The Development and Comparison of Robust Methodsfor Estimating the Fundamental Matrix

  • Authors:

  • P. H. S. Torr;D. W. Murray

  • Affiliations:

  • Department of Engineering Science, University of Oxford, Parks Road, Oxford, OX1 3PJ, UK. E-mail: phst@robots.ox.ac.uk, dwm@robots.ox.ac.uk;Department of Engineering Science, University of Oxford, Parks Road, Oxford, OX1 3PJ, UK. E-mail: phst@robots.ox.ac.uk, dwm@robots.ox.ac.uk

  • Venue:
  • International Journal of Computer Vision
  • Year:
  • 1997

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Abstract

This paper has two goals. The first is to develop a variety of robustmethods for the computation of the Fundamental Matrix, thecalibration-free representation of camera motion. The methods aredrawn from the principal categories of robust estimators, viz. casedeletion diagnostics, M-estimators and random sampling, and the paperdevelops the theory required to apply them to non-linear orthogonalregression problems. Although a considerable amount of interest hasfocussed 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. Thesecond goal is therefore to compare and judge the methods.Comparative tests are carried out using correspondences generatedboth synthetically in a statistically controlled fashion and fromfeature matching in real imagery. In contrast with previouslyreported methods the goodness of fit to the synthetic observations isjudged not in terms of the fit to the observations per se butin terms of fit to the ground truth. A variety of error measures areexamined. The experiments allow a statistically satisfying andquasi-optimal method to be synthesized, which is shown to be stablewith up to 50 percent outlier contamination, and may still be used ifthere are more than 50 percent outliers. Performance bounds areestablished for the method, and a variety of robust methods toestimate the standard deviation of the error and covariance matrix ofthe parameters are examined.The results of the comparison have broad applicability to visionalgorithms where the input data are corrupted not only by noise butalso by gross outliers.