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Non-rigid Shape Correspondence Using Pointwise Surface Descriptors and Metric Structures

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Innovations for Shape Analysis

Part of the book series: Mathematics and Visualization ((MATHVISUAL))

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Abstract

Finding a correspondence between two non-rigid shapes is one of the cornerstone problems in the field of three-dimensional shape processing. We describe a framework for marker-less non-rigid shape correspondence, based on matching intrinsic invariant surface descriptors, and the metric structures of the shapes. The matching task is formulated as a quadratic optimization problem that can be used with any type of descriptors and metric. We minimize it using a hierarchical matching algorithm, to obtain a set of accurate correspondences. Further, we present the correspondence ambiguity problem arising when matching intrinsically symmetric shapes using only intrinsic surface properties. We show that when using isometry invariant surface descriptors based on eigendecomposition of the Laplace-Beltrami operator, it is possible to construct distinctive sets of surface descriptors for different possible correspondences. When used in a proper minimization problem, those descriptors allow us to explore a number of possible correspondences between two given shapes.

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Acknowledgements

This research was supported by European Community’s FP7- ERC program, grant agreement no. 267414.

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Authors and Affiliations

  1. Technion, Israel Institute of Technology, Haifa, Israel

    Anastasia Dubrovina & Dan Raviv

  2. Technion, Department of Computer Science, Israel Institute of Technology, Haifa, Israel

    Ron Kimmel

Authors
  1. Anastasia Dubrovina
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  2. Dan Raviv
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  3. Ron Kimmel
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Corresponding author

Correspondence to Anastasia Dubrovina .

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Editors and Affiliations

  1. , Inst. for Appl. Math.&Scient.Comp., Brandenburg Technical University, Platz der Deutschen Einheit 1, Cottbus, 03046, Germany

    Michael Breuß

  2. Department of Computer Science, Technion-Israel Institute of Technology, Haifa, 32000, Israel

    Alfred Bruckstein

  3. School of Electrical &, Computer Engineering, National Technical University of Athens, Athens, 15773, Greece

    Petros Maragos

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Dubrovina, A., Raviv, D., Kimmel, R. (2013). Non-rigid Shape Correspondence Using Pointwise Surface Descriptors and Metric Structures. In: Breuß, M., Bruckstein, A., Maragos, P. (eds) Innovations for Shape Analysis. Mathematics and Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34141-0_15

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