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.

References

[1]

S. Belongie, J. Malik, and J. Puzicha. Shape matching and object recognition using shape contexts. Trans. PAMI, pages 509--522, 2002.

Digital Library

[2]

M. Ben-Chen, O. Weber, and C. Gotsman. Characterizing shape using conformal factors. In Proc. 3DOR, 2008.

Digital Library

[3]

P. Bérard, G. Besson, and S. Gallot. Embedding riemannian manifolds by their heat kernel. Geometric and Functional Analysis, 4(4):373--398, 1994.

[4]

S. Biasotti, S. Marini, M. Mortara, and G. Patané. An overview on properties and efficacy of topological skeletons in shape modeling. In Proc. SMI, pages 245--254, 2003.

Digital Library

[5]

A. M. Bronstein, M. M. Bronstein, A. M. Bruckstein, and R. Kimmel. Analysis of two-dimensional non-rigid shapes. IJCV, 78(1):67--88, 2008.

Digital Library

[6]

A. M. Bronstein, M. M. Bronstein, U. Castellani, B. Falcidieno, A. Fusiello, A. Godil, L. J. Guibas, I. Kokkinos, Z. Lian, M. Ovsjanikov, G. Patané, M. Spagnuolo, and R. Toldo. Shrec 2010: robust large-scale shape retrieval benchmark. In Proc. 3DOR, 2010.

[7]

A. M. Bronstein, M. M. Bronstein, and R. Kimmel. Generalized multidimensional scaling: a framework for isometry-invariant partial surface matching. PNAS, 103(5):1168--1172, 2006.

[8]

A. M. Bronstein, M. M. Bronstein, and R. Kimmel. Numerical geometry of non-rigid shapes. Springer-Verlag New York Inc, 2008.

Digital Library

[9]

A. M. Bronstein, M. M. Bronstein, M. Ovsjanikov, and L. J. Guibas. Shape google: a computer vision approach to invariant shape retrieval. In Proc. NORDIA, 2009.

[10]

M. M. Bronstein and I. Kokkinos. Scale-invariant heat kernel signatures for non-rigid shape recognition. In Proc. CVPR, 2010.

[11]

U. Clarenz, M. Rumpf, and A. Telea. Robust feature detection and local classification for surfaces based on moment analysis. Trans. Visualization and Computer Graphics, 10(5):516--524, 2004.

Digital Library

[12]

A. Dubrovina and R. Kimmel. Matching shapes by eigendecomposition of the Laplace-Beltrami operator. In Proc. 3DPVT, 2010.

[13]

A. Elad and R. Kimmel. Bending invariant representations for surfaces. In Proc. CVPR, pages 168--174, 2001.

[14]

R. Gal, A. Shamir, and D. Cohen-Or. Pose-oblivious shape signature. Trans. Visualization and Computer Graphics, 13(2):261--271, 2007.

Digital Library

[15]

N. Gelfand, N. J. Mitra, L. J. Guibas, and H. Pottmann. Robust global registration. In Proc. SGP, 2005.

Digital Library

[16]

M. Hilaga, Y. Shinagawa, T. Kohmura, and T. Kunii. Topology matching for fully automatic similarity estimation of 3D shapes. In Proc. Computer Graphics and Interactive Techniques, pages 203--212, 2001.

Digital Library

[17]

A. Ion, G. Peyré, Y. Haxhimusa, S. Peltier, W. G. Kropatsch, and L. Cohen. Shape matching using the geodesic eccentricity transform--a study. In Proc. Workshop of the Austrian Association for Pattern Recognition (OAGM/AAPR), 2007.

[18]

P. W. Jones, M. Maggioni, and R. Schul. Manifold parametrizations by eigenfunctions of the Laplacian and heat kernels. PNAS, 105(6):1803, 2008.

[19]

M. Kazhdan, T. Funkhouser, and S. Rusinkiewicz. Rotation invariant spherical harmonic representation of 3D shape descriptors. In Proc. SGP, pages 156--164, 2003.

Digital Library

[20]

M. Kazhdan, T. Funkhouser, and S. Rusinkiewicz. Symmetry descriptors and 3D shape matching. In Proc. SGP, pages 115--123, 2004.

Digital Library

[21]

H. Ling and D. W. Jacobs. Shape classification using the inner-distance. Trans. PAMI, 29(2):286--299, 2007.

Digital Library

[22]

D. Lowe. Distinctive image features from scale-invariant keypoint. IJCV, 2004.

Digital Library

[23]

F. Mémoli and G. Sapiro. A theoretical and computational framework for isometry invariant recognition of point cloud data. Foundations of Computational Mathematics, 5:313--346, 2005.

Digital Library

[24]

N. J. Mitra, L. J. Guibas, J. Giesen, and M. Pauly. Probabilistic fingerprints for shapes. In Proc. SGP, 2006.

Digital Library

[25]

M. Novotni and R. Klein. 3D Zernike descriptors for content based shape retrieval. In Proc. ACM Symp. Solid Modeling and Applications, pages 216--225, 2003.

Digital Library

[26]

R. Osada, T. Funkhouser, B. Chazelle, and D. Dobkin. Shape distributions. TOG, 21(4):807--832, 2002.

Digital Library

[27]

E. Paquet, M. Rioux, A. Murching, T. Naveen, and A. Tabatabai. Description of shape information for 2-D and 3-D objects. Signal Processing: Image Communication, 16(1--2):103--122, 2000.

[28]

D. Raviv, A. M. Bronstein, M. M. Bronstein, and R. Kimmel. Symmetries of non-rigid shapes. In Proc. NRTL, 2007.

[29]

M. Reuter, F.-E. Wolter, and N. Peinecke. Laplace-spectra as fingerprints for shape matching. In Proc. ACM Symp. Solid and Physical Modeling, pages 101--106, 2005.

Digital Library

[30]

R. Rustamov. Robust volumetric shape descriptor. In Proc. 3DOR, 2010.

Digital Library

[31]

R. M. Rustamov. Laplace-Beltrami eigenfunctions for deformation invariant shape representation. In Proc. SGP, pages 225--233, 2007.

Digital Library

[32]

P. Shilane and T. Funkhauser. Selecting distinctive 3D shape descriptors for similarity retrieval. In Proc. Shape Modelling and Applications, 2006.

Digital Library

[33]

P. Shilane, P. Min, M. Kazhdan, and T. Funkhouser. The Princeton shape benchmark. In Proc. SMI, pages 167--178, 2004.

Digital Library

[34]

J. Sivic and A. Zisserman. Video google: A text retrieval approach to object matching in videos. In Proc. CVPR, 2003.

[35]

R. Sumner and J. Popović. Deformation transfer for triangle meshes. In Proc. Conf. Computer Graphics and Interactive Techniques, pages 399--405, 2004.

Digital Library

[36]

J. Sun, M. Ovsjanikov, and L. J. Guibas. A concise and provably informative multi-scale signature based on heat diffusion. In Proc. SGP, 2009.

Digital Library

[37]

H. Sundar, D. Silver, N. Gagvani, and S. Dickinson. Skeleton based shape matching and retrieval. In Proc. SMI, volume 130, 2003.

Digital Library

[38]

A. Tal, M. Elad, and S. Ar. Content based retrieval of VRML objects - an iterative and interactive approach. In Proc. Eurographics Workshop on Multimedia, 2001.

Digital Library

[39]

N. Thorstensen and R. Keriven. Non-rigid shape matching using geometry and photometry. In Proc. CVPR, 2009.

[40]

R. Toldo, U. Castellani, and A. Fusiello. Visual vocabulary signature for 3D object retrieval and partial matching. In Proc. 3DOR, 2009.

Digital Library

[41]

A. Zaharescu, E. Boyer, K. Varanasi, and R. Horaud. Surface feature detection and description with applications to mesh matching. In Proc. CVPR, 2009.

[42]

C. Zhang and T. Chen. Efficient feature extraction for 2D/3D objects in meshrepresentation. In Proc. ICIP, volume 3, 2001.

Cited By

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
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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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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.

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Published: 25 October 2010

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October 25, 2010

Firenze, Italy

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Cited By

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
https://doi.org/10.1007/s44150-022-00021-4
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
https://doi.org/10.3390/s21041187
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
https://doi.org/10.1371/journal.pcbi.1008741
Smirnov DSolomon J(2021)HodgeNetACM Transactions on Graphics10.1145/3450626.345979740:4(1-11)Online publication date: 19-Jul-2021
https://dl.acm.org/doi/10.1145/3450626.3459797
Eliasof MTreister ELarochelle HRanzato MHadsell RBalcan MLin H(2020)DiffGCNProceedings of the 34th International Conference on Neural Information Processing Systems10.5555/3495724.3497236(18016-18027)Online publication date: 6-Dec-2020
https://dl.acm.org/doi/10.5555/3495724.3497236
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