v" 
L2 ^ e*t 
c 
— — AV 
Av 
M 
m — -— — 
Xiunguang Zhou 
  
  
sd,) - d |j 2 k-2,.k 2] mn 
Figure 5 demonstrates the search procedure. In figure 5, d. d, ; d, and d, are the 
? 
Hl? 
tracing paths. à 
Lao fp). We also have the j ; : 
Now we have conjugate feature point pairs ( fp: , fp; ), (fp... 
directions from fp/, pi, p; and ps to. fp; ,, respectively. The dashed lines are the 
1 4 P 
extracted points p; , forkz1 — n, between fp; and fp! ,, and the extracted points p; , 9 "et 2 
for k=1 - n, between fp; and fp;.,. Note that the number of extracted points between fp: p: 
two feature points on the left edge may be different with that on the right image edge. 
Le., m may not equal to n. For these non-feature edge points, it is reasonable that a 
linear segmentation is used to determine there correspondence. That is 
Fig. 5 Guide direction 
  
  
  
A k 
p; = p, j » Round (— *7) fork=1 ~m (8) 
m 
The above procedure was applied to each two-feature-points (including the starting point and the ending point) to obtain 
all conjugate edge points on the conjugate edge pair. Figure 3 (a) and (b) show the matched edges. 
6 GEOMETRY CONSTRAINT CROSS CORRELATION 
The edge matching sub-algorithm only provides conjugate point pairs on edges. These matched points are only a small 
percentage of the whole image. In order to get conjugate point pairs that are not on edges, a sub-algorithm named 
Geometry Constraint Cross-correlation was applied. Cross-correlation is a simple matching algorithm. It only works in 
case that there is no geometry difference between the left and right images. In most remote sensing stereo images, 
geometry difference is the common case. We modified the traditional cross-correlation by introducing a local affine 
transform. The coefficients of the affine transform can be derived from the results of the edge matching sub-algorithm. 
6.1 Local Geometry Correspondence Based On Edge Correspondence 
The local geometry correspondence of the stereo images is described by six affine transform coefficients. Though the 
geometry difference is in general non-linear in the range of whole scene, it can be approximated to be linear if the local 
geometry difference is concerned. Just like an arbitrary curve can be approximated by piece wise lines, the general non- 
linear geometry difference can be described by all linear local differences. The local geometry correspondences of all 
matched edge points were first determined by using the edge correspondences. The Least Square Fitting was used to 
determine the affine transform coefficients. Let p' and p' be a conjugate edge point pair; let Sy and sy be two edge 
point sets, each contains the edge point (p' or p') as well as their neighbor edge points; let C, be local geometry 
affine transform coefficients matrix, we have 
T -1 T 
C, z(AT-AL)'-AT-B, (9) 
where A, = In, S, | is the coefficient matrix combining a unit vector 1 and the left edge point set S,,, B, — IL S, | 
is the observation matrix combining a unit vector 1 and the right edge point set S, : 
In order to let Sy and Sy correctly represent the local geometry correspondence, the edge points in S, should have a 
good distribution surrounding p'. The best distribution is that there are edge points located in the upper-left, upper- 
right, lower-left and lower-right quarters of the location of p'. The selection of Sy was automatically performed by 
scanning the neighbors of p' . 
The local geometry correspondences of non-edge-points were obtained by interpolating the determined geometry 
correspondences on edge points. Therefore we had the local geometry correspondence at every point in the stereo 
images. 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 1059