@inproceedings{2b0fb6ca406441cdbe6829da018fa65c,
title = "The Average Mixing Kernel Signature",
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).",
keywords = "Quantum walks, Shape analysis, Shape representation",
author = "Luca Cosmo and Giorgia Minello and Michael Bronstein and Luca Rossi and Andrea Torsello",
note = "Funding Information: Acknowledgements. Luca Cosmo was supported by the ERC Starting Grant No. 802554 (SPECGEO) and the ERC Consolidator grant No. 724228 (LEMAN). Publisher Copyright: {\textcopyright} 2020, Springer Nature Switzerland AG.; 16th European Conference on Computer Vision, ECCV 2020 ; Conference date: 23-08-2020 Through 28-08-2020",
year = "2020",
month = aug,
doi = "10.1007/978-3-030-58565-5_1",
language = "English",
isbn = "9783030585648",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Science and Business Media Deutschland GmbH",
pages = "1--17",
editor = "Andrea Vedaldi and Horst Bischof and Thomas Brox and Jan-Michael Frahm",
booktitle = "Computer Vision – ECCV 2020 - 16th European Conference 2020, Proceedings",
address = "Germany",
}