Xiunguang Zhou 
  
correspond to more than one point in the right image. For the matching task at level j+1 the same geometry constraint 
cross-correlation sub-algorithm as described in section 6 was employed. In stead of using the edge correspondence to 
determine the local geometry correspondence in section 6, the local geometry affine transform coefficient matrix was 
derived from the coordinates of the matched points at the higher level. For the reliability, we expanded the searching 
range one pixel more both in x and y direction. 
7.2 Least Square Matching 
After the matching iteration procedure was finished at the base level of the image pyramid, for each point in the left 
image we obtained its conjugate point in the right image in pixel accuracy. In the final matching step, the Least Square 
Matching (LSM) was performed at the base level to get sub-pixel accuracy. As Least Square Matching is a very popular 
and well known algorithm, it is not necessary to describe the algorithm here. We added a constraint in LSM to 
guarantee that each matched pair has a logical geometric relationship to its neighbors. The constraint is: if a point is on 
the left (or, right, upper, lower) side of another point in one image, this characteristic must be kept in the other image. A 
conflict can easily happen, if the LSM is applied to each pixel in the image. For each output from LSM iteration we 
checked the logical relationship with its neighbors. If a conflict happened, we stopped the LSM and took the last 
iteration result as the output. If the check failed at the first iteration, we simply took the initial coordinates as the output 
of LSM. 
8 RESULTS AND CONCLUSION 
We used different MOMS stereo images in our experiments. The resolution of MOMS image is 13.5 m / pixel. Figure 7 
shows a MOMS stereo image pair that we already used as examples to show the image pyramid and edge extraction. It 
is clear that there are non-linear geometry differences between the two images. Due to the different perspective view of 
the left and right image, the scale difference and orientation difference are quite large. Our technique produced very 
good matching results. The quality of the matching result can be checked by verifying the generated DEM and its 
shaded-relief. In this paper we only use this check method. Each point in the generated DEM was directly obtained by 
the forward intersection without any interpolation. This will show how good of each matched point pair is. Compare the 
shaded-relief image with the original image, you can see what details are obtained in the DEM. Figure 8 shows a DEM 
that generated in such a way. Figure 9 shows the shaded-relief image. Figure 10 shows the location of the shaded-relief 
image in the original image. 
   
   
  
    
| Fig. 7 A MOMS stereo image pair 
? (a) left image (b) right image 
  
(a) (b) 
    
  
  
  
  
Fig.8 Generated DEM Fig.9 Shaded-relief image Fig 10 The location of the shaded- 
relief image. 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 1061