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Unified Computation of Strict Maximum Likelihood for Geometric Fitting

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Abstract

A new numerical scheme is presented for computing strict maximum likelihood (ML) of geometric fitting problems having an implicit constraint. Our approach is orthogonal projection of observations onto a parameterized surface defined by the constraint. Assuming a linearly separable nonlinear constraint, we show that a theoretically global solution can be obtained by iterative Sampson error minimization. Our approach is illustrated by ellipse fitting and fundamental matrix computation. Our method also encompasses optimal correction, computing, e.g., perpendiculars to an ellipse and triangulating stereo images. A detailed discussion is given to technical and practical issues about our approach.

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Authors and Affiliations

  1. Department of Computer Science, Okayama University, Okayama, 700-8530, Japan

    Kenichi Kanatani

  2. Department of Computer Science and Engineering, Toyohashi University of Technology, Toyohashi, Aichi, 441-8580, Japan

    Yasuyuki Sugaya

Authors
  1. Kenichi Kanatani
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  2. Yasuyuki Sugaya
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Correspondence to Kenichi Kanatani.

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Kanatani, K., Sugaya, Y. Unified Computation of Strict Maximum Likelihood for Geometric Fitting. J Math Imaging Vis 38, 1–13 (2010). https://doi.org/10.1007/s10851-010-0206-6

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  • DOI: https://doi.org/10.1007/s10851-010-0206-6

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