Optimal structure from motion: local ambiguities and globalestimates
Soatto, S.
Brockett, R.
Washington Univ., St. Louis, MO;
This paper appears in: Computer Vision and Pattern Recognition, 1998. Proceedings. 1998 IEEE Computer Society Conference on
Publication Date: 23-25 Jun 1998
On page(s): 282-288
Meeting Date: 06/23/1998 - 06/25/1998
Location: Santa Barbara, CA, USA
ISSN: 1063-6919
ISBN: 0-8186-8497-6
References Cited: 20
INSPEC Accession Number: 5985857
Digital Object Identifier: 10.1109/CVPR.1998.698621
Current Version Published: 2002-08-06
Abstract
We present an analysis of SFM from the point of view of noise.
This analysis results in an algorithm that is provably convergent and
provably optimal with respect to a chosen norm. In particular, we cast
SFM as a nonlinear optimization problem and define a bilinear projection
iteration that converges to fixed points of a certain cost-function. We
then show that such fixed points are “fundamental”, i.e.
intrinsic to the problem of SFM and not an artifact introduced by our
algorithm. We classify and characterize geometrically local extrema, and
we argue that they correspond to phenomena observed in visual
psychophysics. Finally, we show under what conditions it is
possible-given convergence to a local extremum-to “jump” to
the valley containing the optimum; this leads us to suggest a
representation of the scene which is invariant with respect to such
local extrema
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