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extracted straight line segments in the 500 x 500-pixel picture with a minimum length of 15 pixels is about 300 in each 
case. The average length of the extracted segments is about 26 pixels. More particular, the edge detection performed on 
the grey-level image lacks to detect some important image features, e.g. the roof border denoted with ' 1^ in Figure (1, a). 
The method based on the maximum of gradients of the three color bands shows the tendency to produce longer contiguous 
line segments, better capturing the underlying image data. Remarkably it fails to detect some important boundaries, e.g. 
the roof ridge marked as '2" in Figure (1, b). The method based on the vector gradient produces results similar to those of 
the maximum method. The extra computational load does not pay off, it seems. 
Taking into account the completeness of the obtained edge-map and the computational simplicity, we advocate using the 
maximum of the norm of the gradients in the single bands, especially if a single edge detection method is to be used. 
In cases where higher computational load is tolerable, it is possible to overcome the individual failures of each method 
by additionally applying a simple fusion step: starting with the edges obtained via one method, one iterates through the 
edge-maps obtained by the other methods and adds isolated edges which are not already present in the initial edge-map. 
  
    
  
  
  
  
  
  
(a) (b) (c) 
Figure 1: Edge detection results for the same image using (a) intensity gradient of grey-level image, (b) maximum of 
gradients in color bands and (c) spatial gradient. The number of detected line segments with a minimum length of 15 
pixels after merging collinear lines was 338 / 317 / 343; the average length of the segments was 26.2 / 26.7 / 26.1 pixels 
respectively. 
3 LINESEGMENT STEREO MATCHING 
Suppose line segments have been determined in both images of a given stereo pair by means of a method described in the 
previous section. Given a line segment in one image, the goal is to find the corresponding line segment (if available) in the 
second image. A first step in this direction is to select those line segments from the second view, which possibly can match 
the given line segment in the first view, thus reducing the search space. Two types of criteria are used for selecting these 
match candidates: geometric constraints based on the geometric relations between the images, and chromatic constraints 
based on the comparison of color properties between flanking regions of (possibly) corresponding line segments. 
31 The geometric constraints 
* Epipolar strip constraint 
Given a line segment 1 in the first view, the epipolar relation between two images of a stereo pair yields a weak 
constraint on the matching line segment in the second view. As depicted in Figure (2), the two endpoints p; and pa 
of the given line segment 1 define two epipolar lines in the second view (1, I, p). on which the corresponding 
points must be found. It is clear that the line segment 1’, corresponding to 1 in the second view, must have a nonempty 
intersection with the image region between the two epipolar lines called the epipolar strip. Hence only the line 
segments that are contained at least partially in this epipolar strip in the second view can be candidate matches for 1. 
Further geometric constraints 
Due to image acquisition, the relative orientation of the two images is known. This restricts possible candidates l’ to 
have less than a maximum angle deviation from the line segment 1 in the first image. 
If we have some indication about the maximum building height in the investigated area, again, due to known external 
camera calibration, we can restrict the region in the second view, where possible match candidates can be found. Still 
there is a huge number of candidates and no further geometrical restrictions can be made. 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 817