Proceeding from a point P’ in the image I; all epipolar 
lines E, ,, in D and E, ,4 in I5 are being derived, on 
which candidates P,”, P,"" and P," resp. P4", P," and 
P," may be assumed to be found. An unambiguous deter- 
mination of the particle image corresponding to P^ can 
neither be found in I, nor in I4. However if all epipolar 
lines E (,_,4) of all candidates ©; in I are being inter- 
sected with the epipolar line E, _, 4, there will be a large 
probability that only one of the intersection points will be 
close at one of the candidates in I, (in Figure 4: P"). 
This consideration has been implemented via a combina- 
torics algorithm which tries to find such consistent triplets 
in the three datasets and rejects points which are members 
of more than one consistent triplet. Such an unambigous 
consistent triplet is a necessary and sufficient condition for 
the establishment of a correct correspondence. A similar, 
iterative approach can be found in (Kearney, 1991). 
This procedure can reduce the probability of ambiguities 
drastically, but not totally. The remaining unsolvable, but 
detectable ambiguities can be seperated into three cases: 
1. a *wrong' candidate Q" on the epipolar line E, _,, has 
got a corresponding particle image Q"' on E, ,,, 
which accidently falls onto the epipolar line E, _, 3 : 
  
  
  
  
  
  
h 
P hia 
e 2 
p" Q" 
h b 
  
  
  
  
  
© ‘correct’ candidate © ‘wrong’ candidate 
Figure 5: intersection of epipolar lines - first kind of ambiguity 
For a point P centered in object space we get with: 
  
home bi, : (Z ax Emin) 
7 Zmin : Zmaz 
I bys : (Zaz min) 
| Zin : Zar 
(Eq. 5) 
hzc by 1 (Zar min) 
2 Z nin ; Z nat 
4.¢? 
f57K, 40K), na 
and with 
25 (n-— 1) “CE b: (Z max 7 nin) 
Pip = Fg s (Eq. 6) 
min max 
   
= Jas = 2-277 in mar (E 7 
CUN iles aum rmi MN NR 
max min) 
  
P, 
the probability P, of this first kind of ambiguities be- 
comes 
4- (n-1)  - b, 
; Eq. 8 
F :b34: sina (E 
Pac) = Pa Pa > 
2. the epipolar line E,_,, of a ‘wrong’ candidate Q” on 
the epipolar line E, _,, does also hit the ‘correct’ can- 
didate P”” on E,_,, , because a candidate Q" is 
placed too close at the ‘correct’ candidate P"', or be- 
cause a too short base component b;4 has been chosen: 
  
  
  
  
  
  
  
  
  
  
  
© ‘correct’ candidate © ‘wrong’ candidate 
Figure 6: intersection of epipolar lines - second kind of ambiguity 
With (Eq. 5), (Eq. 6) the probability for this second kind 
of ambiguity is 
f 
Pay = Pug 
4-(n-l) -€- 5, 
UEM SE (En 
3. A second candidate R"'" is found at the intersection of 
the epipolar lines E, ,4 and E, ,4 ofthe ‘correct’ 
candidate P'/P" - an event which is often correlated 
with the occurence of an overlap: 
  
  
  
  
  
  
h b 
  
  
  
  
  
Q ‘correct’ candidate © ‘wrong’ candidate 
Figure 7: 
    
intersection of epipolar lines - third kind of ambiguity