the intensity 
values of neighbouring pixels are significantly different 
(Haralick, 1984). The edge detection is performed in a 
two step procedure. First the image is smoothed by 
Gaussian convolution. Then the edges are computed. 
Here, Haralick's (1984) method for the detection of step 
  
processing left image 
! ! 
extraction of edges 
processing right image 
  
  
extraction of edges 
  
  
  
  
  
  
suitable for hypothetical suitable for hypothetical 
matches matches 
prediction of hypotheses 
  
  
! 
propagation of the 
hypotheses with the help 
of the graph 
! 
solving ambiguous 
matches 
computation of object 
space coordinates 
! 
interactive selection of 
points for further 
processing 
  
  
  
  
  
  
  
  
  
  
  
Fig. 1.2. The matching procedure. Graph-based matching and 
derivation of object space coordinates. 
edges from zero crossings of the second directional 
derivative was implemented according to the suggestions 
given by Hummel and Lowe (1989). 
The main problem in the detection of edges from 
zero crossings of the second derivative of the brightness 
function is due to the fact that the second derivative is 
zero for step edge pixels as well as for pixels where the 
brightness function values are constant. Therefore, the 
zero-crossing pixels have to be tested for edge quality. 
This is done according to Berzins (1984) who has noted 
that a zero crossing is a gradient maximum, if and only if 
Sfi Miro 
gn an? (2.1) 
9... ACH Qt ne 
where a is the directional derivative. 
3. Segment and Corner Generation 
The edge pixels and non-edge pixels are given in the 
form of a binary image. It is not explicitly known how 
edge pixels are connected to long chains of edge pixels, 
and where these chains begin or end. Therefore, it is 
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