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Extensions of Invariant Signatures for Object Recognition

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Abstract

A refinement of the method of differential invariant signatures for object recognition is presented. The value of the method lies in its compromise between local and global identifying properties, thereby allowing us to distinguish non-congruent curves whose Euclidean signatures have identical trace.

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Notes

  1. “Non-overlapping” means they have at most one endpoint in common.

  2. In [10], the older term “classifying submanifold” is used in place of “signature submanifold”.

  3. As noted above, one could experiment with other (weighted) norms, but the Euclidean norm suffices for our purposes.

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Authors and Affiliations

  1. Department of Mathematics, University of California, San Diego, La Jolla, CA, 92093, USA

    Daniel J. Hoff

  2. School of Mathematics, University of Minnesota, Minneapolis, MN, 55455, USA

    Peter J. Olver

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  1. Daniel J. Hoff
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  2. Peter J. Olver
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Correspondence to Peter J. Olver.

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Supported in part by NSF Grant DMS 08–07317.

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Hoff, D.J., Olver, P.J. Extensions of Invariant Signatures for Object Recognition. J Math Imaging Vis 45, 176–185 (2013). https://doi.org/10.1007/s10851-012-0358-7

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