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Issue No. 12 - Dec. (2012 vol. 34)
ISSN: 0162-8828
pp: 2303-2314
R. Hartley , Sch. of Eng. (RSISE), Australian Nat. Univ., Canberra, ACT, Australia
Hongdong Li , Sch. of Eng. (RSISE), Australian Nat. Univ., Canberra, ACT, Australia
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.
polynomials, eigenvalues and eigenfunctions, Gaussian processes, image sensors, iterative methods, motion estimation, dedicated root-polishing procedure, hidden variable approach, minimal-case camera motion estimation, five-point relative orientation problem, six-point focal-length problem, multivariate polynomial systems, monomials, linear equations, polynomial eigenvalue problem, quotient-free Gaussian elimination, Levinson-Durbin iteration, Polynomials, Cameras, Eigenvalues and eigenfunctions, Calibration, Motion estimation, Mathematical model, polynomial root finding, Camera calibration, camera motion estimation, epipolar geometry, minimal solver

Hongdong Li and R. Hartley, "An Efficient Hidden Variable Approach to Minimal-Case Camera Motion Estimation," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 34, no. , pp. 2303-2314, 2012.
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