An Alternative Formulation for Five Point Relative Pose Problem

The "Five Point Relative Pose Problem" is to find all possible camera configurations between two calibrated views of a scene given five point-correspondences. We take a fresh look at this well-studied problem with an emphasis on the parametrization of Essential Matrices used by various methods over the years. Using one of these parametrizations, a novel algorithm is proposed, in which the solution to the problem is encoded in a system of nine quadratic equations in six variables, and is reached by formulating this as a constrained optimization problem. We compare our algorithm with an existing 5-point method, and show our formulation to be more robust in the presence of noise.

[1]  David Nister,et al.  Recent developments on direct relative orientation , 2006 .

[2]  David Nistér,et al.  An efficient solution to the five-point relative pose problem , 2004, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[3]  Anders Heyden,et al.  Reconstruction from Calibrated Cameras—A New Proof of the Kruppa-Demazure Theorem , 1999, Journal of Mathematical Imaging and Vision.

[4]  William H. Press,et al.  Numerical recipes in C , 2002 .

[5]  Wei Wang,et al.  A SVD decomposition of essential matrix with eight solutions for the relative positions of two perspective cameras , 2000, Proceedings 15th International Conference on Pattern Recognition. ICPR-2000.

[6]  Bill Triggs Routines for Relative Pose of Two Calibrated Cameras from 5 Points , 2000 .

[7]  J. Philip A non-iterative algorithm for determining all essential matrices corresponding to five point pairs , 1996 .

[8]  S. P. Mudur,et al.  Three-dimensional computer vision: a geometric viewpoint , 1993 .

[9]  Thomas S. Huang,et al.  Theory of Reconstruction from Image Motion , 1992 .

[10]  William H. Press,et al.  Numerical Recipes in C, 2nd Edition , 1992 .

[11]  O. Faugeras,et al.  Motion from point matches: Multiplicity of solutions , 1989, [1989] Proceedings. Workshop on Visual Motion.

[12]  H. C. Longuet-Higgins The reconstruction of a plane surface from two perspective projections , 1986, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[13]  Forman S. Acton,et al.  Numerical methods that work , 1970 .