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Binocular Computer Vision Based on Conformal Geometric Algebra

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Abstract

We apply the conformal geometric algebra (CGA) to the generalized binocular vision problem. More precisely, we reconstruct a 3D line from its images on the image planes of two cameras whose mutual position is specified by a given Euclidean transformation which depends on an arbitrary number of parameters. We represent all transformations by CGA elements which allows us to derive the general equations of 3D line reconstruction by formal CGA elements manipulation. The transformation equations can be solved w.r.t. either motor or projection unknown parameters. We present two specific examples, show the explicit form of two particular motors and solve the appropriate equations completely.

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Authors and Affiliations

  1. Faculty of Mechanical Engineering Institute of Mathematics, Brno University of Technology, Brno, Czech Republic

    Jaroslav Hrdina & Aleš Návrat

Authors
  1. Jaroslav Hrdina
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  2. Aleš Návrat
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Corresponding author

Correspondence to Jaroslav Hrdina.

Additional information

This work was supported by Grants of the Grant Agency of the Czech Republic 17-21360S, “Advances in Snake-like Robot Control”.

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Hrdina, J., Návrat, A. Binocular Computer Vision Based on Conformal Geometric Algebra. Adv. Appl. Clifford Algebras 27, 1945–1959 (2017). https://doi.org/10.1007/s00006-017-0764-4

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  • DOI: https://doi.org/10.1007/s00006-017-0764-4

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