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The Average Mixing Kernel Signature

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Computer Vision – ECCV 2020 (ECCV 2020)

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Abstract

We introduce the Average Mixing Kernel Signature (AMKS), a novel signature for points on non-rigid three-dimensional shapes based on the average mixing kernel and continuous-time quantum walks. The average mixing kernel holds information on the average transition probabilities of a quantum walk between each pair of vertices of the mesh until a time T. We define the AMKS by decomposing the spectral contributions of the kernel into several bands, allowing us to limit the influence of noise-dominated high-frequency components and obtain a more descriptive signature. We also show through a perturbation theory analysis of the kernel that choosing a finite stopping time T leads to noise and deformation robustness for the AMKS. We perform an extensive experimental evaluation on two widely used shape matching datasets under varying level of noise, showing that the AMKS outperforms two state-of-the-art descriptors, namely the Heat Kernel Signature (HKS) and the similarly quantum-walk based Wave Kernel Signature (WKS) .

L. Cosmo and G. Minello—Equal contribution.

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Notes

  1. 1.

    https://github.com/lcosmo/amks-descriptor.

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Acknowledgements

Luca Cosmo was supported by the ERC Starting Grant No. 802554 (SPECGEO) and the ERC Consolidator grant No. 724228 (LEMAN).

Author information

Authors and Affiliations

  1. Sapienza University of Rome, Rome, Italy

    Luca Cosmo

  2. University of Lugano, Lugano, Switzerland

    Luca Cosmo & Michael Bronstein

  3. Università Ca’ Foscari Venezia, Venice, Italy

    Giorgia Minello & Andrea Torsello

  4. Imperial College London, London, UK

    Michael Bronstein

  5. Twitter, London, UK

    Michael Bronstein

  6. Queen Mary University of London, London, UK

    Luca Rossi

Authors
  1. Luca Cosmo
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  2. Giorgia Minello
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  3. Michael Bronstein
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  4. Luca Rossi
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  5. Andrea Torsello
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Corresponding author

Correspondence to Luca Rossi .

Editor information

Editors and Affiliations

  1. University of Oxford, Oxford, UK

    Andrea Vedaldi

  2. Graz University of Technology, Graz, Austria

    Horst Bischof

  3. University of Freiburg, Freiburg im Breisgau, Germany

    Thomas Brox

  4. University of North Carolina at Chapel Hill, Chapel Hill, NC, USA

    Jan-Michael Frahm

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Cosmo, L., Minello, G., Bronstein, M., Rossi, L., Torsello, A. (2020). The Average Mixing Kernel Signature. In: Vedaldi, A., Bischof, H., Brox, T., Frahm, JM. (eds) Computer Vision – ECCV 2020. ECCV 2020. Lecture Notes in Computer Science(), vol 12365. Springer, Cham. https://doi.org/10.1007/978-3-030-58565-5_1

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  • DOI: https://doi.org/10.1007/978-3-030-58565-5_1

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