The Development and Comparison of Robust Methods for Estimating the Fundamental Matrix
 P.H.S. Torr,
 D.W. Murray
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This paper has two goals. The first is to develop a variety of robust methods for the computation of the Fundamental Matrix, the calibrationfree representation of camera motion. The methods are drawn from the principal categories of robust estimators, viz. case deletion diagnostics, Mestimators and random sampling, and the paper develops the theory required to apply them to nonlinear orthogonal regression problems. Although a considerable amount of interest has focussed on the application of robust estimation in computer vision, the relative merits of the many individual methods are unknown, leaving the potential practitioner to guess at their value. The second goal is therefore to compare and judge the methods.
Comparative tests are carried out using correspondences generated both synthetically in a statistically controlled fashion and from feature matching in real imagery. In contrast with previously reported methods the goodness of fit to the synthetic observations is judged not in terms of the fit to the observations per se but in terms of fit to the ground truth. A variety of error measures are examined. The experiments allow a statistically satisfying and quasioptimal method to be synthesized, which is shown to be stable with up to 50 percent outlier contamination, and may still be used if there are more than 50 percent outliers. Performance bounds are established for the method, and a variety of robust methods to estimate the standard deviation of the error and covariance matrix of the parameters are examined.
The results of the comparison have broad applicability to vision algorithms where the input data are corrupted not only by noise but also by gross outliers.
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 Title
 The Development and Comparison of Robust Methods for Estimating the Fundamental Matrix
 Journal

International Journal of Computer Vision
Volume 24, Issue 3 , pp 271300
 Cover Date
 19970901
 DOI
 10.1023/A:1007927408552
 Print ISSN
 09205691
 Online ISSN
 15731405
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 robust methods
 fundamental matrix
 matching
 Industry Sectors
 Authors

 P.H.S. Torr ^{(1)}
 D.W. Murray ^{(1)}
 Author Affiliations

 1. Department of Engineering Science, University of Oxford, Parks Road, Oxford, OX1 3PJ, UK