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Non-rigid Shape Correspondence Using Surface Descriptors and Metric Structures in the Spectral Domain

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Perspectives in Shape Analysis

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

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Abstract

Finding correspondence between non-rigid shapes is at the heart of three-dimensional shape processing. It has been extensively addressed over the last decade, but efficient and accurate correspondence detection still remains a challenging task. Generalized Multidimensional Scaling (GMDS) is an approach that finds correspondence by mapping one shape into another, while attempting to preserve distances between pairs of corresponding points on the two shapes. A different approach consists in detecting correspondence between shapes by matching their pointwise surface descriptors. Recently, the Spectral GMDS (SGMDS) approach was introduced, according to which the GMDS was re-formulated in the natural spectral domain of the shapes. Here, we propose a method that combines matching based on geodesic distances and pointwise surface descriptors . Following SGMDS, in the proposed solution the entire problem is translated into the spectral domain, resulting in efficient correspondence computation. Efficiency and accuracy of the proposed method are demonstrated by comparing it to state-of-the-art approaches, using a standard correspondence benchmark.

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Acknowledgements

We thank Alon Shtern for fruitful discussions. 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, Yonathan Aflalo & Ron Kimmel

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  1. Anastasia Dubrovina
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  2. Yonathan Aflalo
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  3. Ron Kimmel
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Correspondence to Anastasia Dubrovina .

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Editors and Affiliations

  1. Institute for Applied Mathematics and Scientific Computing, Brandenburg University of Technology, Cottbus, Germany

    Michael Breuß

  2. Israel Institute of Technology Technion, Haifa, Israel

    Alfred Bruckstein

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

    Petros Maragos

  4. INRIA, Grenoble Rhône-Alpes, Saint Ismier, France

    Stefanie Wuhrer

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Dubrovina, A., Aflalo, Y., Kimmel, R. (2016). Non-rigid Shape Correspondence Using Surface Descriptors and Metric Structures in the Spectral Domain. In: Breuß, M., Bruckstein, A., Maragos, P., Wuhrer, S. (eds) Perspectives in Shape Analysis. Mathematics and Visualization. Springer, Cham. https://doi.org/10.1007/978-3-319-24726-7_13

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