Complexity analysis for the establishment of image
correspondences of dense spatial target fields
Hans-Gerd Maas
Institute of Geodesy and Photogrammetry, Swiss Federal Institute of Technology
STH - Hoenggerberg, CH - 8093 Zurich
Abstract:
The establishment of stereoscopic correspondences for a large number of targets in a true 3-D application without a contin-
uous surface connecting the targets does often pose difficult problems to automatic or semiautomatic processing systems. If
the targets do not show any features which allow for a reliable distinction of candidates, only the geometric criterium of the
perpendicular distance of a candidate to the epipolar linc can be applied. Depending on the number of targets and the depth
extension of object space this may lead to unsolvable ambiguitics. As an example for this problem an application of digital
photogrammetry to 3-D particle tracking velocimetry can be considered. In this paper two methods will be discussed to
reduce the number of ambiguities drastically by employing three or more cameras in special configurations: the method of
intersection of epipolar lines and a method with asymmetric arrangement of three cameras known from computer vision. In a
detailed analysis of the methods the reduction of the number of expcctable ambiguities, which can amount to a reduction
factor of up to 100, will be proven and quantified.
1. Introduction
Three-dimensional particle tracking velocimetry (3-D
PTV) is one of the most powerful flow measurement tech-
niques. It is based on seeding a flow with small, reflecting,
neutrally buoyant particles and recording image sequences
of these particles by a stereoscopic camcra sctup. To
achieve a sufficiently high spatial resolution a dense
seeding of the flow (1000 - 2000 particles) is usually
required. With video technique and methods of digital
photogrammetry completely automatic PTV systems can
be developed today (Papantoniou/Maas, 1990). Trying to
judge the reliability of such a system one has to cope the
fact that the high target density causes ambiguities in some
steps of the processing of image sequences in order to
derive particle trajectories. The data processing from
images to trajectories can be divided into the following
major processing steps (Maas, 1990):
- Image segmentation / determination of particle image
coordinates
» Establishment of correspondences between particle im-
ages in different views
+ Computation of spatial coordinates
+ Tracking
* (Interpolation to regular grid)
Ambiguities may occur as particles partly or totally over-
lapping cach other in one or more views in the scgmenta-
tion step, as multiple candidates in the cpipolar scarch
window in the procedure of the establishment of sterco-
scopic correspondences and as multiple solutions in:
tracking. This paper will only address ambiguitics in the
photogrammetric matching process; ambiguities in image
segmentation and in tracking can be estimated following
Maas (1992) or Adrian (1991).
Figure 1: Example of particle image (~ 1400 particles)
Figure 1 shows an example of a typical particle image with
some 1400 imaged particles. Once the image coordinates of
all particles in all images have been determined, corre-
spondences between data of the different images have to be
established to be able to calculate the 3-D coordinates. In
photogrammetry we employ the epipolar geometry to solve
this problem. Knowing the orientation parameters of the
cameras from a calibration procedure, proceeding from a
point P'/ in onc image an cpipolar linc in an other image
can be defined on which the corresponding point has to be
found. In the strict mathematical formulation this linc is a
straight line, in the more general case with convergent
