204 
5 STEREO CORRESPONDENCE 
The stereo correspondence problem is to find for a given trajectory in the right (left) camera coordinate sy- 
stem the corresponding trajectory in the left (right) camera coordinate system. With respect to the con- 
straints itis possible to find correspondence criteria to match the trajectories fast and reliable. 
5.1 Constraints 
The following constraints can be found: 
- uniqueness (5.1) 
- epipolar constraint (523 
- correspondence has to match for the whole trajectory (5.3) 
Because each particle exists physically exactly one time the corrsepondence must be solved unique. Ambiguties 
not being resolved indicate an error in the particle tracking respectively to high particle densities. 
A point in the right image corresponding to a point in the left image must lie somewhere on a particular line. This 
line is the epipolar line. The length of the epipolar line can be resctricted with the knowledge of the size of the illu- 
minated light sheet. The position of the epipolar line is estimated using a 3D grid positioned in the light sheet. 
A single trajectory can only be created by a single particle. Thus the correspondence has to be carried out for all 
points of a trajectory. not for some part(s) of the trajectory. 
52. Correspondence criteria 
Single particles don *t distinguish in size, shape or light intensity. Thus features resulting of the epipolar con- 
straint are used to match correspending trajectories. Considering the multimedia geometry (Maas 1992), the 
epipolar line is a curve, which can be approximated by a polygon. Adding a tolerance to this po ygone given by the 
accuracy of the camera coordinates, we get a two dimensional search area, to find the point of a possible cor- 
responding trajectory. This criterion has to be satisfied for every single point of the corresponding trajectory. 
To save computation time a rectangle is used as the search area instead of the polygon. 
Alcan this criterion creates a linked list of correspondence candidates, containing null, one or multiple can- 
didates. The following cases can be found: 
-11 Both, the left and right trajectory have just a single candidate, the trajectories correspond 
Thee 
A CS 
- tm(m:f) the left (right) trajectory has multiple right (left) candidates. These again have exactly this 
left (right) trajectory as a candidate. 
Example: the lower trajectory got parted by a disturbance in the particle tracking 
TT 1e 
-m:m the left trajectory has multiple right candidates and these by themselves have multiple left 
trajectories as candidates 
IAPRS, Vol. 30, Part 5W1, ISPRS Intercommission Workshop "From Pixels to Sequences", Zurich, March 22-24 1995