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arranging the projective centers in a square (-> intersection 
of epipolar lines) or on a line (-> double verification of 
possible matches). Such an arrangement will lead to a 
reduction factor of at least 100 and almost press the number 
of remaining ambiguities against zero. An extension to an 
arbitrary number of cameras is also possible but will rarely 
be necessary. 
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Figure 11: Intersection of epipolar lines in a four-camera 
arrangement 
All the above considerations are only valid for targets 
randomly distributed in space without a continuous surface. 
Not randomly distributed targets, e.g. regular dot patterns 
projected onto a surface to generate an artificial texture 
(Maas, 1991) may lead to no overlapping targets but much 
larger numbers of ambiguities, if the pattern is oriented in a 
way that it is parallel with the epipolar lines in one or more 
images. 
3. Results 
To test the method it has been applied to simulated datasets 
and in several real experiments under various conditions 
with good success. In the particle tracking velocimetry 
experiments a maximum of about 1000 instantaneous 
velocity vectors could be determined with a three camera 
setup. To achieve a much higher yield seems to be difficult 
with current CCD-sensor resolution mainly due to image 
quality and because the number of overlapping particles 
becomes too large. A two camera system could only give 
reliable results if the number of particles in the test section 
and the depth range (i.e. the thickness of the illuminated 
layer in the water) were strictly controlled. A sample result 
of particle tracking velocimetry with three cameras is 
shown in Figure 12 
  
A much higher spatial resolution was achieved when prob- 
lems with overlapping targets or with ambiguities in 
tracking could be avoided; in an application of surface 
measurement with a regular dot pattern projected on a 
surface of an industrial object which did not show any 
natural texture (Maas, 1991) it was possible to establish 
correspondences between more than 5000 discrete points 
per image of 720 x 574 pixels. 
  
   
     
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Figure 12: Example results (0.5 sec. flow data in a stirred aquarium) 
References: 
1. Adrian, R., 1991: Particle-Imaging Techniques for Ex- 
perimantal Fluid Mechanics. Annual Review of Fluid 
Mechanics, Vol. 23 
2. Kearney, J.K., 1991: Trinocular Correspondence for 
Particles and Streaks. Dept. of Computer Science, The 
University of Iowa, Technical Report 91-01 
3. Lotz, R., Fróschle, E., 1990: 3D-Vision mittels Stereo- 
bildauswertung bei Videobildraten. 12. DAGM-Sympo- 
sium Mustererkennung, Informatik Fachberichte 254, 
Springer Verlag 
4. Maas, H.-G., 1990: Digital Photogrammetry for Deter- 
mination of Tracer Particle Coordinates in Turbulent 
Flow Research. ISPRS Com. V Symposium “Close 
Range Photogrammetry Meets Machine Vision", 3.-7. 
September 1990, Zurich, Switzerland, published in 
SPIE Proceedings Series Vol 1395, Part 1 
5. Maas, H.-G., 1991: Automated Surface Reconstruction 
with Structured Light. Int. Conference on Industrial Vi- 
sion Metrology, Winnipeg, July 11-12, SPIE Proceed- 
ings Series Vol. 1526 
6. Maas, H.-G., 1992: Complexity analysis for the deter- 
mination of dense spatial target fields. 2nd International 
Workshop on Robust Computer Vision, March 9-12, 
Bonn, Germany 
7. Papantoniou, D., Maas, H.-G., 1990: Recent Advances 
in 3-D Particle Tracking Velocimetry. Proceedings 5th 
International Symposium on the Application of Laser 
Techniques in Fluid Mechanics, Lisbon, July 9-12