Herbert Jahn 
  
instead of the blurred images g, (8). The original image g used here besides g, preserves detail, and hence reduces the 
number of wrong disparities in image regions with fine structure. Some experiments showed that & = 0» — 1 seem to 
be good values, and that, using 2, instead of , , the number of necessary pyramid layers can be reduced. 
The method can be enhanced further if instead of the gray values alone additional local image features are taken into 
account. Here, the image gradients in x- and y- direction have been used. Then, the algorithm (4) is applied to 
JG ss = le Gi) geli+s, +s, fF +7, IV.8.6G.0)-V.geli +5, t 
> (11) 
+, Tan 6 Val HS hs, J 
This gives considerably better results because some ambiguity is removed. The problem of choosing adequate features 
is not considered here. It seems that wavelet transform coefficients give good results which also have been applied in a 
coarse-to-fine pyramid (Kim et al, 1997). (11) shows how such and other features can be used in the algorithm 
described here. It was not investigated which the best choice of the parameters yj, Y,, Y; is. The results presented in 
section 3 were obtained with y, = y = y, = 1. 
The steps (8), (10), (11) for reducing ambiguity are not sufficient. Other measures are necessary. In the literature many 
constraints have been formulated (Klette et al., 1998) which can be exploited to reduce ambiguity further. Here, the so- 
called ordering constraint (Klette et al., 1998, Wei et al., 1998) is used. This means that (in x-direction) if gr(i+s,(i,j).j) 
is matched to g;(i,j) and gg(i+1+s,(i+1,)) to g;(i+1,j) then 
i s, (i, j) £i 139 s, (i 1, j) (12) 
must be fulfilled. (The same holds in y-direction). This is equivalent to the condition that the distance 
d,G, j) 21 s, G1, j) - s, Q, J) (13) 
of successive matched image points i’, i’+1 (i’ = i+s,(7)) of the gx — image must be non-negative. 
The condition (12) can be violated if there exist objects which are located in front of other objects (or the background) 
such that there is no continuous surface (see e.g. Klette et al., 1998). In aerial images this case is met when single clouds 
are present. In cloud free conditions it is met seldom. Up to now (12) is used not very often to enhance matching. One 
of the exceptions is the algorithm of Gimel'farb, 1999 which is based on dynamic programming and which gives good 
results for epipolar geometry. 
The condition (12) has to be fulfilled in each iteration of the algorithm (4). To guarantee this the step width As'(i,j) 
must be limited. If e.g. AsV, j) > O then the point (i + s 
X 
(i, j).j) will be shifted in positive x-direction. To 
fulfill (12) even if the next point (i +1+ si +1, i) j) is shifted in negative x—direction the increment As, J) 
can be limited as follows: 
d") — wy xev kso ati V2 
(6) 
AS j)-]-a"(9-17y2 ^ "gy x, v JG js )y«-4" 071 j)y/2 (14^ 
X 
K, V.J(i, jis?) elsewhere 
The condition (14) is essential for the reduction of ambiguity because it prevents outliers (which do not obey the order 
constraint and which can be very frequent without application of (14)) of the disparity generated by noise and other 
deviations of both images. Of course, because (14) reduces the possible step size in each iteration many iterations may 
be necessary if the disparities are big. This is a drawback which might be reduced if the directions of VJ in the right 
and left neighbors of point i are taken into account but this was not studied up to now. 
  
440 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000.