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Biharmonic density estimate: a scale-space descriptor for 3-D deformable surfaces

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Abstract

The wide variability in deformable three-dimensional (3-D) shapes calls for the formulation of a multiscale surface signature for effective characterization and analysis of the underlying 3-D intrinsic geometry. To this end, a novel intrinsic geometric scale-space descriptor for 3-D deformable surfaces, termed as the biharmonic density estimate (BDE), is proposed. The BDE, derived from the biharmonic distance measure, is shown to provide an intrinsic geometric scale-space signature for multiscale surface feature-based representation of deformable 3-D shapes that is both effective and useful for practical applications. The proposed BDE signature provides a theoretical framework for the concept of intrinsic geometric scale space, resulting in a highly descriptive characterization of both the local surface structure and the global metric of the underlying 3-D shape. The compactness and robustness of the BDE are experimentally demonstrated on two standard benchmark datasets. The applications of the BDE in the detection of key components on a deformable 3-D surface and determination of sparse point correspondences between two deformable 3-D shapes are also demonstrated.

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Authors and Affiliations

  1. Department of Computer Science, The University of Georgia, 415 Boyd GSRC Building, Athens, GA, 30602-7404, USA

    Anirban Mukhopadhyay & Suchendra M. Bhandarkar

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  1. Anirban Mukhopadhyay
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  2. Suchendra M. Bhandarkar
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Correspondence to Suchendra M. Bhandarkar.

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Mukhopadhyay, A., Bhandarkar, S.M. Biharmonic density estimate: a scale-space descriptor for 3-D deformable surfaces. Pattern Anal Applic 20, 1261–1273 (2017). https://doi.org/10.1007/s10044-017-0610-2

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  • DOI: https://doi.org/10.1007/s10044-017-0610-2

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