research-article

A concise and provably informative multi-scale signature based on heat diffusion

Authors:

Maks Ovsjanikov,

Leonidas GuibasAuthors Info & Claims

SGP '09: Proceedings of the Symposium on Geometry Processing

Pages 1383 - 1392

Published: 15 July 2009 Publication History

Abstract

We propose a novel point signature based on the properties of the heat diffusion process on a shape. Our signature, called the Heat Kernel Signature (or HKS), is obtained by restricting the well-known heat kernel to the temporal domain. Remarkably we show that under certain mild assumptions, HKS captures all of the information contained in the heat kernel, and characterizes the shape up to isometry. This means that the restriction to the temporal domain, on the one hand, makes HKS much more concise and easily commensurable, while on the other hand, it preserves all of the information about the intrinsic geometry of the shape. In addition, HKS inherits many useful properties from the heat kernel, which means, in particular, that it is stable under perturbations of the shape. Our signature also provides a natural and efficiently computable multi-scale way to capture information about neighborhoods of a given point, which can be extremely useful in many applications. To demonstrate the practical relevance of our signature, we present several methods for non-rigid multi-scale matching based on the HKS and use it to detect repeated structure within the same shape and across a collection of shapes.

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Cited By

Attaiki SOvsjanikov MOh ANaumann TGloberson ASaenko KHardt MLevine S(2023)Shape Non-rigid Kinematics (SNK)Proceedings of the 37th International Conference on Neural Information Processing Systems10.5555/3666122.3669190(70012-70032)Online publication date: 10-Dec-2023
https://dl.acm.org/doi/10.5555/3666122.3669190
Loiseaux DScoccola LCarrière MBotnan MOudot SOh ANaumann TGloberson ASaenko KHardt MLevine S(2023)Stable vectorization of multiparameter persistent homology using signed barcodes as measuresProceedings of the 37th International Conference on Neural Information Processing Systems10.5555/3666122.3669109(68316-68342)Online publication date: 10-Dec-2023
https://dl.acm.org/doi/10.5555/3666122.3669109
Luo YShi LThost VOh ANaumann TGloberson ASaenko KHardt MLevine S(2023)Improving self-supervised molecular representation learning using persistent homologyProceedings of the 37th International Conference on Neural Information Processing Systems10.5555/3666122.3667597(34043-34073)Online publication date: 10-Dec-2023
https://dl.acm.org/doi/10.5555/3666122.3667597
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Index Terms

A concise and provably informative multi-scale signature based on heat diffusion
1. Computing methodologies
  1. Artificial intelligence
    1. Computer vision
      1. Computer vision problems
      2. Computer vision tasks
        Scene understanding
  2. Computer graphics
    1. Shape modeling
2. Theory of computation
  1. Randomness, geometry and discrete structures
    1. Computational geometry

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Published In

cover image Guide Proceedings

SGP '09: Proceedings of the Symposium on Geometry Processing

July 2009

278 pages

Conference Chair:
Konrad Polthier
Freie Universität Berlin
,
Program Chairs:
Marc Alexa
Technische Universität Berlin
,
Michael Kazhdan
Johns Hopkins University

Publisher

Eurographics Association

Goslar, Germany

Publication History

Published: 15 July 2009

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Cited By

Attaiki SOvsjanikov MOh ANaumann TGloberson ASaenko KHardt MLevine S(2023)Shape Non-rigid Kinematics (SNK)Proceedings of the 37th International Conference on Neural Information Processing Systems10.5555/3666122.3669190(70012-70032)Online publication date: 10-Dec-2023
https://dl.acm.org/doi/10.5555/3666122.3669190
Loiseaux DScoccola LCarrière MBotnan MOudot SOh ANaumann TGloberson ASaenko KHardt MLevine S(2023)Stable vectorization of multiparameter persistent homology using signed barcodes as measuresProceedings of the 37th International Conference on Neural Information Processing Systems10.5555/3666122.3669109(68316-68342)Online publication date: 10-Dec-2023
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Luo YShi LThost VOh ANaumann TGloberson ASaenko KHardt MLevine S(2023)Improving self-supervised molecular representation learning using persistent homologyProceedings of the 37th International Conference on Neural Information Processing Systems10.5555/3666122.3667597(34043-34073)Online publication date: 10-Dec-2023
https://dl.acm.org/doi/10.5555/3666122.3667597
Huguet GTong ADe Brouwer EZhang YWolf GAdelstein IKrishnaswamy SOh ANaumann TGloberson ASaenko KHardt MLevine S(2023)A heat diffusion perspective on geodesic preserving dimensionality reductionProceedings of the 37th International Conference on Neural Information Processing Systems10.5555/3666122.3666428(6986-7016)Online publication date: 10-Dec-2023
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Chen GDai HZhou TShen JShao L(2023)Automatic Schelling Point Detection From MeshesIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2022.314414329:6(2926-2939)Online publication date: 1-Jun-2023
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