Optimization and Systems Theory Seminar
Tuesday, May 25, 1999, 11.00-12.00, Room 3721, Lindstedtsv. 25

Jana Kosecka and Shankar Sastry
Electrical Engineering and Computer Science
University of California
Berkeley, California, USA

Multiview geometry revisited: A differential geometric approach

Multiview geometry has been traditionally developed in the framework of projective geometry. In this talk, we show an alternative approach which uses notation and concepts from differential geometry. We review projective (multilinear) constraints and Euclidean invariants associated with the problem of structure and motion recovery from n views. As a consequence of the study of projective constraints we show geometric dependency of the trilinear and quadrilinear constraints on the bilinear ones and associated conditions on motions which guarantee the dependency. The study of Euclidean invariants leads us to a new derivation and interpretation of Kruppa's equations as a inner product coinvariant of Euclidean transformations in a space with unknown metric. Our differential geometric approach allows us to establish the results in an elegant and concise way and reveal the intrinsic geometric meaning of some classic problems. New results and new algorithms fall naturally out of these new geometric interpretations.
Calendar of seminars
Last update: May 21, 1999 by Anders Forsgren, anders.forsgren@math.kth.se.