International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXIX-B3, 2012 
XXII ISPRS Congress, 25 August — 01 September 2012, Melbourne, Australia 
2.2.2 Constraint of Candidate Lines Based on the 
Modified Homograph Matrix 
In the field of computer vision, the homograph matrix only be 
applied to transfer the features between two images. This paper 
introduces the principle of homograph matrix in the line 
matching algorithm, and realizes the effective location 
constraint for the line segments sets of the left and right images. 
For aerial images, according to the complex surface relief 
especially in the urban areas, if only adopt one homograph 
matrix in the matching process, the offset of homologous lines 
will be very large after the projection of homograph matrix. In 
order to avoid this situation, this paper modifies the homograph 
matrix algorithm. For each line to be matched, it utilizes the 
homologous points in the neighbourhood of line to calculate the 
homograph matrix. 
Firstly, it determines the existing homologous points in the 
neighbourhood of line to be matched, and calculates the 
homograph matrix with them. Then, it projects the line to be 
matched to the right image based on the homograph matrix, and 
determines the possible candidate lines in the right image 
according to the distance between the central points of lines and 
the distance from central point to other lines. The principle is 
shown as Figure 2: 
  
L 
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middle point = > 
vertical point 
  
  
  
  
  
  
Figure 2. Constraint of candidate lines based on the modified 
homograph matrix 
2.3 Gray Similarity Constraint 
Taking the fitted two line sets A and B as the references, and 
comprehensively considering the following three kinds of 
similarity constraints: 
(1) Similarity constraint of line angle 
The slope À of the extracted line can be calculated by 
the coordinates of the two end points, and then the inclination 
6 of this line also can be solved. 
60 = arctan k (5) 
An sim(m,,m,) — cos(8, —O,) (6) 
Where 0, is the inclination of target line 772, , and 9, is the 
inclination of searching line 772 b: 
(2) Similarity constraint of distance from the origin of image to 
the line the polar equation of line is: 
p=x-cos@+y-sinf,0<0<r (7) 
Where pO is the distance from the origin of image to the line in 
the polar space, i.e., the vertical distance from the origin to the 
line. 
Rho sim(m,,m,) ^ abs(p, — p,) (8) 
Where pO, is the distance from the origin of target image to the 
target line M, , and JO, is the distance from the origin of target 
image to the searching line 771, . 
(3) Similarity constraint of overlap between lines 
Lap sim(m,,m,) — overlap(m,, m,) 
(9) 
Where overlap(m,,m,) expresses the overlap length of 
line 772, and line 7, , length(m, ) is the length of line L, 4» and 
length(m,) is the length of line 77, . 
2.4 Epipolar Constraint 
If a pair of matching lines satisfies all the above similarity 
constraints, then the epipolar constraint will be used to find out 
the corresponding overlap segments between the two lines (Wu 
Bo, 2012). For example, for a pair of matching lines AC and 
BD in Fig. 3(a) and (b), the epipolar lines of the end points of 
AC and BD can be derived as illustrated using dashed lines in 
Fig. 3. By intersecting these epipolar lines with the lines AC 
and BD, the overlap segments between these two lines can be 
obtained, which is AD’ and A’D. 
  
  
  
  
  
  
  
  
  
(a) Left image (b) Right image 
Figure 3. Using epipolar constraint to find corresponding 
overlap segments for line matching 
2.5 Brightness Contrast Constraint 
After the epipolar constraint, it obtains the overlap segments of 
homologous lines. The brightness contrast in a local buffering 
region along both sides of the matching lines can be used to 
further disambiguate the line matching. 
  
(left) the supporting region of linear feature 
(right) the decomposition of supporting region 
Figure 4. Linear feature supporting region and decomposition 
Firstly, it needs to introduce the concept of linear feature 
supporting region. As shown in Figure 4 (a), L is a straight 
line segment which length is M in the discrete 1mage surface. 
Then limits a rectangular area with the central axis is L and 
~~ TTT 
min(/ength(m,), length(m,)) 
  
    
  
   
   
    
    
   
    
    
   
   
    
   
    
   
   
   
   
   
   
    
  
   
   
   
  
     
    
    
    
      
  
  
    
    
  
    
     
    
   
    
    
      
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