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Various aproaches to relative pose problem

Keywords:

A.V. Gasilov – Research Engineer, Orel Branch of Institute of Informatics Problems of RAS E-mail: gasilov.av@ya.ru O.A. Yakovlev – Research Engineer, Orel Branch of Institute of Informatics Problems of RAS E-mail: maucra@gmail.com


In this paper we consider various approaches to the problem of relative pose estimation of two cameras from point correspondences based on the epipolar geometry. Two-view geometric way to compute essential matrix which contains data about cameras relative pose is described. We review two algorithms for computation of the essential matrix viz. Hartley’s eight-point algorithm and Nister’s five-point algorithm. Nister’s algorithm uses additional property of the essential matrix that the two non-zero singular values are equal. This property also leads to the theorem of singular value decomposition of the essential matrix that allows to extract relative pose of two cameras. Usage of this theorem gives us four possible solutions and only one of the four choices corresponds to the true configuration. In this paper we propose a method to sift incorrect solutions using triangulated points positions in coordinate system with respect to both cameras.
References:

 

  1. Hartley R., Zisserman A. Multiple view geometry in computer vision. NewYork: CambridgeUniversityPress. 2004. 655 p.
  2. Hartley R. In defense of the eight-point algorithm // IEEE Trans. on Pattern Analysis and Machine Intelligence. 1997. V. 19. № 6. P. 580−593.
  3. Nister D. An efficient solution to the five-point relative pose problem // IEEE Conf. on Computer Vision and Pattern Recognition. 2004. V. 2. P. 195−202.
  4. Krivulin N. An analysis of the Least Median of Squares regression problem // Proc. 10th Symp. on Computational Statistics. Neuchatel. 1992. V. 1. P. 471−476.

 

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