Optimization and Systems Theory Seminar
Wednesday, May 26, 1999, 15.00-16.00, Room 3721, Lindstedtsv. 25
Jana Kosecka and Shankar Sastry
Electrical Engineering and Computer Science
University of California
Berkeley, California, USA
Euclidean reconstruction and reprojection up to subgroups
The necessary and sufficient conditions for being able to estimate
scene structure, motion and camera calibration from a sequence of
images are very rarely satisfied in practice. What exactly, then, can
be estimated in sequences of practical importance, when such
conditions are not satisfied? In this paper we give a complete answer
to this question. For every camera motion that fails to satisfy the
conditions for unique reconstruction, we give an explicit
characterization of the ambiguity in the reconstructed scene, motion
and calibration. When the purpose of the reconstruction is to generate
novel views of the scene, we characterize the vantage points that give
rise to a valid Euclidean reprojection. We also characterize
viewpoints that make the reprojection invariant to the ambiguity.
The key to our findings lies in a powerful result on the dependency of
multilinear constraints: we prove that the coefficients of multilinear
constraints involving any number of images can be generated from
coefficients of bilinear constraints alone. Therefore, all the
analysis can be carried out using only two views at a time.
Calendar of seminars
Last update: May 21, 1999 by
Anders Forsgren,
anders.forsgren@math.kth.se.