Projective least-squares: Global solutions with local optimization

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 jus...

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Bibliographic Details
Published in2009 IEEE Conference on Computer Vision and Pattern Recognition pp. 1216 - 1223
Main Authors Olsson, Carl, Kahl, Fredrik, Hartley, Richard
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.06.2009
Subjects
Australia
Cameras
Computational geometry
Gaussian noise
Least squares methods
Matematik
Mathematics
Maximum likelihood estimation
Motion estimation
Natural Sciences
Naturvetenskap
Optimization methods
Sufficient conditions
Testing
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Summary: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.
ISBN:1424439922
9781424439928
ISSN:1063-6919
1063-6919
DOI:10.1109/CVPR.2009.5206864