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Registration of 2D Points Using Geometric Algebra and Tensor Voting

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Abstract

In this paper, we present a novel algorithm that combines the power of expression of Geometric Algebra with the robustness of Tensor Voting to find the correspondences between two sets of 2D points with an underlying rigid transformation. Unlike other popular algorithms for point registration (like the Iterated Closest Points), our algorithm does not require an initialization, works equally well with small and large transformations between the data sets, performs even in the presence of large amounts of outliers (90% and more), and have less chance to be trapped in “local minima”. Furthermore, we will show how this algorithm can be easily extended to account for multiple overlapping motions and certain non-rigid transformations.

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Authors and Affiliations

  1. Department of Electrical Engineering and Computer Science, CINVESTAV, Unidad Guadalajara, Jalisco, Mexico

    Leo Reyes-Lozano & Eduardo Bayro-Carrochano

  2. Institute for Robotics and Intelligence Systems, University of Southern California, Los Angeles, CA, USA

    Gerard Medioni

Authors
  1. Leo Reyes-Lozano
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  2. Gerard Medioni
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  3. Eduardo Bayro-Carrochano
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Correspondence to Eduardo Bayro-Carrochano.

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Reyes-Lozano, L., Medioni, G. & Bayro-Carrochano, E. Registration of 2D Points Using Geometric Algebra and Tensor Voting. J Math Imaging Vis 37, 249–266 (2010). https://doi.org/10.1007/s10851-010-0205-7

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