ence feature 
tures to the 
med with its 
of each fea- 
ture triangle 
irest features 
T2 between 
IGHT image 
  
and f3 
amongst the 
age then the 
tions are de- 
ole (2). The 
topology be- 
ing features, 
id fa. Even 
neighbouring 
sature match 
(4) 
A, B, C are 
9 of the three 
hing triangle 
stance ratios 
discarded by 
likely match- 
T image that 
e the possible 
iture Correla- 
o a reference 
ite should be 
example only 
CIRCLES are 
d radiometric 
nany features 
which would 
g formed. 
same number 
to only select 
  
candidates with a high correlation value, then only the valid 
candidates for each feature in the reference triangle need to 
be checked. If the features fi, f» and fs of figure 3 have I, J 
and K valid matching candidates respectively then the total 
number of possible triangle combinations will be I * J * K. 
Note that for the example shown above only the two most 
likely candidates are indicated thus 7 — J — K — 2, giving a 
total of eight possible triangle combinations. 
R57 R8 R19 
R57 R8 R33 
R57 | R33 | R19 
R57 i R33 | R33 
R25 R8 | R19 
R25 R8 R33 
R25 | R33 { R19 
R25 | R33 | R33 
  
  
  
  
  
  
Table 3: Possible Matching Triangle Combinations for the 
Triangle L25-L8-L19 
Table 3 shows the possible triangle combinations that can be 
formed to verify the match between features L25 and R25. 
The reference triangle has been formed between features L25, 
L8 and L19. From table 2 the possible matching triangle 
combinations can now be formed, as indicated in table 3. This 
table is arranged such that the most likely matching triangle 
is checked first through to the least likely matching triangle 
last. The correct triangle combination R25-R8-R19 has been 
highlighted in table 2. Note that illegal triangle combinations 
can be formed, such as the fourth combination R57-R33-R33, 
which is automatically discarded by the matching algorithm. 
In this specific example the first four entries in table 3 have 
R57 as the most likely matching candidate for L25. As R57 
in figure 1 is situated far from the correct match R25, the 
scale limit between the two triangles will be violated and all 
four combinations will automatically be discarded. The scale 
limit has been introduced to further reduce the search space 
by limiting the size difference between corresponding sides of 
the reference and candidate triangles to no more than twenty 
percent. 
  
  
  
  
  
  
  
  
  
Figure 4: Similar Triangles for L25 a) and R25 b) 
The reader is referred to figure 4 for the matching trian- 
gles verifying the match between features L25 and R25. The 
nearest neighbours to L25 in the LEFT image are L8 and L19 
respectively, with the feature triangle between the centroids 
707 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996 
     
     
    
    
    
    
   
     
  
      
     
   
   
    
    
     
      
   
   
    
   
    
   
     
   
    
  
    
   
    
      
    
   
   
    
   
    
    
    
   
    
  
   
   
   
      
   
of these features shown in figure 4 a). The corresponding 
triangle in the RIGHT image joins the centroids of R25, R8 
and R19 shown in figure 4 b). Table 2 indicates that R25 is 
the second most likely matching candidate for L25, R19 is the 
most likely matching candidate for L19 and R8 is the most 
likely matching candidate for L8. The confidence index for 
the correct match is 94.30 96. Even though R25 was not the 
most likely matching candidate the correct match was still 
found. 
The sides of the reference triangle have been arranged in 
ascending order in size such that 
a sb<c (5) 
as suggested by Cox and de Jager [4]. 
This has the effect of limiting the ratios used for triangle 
comparison to the range between zero and one i.e. 
0<=<1 and oO od (6) 
C 
eoe 
A confidence index is introduced to quantify the similarity be- 
tween triangles, and is calculated using the Euclidean distance 
between the triangle side ratios. The Euclidean distance e be- 
tween the triangle side ratios is 
  
ed - d» Dr (7) 
which is the error vector between the left and right triangle 
ratios. 
The error vector & can be normalised by introducing the the- 
oretical minima and maxima of equation (7). The minimum 
value for equation (7) (emin = 0) occurs when the matched 
triangles are identical. A maximum for equation (7) arises for 
¢ =% =1, ie an equilateral triangle, and 4 = £ close 
to 0, a theoretical case which will not occur in practise. The 
theoretical maximum is thus Emaz = V2. 
This normalizing factor of V2 is now used to calculate the 
confidence index CT as 
€ 
p (8) 
If the triangle is perfectly matched the Euclidean distance € 
is zero and the confidence index is 100 %. As the Euclidean 
distance increases due to dissimilar triangles the confidence 
index becomes smaller. |t is assumed that corresponding 
sides have the same relationship as the reference triangle i.e. 
A € B € C. In practice however this relationship might not 
hold for an incorrect triangle, which could result in triangle 
side ratios for the right triangle of greater than one, which 
could result in negative values for the confidence index. These 
negative values merely serve as an indication of a very strong 
mismatch between the reference and candidate triangles. 
CI = 100(1 — 
5 RELATIVE ORIENTATION 
The relative orientation is performed using a three step pro- 
cedure that utilizes a "coarse-to-fine" approach. The first ori- 
entation approximation relies on the centroids of the features 
matched in the previous topology-based matching process.