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research-article

Volumetric heat kernel signatures

Authors:

Michael M. Bronstein,

Alexander M. Bronstein,

Ron KimmelAuthors Info & Claims

3DOR '10: Proceedings of the ACM workshop on 3D object retrieval

Pages 39 - 44

https://doi.org/10.1145/1877808.1877817

Published: 25 October 2010 Publication History

Abstract

Invariant shape descriptors are instrumental in numerous shape analysis tasks including deformable shape comparison, registration, classification, and retrieval. Most existing constructions model a 3D shape as a two-dimensional surface describing the shape boundary, typically represented as a triangular mesh or a point cloud. Using intrinsic properties of the surface, invariant descriptors can be designed. One such example is the recently introduced heat kernel signature, based on the Laplace-Beltrami operator of the surface. In many applications, however, a volumetric shape model is more natural and convenient. Moreover, modeling shape deformations as approximate isometries of the volume of an object, rather than its boundary, better captures natural behavior of non-rigid deformations in many cases. Here, we extend the idea of heat kernel signature to robust isometry-invariant volumetric descriptors, and show their utility in shape retrieval. The proposed approach achieves state-of-the-art results on the SHREC 2010 large-scale shape retrieval benchmark.

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https://doi.org/10.1016/j.media.2024.103375
Shu ZWu TShen JXin SLiu L(2024)Semi-Supervised 3D Shape Segmentation via Self RefiningIEEE Transactions on Image Processing10.1109/TIP.2024.337420033(2044-2057)Online publication date: 2024
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Paquet EViktor HMadi KWu J(2023)Deformable Protein Shape Classification Based on Deep Learning, and the Fractional Fokker–Planck and Kähler–Dirac EquationsIEEE Transactions on Pattern Analysis and Machine Intelligence10.1109/TPAMI.2022.314679645:1(391-407)Online publication date: 1-Jan-2023
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Index Terms

Volumetric heat kernel signatures
1. Computing methodologies
  1. Artificial intelligence
    1. Computer vision
      1. Computer vision problems
      2. Computer vision representations
  2. Computer graphics
    1. Image manipulation

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Information

Published In

cover image ACM Conferences

3DOR '10: Proceedings of the ACM workshop on 3D object retrieval

October 2010

96 pages

ISBN:9781450301602

DOI:10.1145/1877808

Program Chairs:
Mohamed Doudi
TELECOM Lille1/LIFL, France
,
Michela Spagnuolo
CNR-IMATI, Italy
,
Remco Veltkamp
Utrecht University, The Netherlands

Copyright © 2010 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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SIGMM: ACM Special Interest Group on Multimedia

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Published: 25 October 2010

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MM '10: ACM Multimedia Conference

October 25, 2010

Firenze, Italy

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Cited By

Banduc TAzzolin LManninger MScherr DPlank GPezzuto SSahli Costabal F(2025)Simulation-free prediction of atrial fibrillation inducibility with the fibrotic kernel signatureMedical Image Analysis10.1016/j.media.2024.10337599(103375)Online publication date: Jan-2025
https://doi.org/10.1016/j.media.2024.103375
Shu ZWu TShen JXin SLiu L(2024)Semi-Supervised 3D Shape Segmentation via Self RefiningIEEE Transactions on Image Processing10.1109/TIP.2024.337420033(2044-2057)Online publication date: 2024
https://doi.org/10.1109/TIP.2024.3374200
Paquet EViktor HMadi KWu J(2023)Deformable Protein Shape Classification Based on Deep Learning, and the Fractional Fokker–Planck and Kähler–Dirac EquationsIEEE Transactions on Pattern Analysis and Machine Intelligence10.1109/TPAMI.2022.314679645:1(391-407)Online publication date: 1-Jan-2023
https://doi.org/10.1109/TPAMI.2022.3146796
Yan YZhou MZhang DGeng S(2023)Average increment scale-invariant heat kernel signature for 3D non-rigid shape analysisMultimedia Tools and Applications10.1007/s11042-023-15346-583:3(8077-8115)Online publication date: 13-Jun-2023
https://doi.org/10.1007/s11042-023-15346-5
Scott OGu JChan A(2022)Classification of Protein-Binding Sites Using a Spherical Convolutional Neural NetworkJournal of Chemical Information and Modeling10.1021/acs.jcim.2c0083262:22(5383-5396)Online publication date: 7-Nov-2022
https://doi.org/10.1021/acs.jcim.2c00832
Lee KDanhaive RMueller C(2022)Spherical harmonic shape descriptors of nodal force demands for quantifying spatial truss connection complexityArchitecture, Structures and Construction10.1007/s44150-022-00021-42:1(145-164)Online publication date: 28-Feb-2022
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Wang ZRosen D(2022)Manufacturing process classification based on heat kernel signature and convolutional neural networksJournal of Intelligent Manufacturing10.1007/s10845-022-02009-934:8(3389-3411)Online publication date: 30-Aug-2022
https://doi.org/10.1007/s10845-022-02009-9
Liu BWang WZhou JLi BLiu X(2021)Detail-Preserving Shape UnfoldingSensors10.3390/s2104118721:4(1187)Online publication date: 8-Feb-2021
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Lin YShnitzer TTalmon RVillarroel-Espindola FDesai SSchalper KKluger Y(2021)Graph of graphs analysis for multiplexed data with application to imaging mass cytometryPLOS Computational Biology10.1371/journal.pcbi.100874117:3(e1008741)Online publication date: 29-Mar-2021
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Smirnov DSolomon J(2021)HodgeNetACM Transactions on Graphics10.1145/3450626.345979740:4(1-11)Online publication date: 19-Jul-2021
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