An efficient hidden variable approach to minimal-case camera motion estimation

IEEE Transactions on Pattern Analysis and Machine Intelligence
Richard Hartley, Hongdong Li

Abstract

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.

References

Jun 27, 2008·IEEE Transactions on Pattern Analysis and Machine Intelligence·David Nistér

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Citations

Jul 12, 2014·IEEE Transactions on Cybernetics·Pedro Miraldo, Helder Araujo
Sep 10, 2015·IEEE Transactions on Pattern Analysis and Machine Intelligence·Gus K Lott
Jul 12, 2018·IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society·Daniel Barath, Levente Hajder

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