Stephan Scholze 
  
  
  
  
  
  
  
P1 / 
1 €,P1 
epipolar strip 
P2 E p 
€,p2 
| (a) Image 1 (b) Image 2 
Figure 2: Epipolar constraint: only the line segments 1’ that are contained at least partially in the epipolar strip can be 
candidate matches for 1. See description in text. 
3.2 The chromatic constraints 
In order to disambiguate line segment matching between views, it proves to by very powerful to take into account infor- 
mation about the neighborhood of the line segments under consideration. In (Schmid and Zisserman, 1997) the intensity 
neighborhood of line segments is exploited to determine the optimal match candidate by computing a similarity measure 
based on cross correlation in the grey-level images. Special attention is payed to determining the correct shape of the 
correlation window, taking into account projective distortions. The idea to assign chromatic region attributes to line seg- 
ments was used in (Henricsson, 1998) for 2D grouping of line segments and extraction of 2D enclosures. The regions 
were basically rectangular, although they were adjusted in order not to extend over other line segments in the image. 
We develop the above ideas further, by using the chromatic information to rule out wrong match candidates in a twofold 
way: First, adaptive flanking regions are defined for each side of an oriented line segment and robust estimators are used to 
characterize the integrated color distribution in each region. For each putative pair we perform a X? test to determine if the 
mean color vector and the covariance matrix of the flanking regions are compatible, at least for one side. After reducing 
the complexity of the problem, the remaining candidates are examined in more detail by computing a cross-correlation 
based similarity measure in the individual color bands, exploiting the pixel-wise one-to-one correspondence induced by 
epipolar geometry. To capture the underlying geometry, the correlation-mask will be delineated through epipolar lines, as 
described in Section (3.4). 
3.2.1 Construction of adaptive flanking regions The flanking regions are defined by translating the given line seg- 
ment in the direction normal to it in the image. The rigid extent of this rectangular region is characterized by two 
parameters: offset and width. The offset quantifies a displacement of the inner region boundary in direction of the normal, 
away from the line segment. The offset is required to reduce color blurring effects occurring at and around the actual 
contour. The width of the region must be chosen to ensure that the region contains enough data samples (pixels) to allow 
a robust statistical analysis of the region properties. We use an offset of one pixel and a width of ten pixels. 
Technically the regions are obtained via an affine transformation which maps the image coordinates into a coordinate 
system, where the flanking region is aligned with the coordinate axes. This transformation allows us to introduce a 
scaling which will be exploited in Section (3.4). To avoid the region from extending over neighboring contours we use 
the simple morphological operator depicted in Figure (3, b). The operator is defined as follows: include the pixel at 
position (7, 7) in the flanking region, if all three shaded pixels already belong to the region and no neighboring contour is 
at position (z, j + 1). Thus the region approaches neighboring contours only up to an offset of one pixel to reduce color 
blurring effects as mentioned above. 
  
  
   
  
   
   
  
Pixels excluded from 
flanking region 
Gij+1 ) | 
Pixels belonging to ES Tt 
neighbouring contour (i,j) | 
| 
  
Pixels belonging to | 
flanking region | 
  
  
  
(a) (b) (c) 
Figure 3: (a): Schematic representation of resulting adaptive flanking region. (b): The morphological 3 x 3 mask used to 
grow the region. (c): Example of a flanking region. Pixels belonging to the region are depicted dark. The missing pixels 
inside the region are chromatic outliers, see Section (3.2.2) for details. 
3.2[2 Computing chromatic attributes To each of the flanking regions, we want to assign attributes which represent 
the chromatic properties of the pixels in the region. Small differences in illumination conditions between images taken in 
  
818 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 
  
C9) Co "M 5