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Stable Semi-local Features for Non-rigid Shapes

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Innovations for Shape Analysis

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

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Abstract

Feature-based analysis is becoming a very popular approach for geometric shape analysis. Following the success of this approach in image analysis, there is a growing interest in finding analogous methods in the 3D world. Maximally stable component detection is a low computation cost and high repeatability method for feature detection in images.In this study, a diffusion-geometry based framework for stable component detection is presented, which can be used for geometric feature detection in deformable shapes.The vast majority of studies of deformable 3D shapes models them as the two-dimensional boundary of the volume of the shape. Recent works have shown that a volumetric shape model is advantageous in numerous ways as it better captures the natural behavior of non-rigid deformations. We show that our framework easily adapts to this volumetric approach, and even demonstrates superior performance.A quantitative evaluation of our methods on the SHREC’10 and SHREC’11 feature detection benchmarks as well as qualitative tests on the SCAPE dataset show its potential as a source of high-quality features. Examples demonstrating the drawbacks of surface stable components and the advantage of their volumetric counterparts are also presented.

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Notes

  1. 1.

    In this evaluation we used SHREC11, rather than SHREC10 that was used previously in 2D. this is due to the fact that results of the 3D and 2D versions were too similar on SHREC10, and dataset with a wider, and more challenging range and strength of transformations was needed to emphasize the difference.

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Acknowledgements

We are grateful to Dan Raviv for providing us his volume rasterization and Laplacian disretization code. M. M. Bronstein is partially supported by the Swiss High-Performance and High-Productivity Computing (HP2C) grant. A. M. Bronstein is partially supported by the Israeli Science Foundation and the German-Israeli Foundation.

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Authors and Affiliations

  1. School of Electrical Engineering, Tel Aviv University, Tel Aviv, Israel

    Roee Litman & Alexander M. Bronstein

  2. Institute of Computational Science, Faculty of Informatics, Universita della Svizzera Italiana, Lugano, Switzerland

    Michael M. Bronstein

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  1. Roee Litman
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  2. Alexander M. Bronstein
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Correspondence to Roee Litman .

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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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Litman, R., Bronstein, A.M., Bronstein, M.M. (2013). Stable Semi-local Features for Non-rigid Shapes. 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_8

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