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Inferring 3D structure from three points in rigid motion

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Abstract

We prove the following: Given four (or more) orthographic views of three points then (a) the views almost surely have no rigid interpretation but (b) if they do then they almost surely have at most thirty-two rigid interpretations. Part (a) means that the measure of “false targets”, viz., the measure of nonrigid motions that project to views having rigid interpretations, is zero. Part (b) means that rigid interpretations, when they exist, are not unique. Uniqueness of interpretation can be obtained if a point is added, but not if views are added. Our proof relies on an upper semicontinuity theorem for proper mappings of complex algebraic varieties. We note some psychophysical motivations of the theory.

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Authors and Affiliations

  1. Department of Mathematics, University of California, 92717, Irvine, California, USA

    B. M. Bennett

  2. Department of Cognitive Science, University of California, 92717, Irvine, California, USA

    D. D. Hoffman

Authors
  1. B. M. Bennett
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  2. D. D. Hoffman
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Bennett, B.M., Hoffman, D.D. Inferring 3D structure from three points in rigid motion. J Math Imaging Vis 4, 401–406 (1994). https://doi.org/10.1007/BF01262405

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