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.