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    Functional Characterization of Deformation Fields

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    Type
    Article
    Authors
    Corman, Etienne
    Ovsjanikov, Maks
    KAUST Grant Number
    2017 3426
    Date
    2019-02-20
    Permanent link to this record
    http://hdl.handle.net/10754/668068
    
    Metadata
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    Abstract
    In this article, we present a novel representation for deformation fields of 3D shapes, by considering the induced changes in the underlying metric. In particular, our approach allows one to represent a deformation field in a coordinate-free way as a linear operator acting on real-valued functions defined on the shape. Such a representation provides both a way to relate deformation fields to other classical functional operators and enables analysis and processing of deformation fields using standard linear-algebraic tools. This opens the door to a wide variety of applications such as explicitly adding extrinsic information into the computation of functional maps, intrinsic shape symmetrization, joint deformation design through precise control of metric distortion, and coordinate-free deformation transfer without requiring pointwise correspondences. Our method is applicable to both surface and volumetric shape representations and we guarantee the equivalence between the operator-based and standard deformation field representation under mild genericity conditions in the discrete setting. We demonstrate the utility of our approach by comparing it with existing techniques and show how our representation provides a powerful toolbox for a wide variety of challenging problems.
    Citation
    Corman, E., & Ovsjanikov, M. (2019). Functional Characterization of Deformation Fields. ACM Transactions on Graphics, 38(1), 1–19. doi:10.1145/3292480
    Sponsors
    Parts of this work were supported by a Competitive Research Grant CRG6 2017 3426 from KAUST, a Google Focused Research Award, and the ERC Starting Grant No. 758800 (EXPROTEA).
    Publisher
    Association for Computing Machinery (ACM)
    Journal
    ACM Transactions on Graphics
    DOI
    10.1145/3292480
    arXiv
    1709.09701
    Additional Links
    https://dl.acm.org/doi/10.1145/3292480
    ae974a485f413a2113503eed53cd6c53
    10.1145/3292480
    Scopus Count
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