ISPRS Commission III, Vol.34, Part 3A „Photogrammetric Computer Vision“, Graz, 2002
These equations provide six independent homogenous equa-
tions in 33 variables. These variables include the trinilear
tensor and the two translation vectors. Therefore, in gen-
eral six cylinder correspondences over three frames pro-
vide us with a linear solution for structure from motion
problem. Once the translational vectors T and U are esti-
mated, The rotation matrices R and S can be easily recov-
ered from F, F and G.
7 CONCLUSION
In this paper, we introduce a canonical representation of
cylinders based on the Pliicker line respresentation. The
basic motion equations for points and lines have been well
described in the computer vision literature. This paper
completes this picture by describing the motion equations
for cylinders. One of the originality of this paper is in
considering the cylinder as an observable geometrical en-
tity instead of only describing the equations provided by
the geometrical constraints of its occluding edges. Based
on this simple and elegant representation all the necessary
structure and motion equations are derived.
This paper also provides a link between the trilinear ten-
sor, defined for points and lines, and the three view ge-
ometry of cylinders. It finally proposes a linear algorithm,
which allows the recovery of structure from motion based
on a minimum of six cylinder correspondences over three
views.
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