Neural Descriptors: Self-supervised Learning of Robust Local Surface Descriptors Using Polynomial Patches

Gal Yona; Roy Velich; Ehud Rivlin; Ron Kimmel

doi:10.1007/978-3-031-92369-2_17

Neural Descriptors: Self-supervised Learning of Robust Local Surface Descriptors Using Polynomial Patches

Gal Yona, Roy Velich, Ehud Rivlin, Ron Kimmel

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

Classical shape descriptors such as Heat Kernel Signature (HKS), Wave Kernel Signature (WKS), and Signature of Histograms of OrienTations (SHOT), while widely used in shape analysis, exhibit sensitivity to mesh connectivity, sampling patterns, and topological noise. While differential geometry offers a promising alternative through its theory of differential invariants, which are theoretically guaranteed to be robust shape descriptors, the computation of these invariants on discrete meshes often leads to unstable numerical approximations, limiting their practical utility. We present a self-supervised learning approach for extracting geometric features from 3D surfaces. Our method combines synthetic data generation with a neural architecture designed to learn sampling-invariant features. By integrating our features into existing shape correspondence frameworks, we demonstrate improved performance on standard benchmarks including FAUST, SCAPE, TOPKIDS, and SHREC’16, showing particular robustness to topological noise and partial shapes.

Original language	English
Title of host publication	Scale Space and Variational Methods in Computer Vision - 10th International Conference, SSVM 2025, Proceedings
Editors	Tatiana A. Bubba, Romina Gaburro, Silvia Gazzola, Kostas Papafitsoros, Marcelo Pereyra, Carola-Bibiane Schönlieb
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	218-230
Number of pages	13
ISBN (Print)	9783031923685
DOIs	https://doi.org/10.1007/978-3-031-92369-2_17
State	Published - 2025
Externally published	Yes
Event	10th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2025 - Dartington, United Kingdom Duration: 18 May 2025 → 22 May 2025

Publication series

Name	Lecture Notes in Computer Science
Volume	15668 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	10th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2025
Country/Territory	United Kingdom
City	Dartington
Period	18/05/25 → 22/05/25

Bibliographical note

Publisher Copyright:
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

Keywords

3D Shape Analysis
Geometric Invariants
Surface Representation

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-031-92369-2_17

Cite this

Yona, G., Velich, R., Rivlin, E., & Kimmel, R. (2025). Neural Descriptors: Self-supervised Learning of Robust Local Surface Descriptors Using Polynomial Patches. In T. A. Bubba, R. Gaburro, S. Gazzola, K. Papafitsoros, M. Pereyra, & C.-B. Schönlieb (Eds.), Scale Space and Variational Methods in Computer Vision - 10th International Conference, SSVM 2025, Proceedings (pp. 218-230). (Lecture Notes in Computer Science; Vol. 15668 LNCS). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-031-92369-2_17

Yona, Gal ; Velich, Roy ; Rivlin, Ehud et al. / Neural Descriptors : Self-supervised Learning of Robust Local Surface Descriptors Using Polynomial Patches. Scale Space and Variational Methods in Computer Vision - 10th International Conference, SSVM 2025, Proceedings. editor / Tatiana A. Bubba ; Romina Gaburro ; Silvia Gazzola ; Kostas Papafitsoros ; Marcelo Pereyra ; Carola-Bibiane Schönlieb. Springer Science and Business Media Deutschland GmbH, 2025. pp. 218-230 (Lecture Notes in Computer Science).

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abstract = "Classical shape descriptors such as Heat Kernel Signature (HKS), Wave Kernel Signature (WKS), and Signature of Histograms of OrienTations (SHOT), while widely used in shape analysis, exhibit sensitivity to mesh connectivity, sampling patterns, and topological noise. While differential geometry offers a promising alternative through its theory of differential invariants, which are theoretically guaranteed to be robust shape descriptors, the computation of these invariants on discrete meshes often leads to unstable numerical approximations, limiting their practical utility. We present a self-supervised learning approach for extracting geometric features from 3D surfaces. Our method combines synthetic data generation with a neural architecture designed to learn sampling-invariant features. By integrating our features into existing shape correspondence frameworks, we demonstrate improved performance on standard benchmarks including FAUST, SCAPE, TOPKIDS, and SHREC{\textquoteright}16, showing particular robustness to topological noise and partial shapes.",

keywords = "3D Shape Analysis, Geometric Invariants, Surface Representation",

author = "Gal Yona and Roy Velich and Ehud Rivlin and Ron Kimmel",

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Yona, G, Velich, R, Rivlin, E & Kimmel, R 2025, Neural Descriptors: Self-supervised Learning of Robust Local Surface Descriptors Using Polynomial Patches. in TA Bubba, R Gaburro, S Gazzola, K Papafitsoros, M Pereyra & C-B Schönlieb (eds), Scale Space and Variational Methods in Computer Vision - 10th International Conference, SSVM 2025, Proceedings. Lecture Notes in Computer Science, vol. 15668 LNCS, Springer Science and Business Media Deutschland GmbH, pp. 218-230, 10th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2025, Dartington, United Kingdom, 18/05/25. https://doi.org/10.1007/978-3-031-92369-2_17

Neural Descriptors: Self-supervised Learning of Robust Local Surface Descriptors Using Polynomial Patches. / Yona, Gal; Velich, Roy; Rivlin, Ehud et al.
Scale Space and Variational Methods in Computer Vision - 10th International Conference, SSVM 2025, Proceedings. ed. / Tatiana A. Bubba; Romina Gaburro; Silvia Gazzola; Kostas Papafitsoros; Marcelo Pereyra; Carola-Bibiane Schönlieb. Springer Science and Business Media Deutschland GmbH, 2025. p. 218-230 (Lecture Notes in Computer Science; Vol. 15668 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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T1 - Neural Descriptors

T2 - 10th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2025

AU - Yona, Gal

AU - Velich, Roy

AU - Rivlin, Ehud

AU - Kimmel, Ron

N1 - Publisher Copyright: © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

PY - 2025

Y1 - 2025

N2 - Classical shape descriptors such as Heat Kernel Signature (HKS), Wave Kernel Signature (WKS), and Signature of Histograms of OrienTations (SHOT), while widely used in shape analysis, exhibit sensitivity to mesh connectivity, sampling patterns, and topological noise. While differential geometry offers a promising alternative through its theory of differential invariants, which are theoretically guaranteed to be robust shape descriptors, the computation of these invariants on discrete meshes often leads to unstable numerical approximations, limiting their practical utility. We present a self-supervised learning approach for extracting geometric features from 3D surfaces. Our method combines synthetic data generation with a neural architecture designed to learn sampling-invariant features. By integrating our features into existing shape correspondence frameworks, we demonstrate improved performance on standard benchmarks including FAUST, SCAPE, TOPKIDS, and SHREC’16, showing particular robustness to topological noise and partial shapes.

AB - Classical shape descriptors such as Heat Kernel Signature (HKS), Wave Kernel Signature (WKS), and Signature of Histograms of OrienTations (SHOT), while widely used in shape analysis, exhibit sensitivity to mesh connectivity, sampling patterns, and topological noise. While differential geometry offers a promising alternative through its theory of differential invariants, which are theoretically guaranteed to be robust shape descriptors, the computation of these invariants on discrete meshes often leads to unstable numerical approximations, limiting their practical utility. We present a self-supervised learning approach for extracting geometric features from 3D surfaces. Our method combines synthetic data generation with a neural architecture designed to learn sampling-invariant features. By integrating our features into existing shape correspondence frameworks, we demonstrate improved performance on standard benchmarks including FAUST, SCAPE, TOPKIDS, and SHREC’16, showing particular robustness to topological noise and partial shapes.

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SN - 9783031923685

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BT - Scale Space and Variational Methods in Computer Vision - 10th International Conference, SSVM 2025, Proceedings

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A2 - Gaburro, Romina

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Yona G, Velich R, Rivlin E, Kimmel R. Neural Descriptors: Self-supervised Learning of Robust Local Surface Descriptors Using Polynomial Patches. In Bubba TA, Gaburro R, Gazzola S, Papafitsoros K, Pereyra M, Schönlieb CB, editors, Scale Space and Variational Methods in Computer Vision - 10th International Conference, SSVM 2025, Proceedings. Springer Science and Business Media Deutschland GmbH. 2025. p. 218-230. (Lecture Notes in Computer Science). doi: 10.1007/978-3-031-92369-2_17