Journal
IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
Volume 34, Issue 12, Pages 2303-2314Publisher
IEEE COMPUTER SOC
DOI: 10.1109/TPAMI.2012.43
Keywords
Camera calibration; camera motion estimation; epipolar geometry; minimal solver; polynomial root finding
Funding
- Australian Research Council-ARC
- Australian Government
- Australian Research Council through the ICT Centre of Excellence Program
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In this paper, we present an efficient new approach for solving two-view minimal-case problems in camera motion estimation, most notably the so-called five-point relative orientation problem and the six-point focal-length problem. Our approach is based on the hidden variable technique used in solving multivariate polynomial systems. The resulting algorithm is conceptually simple, which involves a relaxation which replaces monomials in all but one of the variables to reduce the problem to the solution of sets of linear equations, as well as solving a polynomial eigenvalue problem (polyeig). To efficiently find the polynomial eigenvalues, we make novel use of several numeric techniques, which include quotient-free Gaussian elimination, Levinson-Durbin iteration, and also a dedicated root-polishing procedure. We have tested the approach on different minimal cases and extensions, with satisfactory results obtained. Both the executables and source codes of the proposed algorithms are made freely downloadable.
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