for position 
idates in the 
1 and +1 in 
idate and the 
extract the 
f conjugated 
ple, the final 
/s in Table 3. 
matching 
0.0 12.0 
  
ng algorithm 
features, but 
ye the critical 
experiments 
the correct 
ased on our 
us attributes 
ached was to 
tion to their 
ich expresses 
F(J) |,etc.),so 
> that in the 
od attributes. 
possibility of 
| positions of 
signed to the 
n to other 
es which are 
naller weight 
on about the 
stics etc. As 
as chosen: 
D] @) 
)-GL()| 
    
If it is peak-to-valley or valley-to-peak: 
d(LJ) --[I*|PS(D-PSQ)|-0.05*|SF(D-SF)| (3) 
+0.05* |SB(D-SB(J) | -0.01* |GL(I)-GL()|] 
The magnitude of the peak/valley is a very important 
characteristic to be used even if its value is not so 
reliable. Although peaks cannot match with valleys, we 
cannot give the amplitude of a valley a minus value or 
it would destroy the characteristic of the function 
model, which is mainly controlled by the position 
feature. The alternative found was to still treat the 
amplitude of a valley as a positive value but change the 
sign to minus for the resulting distance and use its 
absolute value for searching the smallest value. This 
means that we can still keep the candidacy of a valley 
which would be matched by the peak, but which we 
would never allow to happen. This would stop the peak 
trying to match the other peaks behind the valley and 
would occupy the chance of another pair to match (in 
Fig. 2, let peak c still matches valley d, otherwise peak 
c would match f and prevent e from matching f). This 
is very useful for correct matching in dense peak/valley 
situations. 
| vr Sn 
   
» 
Dez 
(D 
0 
Fig. 2: Keeping the "peak-to-valley" matching to avoid 
mismatching 
Since most of the time a valley shows up after a peak 
(or vice versa), it is also a form of powerful control. 
The way of judging the quality of the cost function 
model is to analyze the distance matrix. It will be a bad 
cost function model if the positions of the smallest 
distance values are distant from the diagonal axis of the 
matrix and their values are rather large. 
The marking technique should be improved to avoid 
leading to one-to-many matching in cases where we 
only apply the simple marking technique mentioned 
before (mark +1 in the marking column/row for the 
minimum distance you want to reserve, mark -1 for the 
one you want to abandon). By examining the results of 
the experiment carefully, we can detect the difficult 
situations where simple making techniques will lead to 
incorrect results (Fig.3). 
475 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
Minimum Marking 
Distance Map Column 
1 2 +1 +] o 1 +1 
3 -1 3 -1 
Marking| *1 -1 -1 #1 
row +1 +1 
Case 1 Case 2 
wrong marking correct marking 
  
  
  
  
  
  
  
  
  
  
  
  
1 +1 1 +1 
2° 5 | -1 +1 3 2 -1 +1 
+1 +1 
*1 -1 -1 + 
Case 3 Case 4 
wrong marking wrong marking 
Fig. 3: The cases where simple marking techniques lead 
to incorrect results 
In Fig. 3, there are three possible cases which might | 
lead to one-to-many matching. These cases are 
presented by their minimum distance map and marking 
column/row. In the first case, searching the first row 
leads to mark [+ 1,-1] in the marking row; searching the 
second row however leads to a change in the first 
decision (i.e., the -1 mark becomes +1), which leads to 
one-to-many matching situations. A similar problem is 
shown in cases 3 and 4. The ambiguity comes from the 
case where the element is "abandoned" during the 
sorting of the previous column/row and is then 
reassigned "reserved" status. Thus, the principle of 
marking would be that once the element has been 
"abandoned", there is no way to change it back to be 
"reserved". Therefore, the marking technique is so 
modified that we initial all elements of marking 
column/row with 0, then we add 1 (instead of replacing 
the marker by +1) to the element that has to be 
reserved, but we subtract a large number (instead of 
replacing the marker by -1) from that element if it has 
to be abandoned. From experiments, this large number 
is assigned to be 3, because there should be no more 
than three "candidates" in one column/row if the cost 
function model is good enough. 
As the linear features should show up continuously in 
adjacent epipolar lines, the matching pairs between 
adjacent epipolar lines are compared with each other. 
If the differences in position of both corresponding 
elements are small and equal to three pixels in size 
(because the location of the detected linear feature 
cannot be defined very exact from a complex terrain 
image after applying the conditional rankorder 
operator), we keep this as the final reliable result. If