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Projective Least-Squares: Global Solutions with Local Optimization

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Author

Summary, in English

Recent work in multiple view geometry has focused on obtaining globally optimal solutions at the price of computational time efficiency. On the other hand, traditional bundle adjustment algorithms have been found to provide good solutions even though there may be multiple local minima. In this paper we justify this observation by giving a simple sufficient condition for global optimality that can be used to verify that a solution obtained from any local method is indeed global. The method is tested on numerous problem instances of both synthetic and real data sets. In the vast majority of cases we are able to verify that the solutions are optimal, in particular for small-scale problems. We also develop a branch and bound procedure that goes beyond verification. In cases where the sufficient condition does not hold, the algorithm returns either of the following two results: (i) a certificate of global optimality for the local solution or (ii) the global solution.

Publishing year

2009

Language

English

Pages

1216-1223

Publication/Series

CVPR: 2009 IEEE Conference on Computer Vision and Pattern Recognition

Document type

Conference paper

Publisher

IEEE - Institute of Electrical and Electronics Engineers Inc.

Topic

  • Mathematics

Conference name

IEEE-Computer-Society Conference on Computer Vision and Pattern Recognition Workshops, 2009

Conference date

2009-06-20 - 2009-06-25

Conference place

Miami Beach, FL, United States

Status

Published

ISBN/ISSN/Other

  • ISSN: 1063-6919