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Shape Metrics Based on Elastic Deformations

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Abstract

Deformations of shapes and distances between shapes are an active research topic in computer vision. We propose an energy of infinitesimal deformations of continuous 1- and 2-dimensional shapes that is based on the elastic energy of deformed objects. This energy defines a shape metric which is inherently invariant with respect to Euclidean transformations and yields very natural deformations which preserve details. We compute shortest paths between planar shapes based on elastic deformations and apply our approach to the modeling of 2-dimensional shapes.

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Authors and Affiliations

  1. Dept. of Mathematics, Univ. of Innsbruck, Innsbruck, Austria

    Matthias Fuchs & Otmar Scherzer

  2. RICAM, Austrian Acad. of Science, Linz, Austria

    Otmar Scherzer

  3. Inst. of Applied Geometry, Univ. of Linz, Linz, Austria

    Bert Jüttler & Huaiping Yang

Authors
  1. Matthias Fuchs
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  2. Bert Jüttler
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  3. Otmar Scherzer
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  4. Huaiping Yang
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Correspondence to Matthias Fuchs.

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Fuchs, M., Jüttler, B., Scherzer, O. et al. Shape Metrics Based on Elastic Deformations. J Math Imaging Vis 35, 86–102 (2009). https://doi.org/10.1007/s10851-009-0156-z

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  • DOI: https://doi.org/10.1007/s10851-009-0156-z

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