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

Richard Hartley*, Hongdong Li

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    75 Citations (Scopus)


    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.

    Original languageEnglish
    Article number6143948
    Pages (from-to)2303-2314
    Number of pages12
    JournalIEEE Transactions on Pattern Analysis and Machine Intelligence
    Issue number12
    Publication statusPublished - 2012


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