Fundamental matrix estimation A study of error criteria

The fundamental matrix (FM) describes the geometric relations that exist between two images of the same scene Different error criteria are used for estimating FMs from an Input set of correspondences In this paper the accuracy and efficiency aspects of the different error criteria are studied We mathematically and experimentally proved that the most popular error criterion the symmetric epipolar distance is biased It was also shown that despite the similarity between the algebraic expressions of the symmetric epipolar distance and Sampson distance they have different accuracy properties In addition a new error criterion Kanatani distance was proposed and proved to be the most effective for use during the outlier removal phase from accuracy and efficiency perspectives To thoroughly test the accuracy of the different error criteria we proposed a randomized algorithm for Reprojection Error-based Correspondence Generation (RE-CG) As Input RE-CG takes an FM and a desired reprojecnon error value d As output RE-CG generates a random correspondence having that error value Mathematical analysis of this algorithm revealed that the success probability for any given trial is 1 - (2/3)(2) at best and is 1 - (6/7)(2) at worst while experiments demonstrated that the algorithm often succeeds after only one trial (C) 2010 Elsevier B V All rights reserved