Neural Geometry Processing via Spherical Neural Surfaces.
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| Title: | Neural Geometry Processing via Spherical Neural Surfaces. |
|---|---|
| Authors: | Williamson, Romy1 (AUTHOR), Mitra, Niloy J.1,2 (AUTHOR) |
| Source: | Computer Graphics Forum. May2025, Vol. 44 Issue 2, p1-14. 14p. |
| Subjects: | Computational geometry, Spherical geometry, Geometric shapes, Directional derivatives, Geometric analysis, Spectral theory |
| Abstract: | Neural surfaces (e.g., neural map encoding, deep implicit, and neural radiance fields) have recently gained popularity because of their generic structure (e.g., multi‐layer perceptron) and easy integration with modern learning‐based setups. Traditionally, we have a rich toolbox of geometry processing algorithms designed for polygonal meshes to analyze and operate on surface geometry. Without an analogous toolbox, neural representations are typically discretized and converted into a mesh, before applying any geometry processing algorithm. This is unsatisfactory and, as we demonstrate, unnecessary. In this work, we propose a spherical neural surface representation for genus‐0 surfaces and demonstrate how to compute core geometric operators directly on this representation. Namely, we estimate surface normals and first and second fundamental forms of the surface, as well as compute surface gradient, surface divergence and Laplace Beltrami operator on scalar/vector fields defined on the surface. Our representation is fully seamless, overcoming a key limitation of similar explicit representations such as Neural Surface Maps [MAKM21]. These operators, in turn, enable geometry processing directly on the neural representations without any unnecessary meshing. We demonstrate illustrative applications in (neural) spectral analysis, heat flow and mean curvature flow, and evaluate robustness to isometric shape variations. We propose theoretical formulations and validate their numerical estimates, against analytical estimates, mesh‐based baselines, and neural alternatives, where available. By systematically linking neural surface representations with classical geometry processing algorithms, we believe this work can become a key ingredient in enabling neural geometry processing. Code is available via the project webpage. [ABSTRACT FROM AUTHOR] |
| Copyright of Computer Graphics Forum is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Header | DbId: egs DbLabel: Engineering Source An: 186773083 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Neural Geometry Processing via Spherical Neural Surfaces. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Williamson%2C+Romy%22">Williamson, Romy</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Mitra%2C+Niloy+J%2E%22">Mitra, Niloy J.</searchLink><relatesTo>1,2</relatesTo> (AUTHOR) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Computer+Graphics+Forum%22">Computer Graphics Forum</searchLink>. May2025, Vol. 44 Issue 2, p1-14. 14p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Computational+geometry%22">Computational geometry</searchLink><br /><searchLink fieldCode="DE" term="%22Spherical+geometry%22">Spherical geometry</searchLink><br /><searchLink fieldCode="DE" term="%22Geometric+shapes%22">Geometric shapes</searchLink><br /><searchLink fieldCode="DE" term="%22Directional+derivatives%22">Directional derivatives</searchLink><br /><searchLink fieldCode="DE" term="%22Geometric+analysis%22">Geometric analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Spectral+theory%22">Spectral theory</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Neural surfaces (e.g., neural map encoding, deep implicit, and neural radiance fields) have recently gained popularity because of their generic structure (e.g., multi‐layer perceptron) and easy integration with modern learning‐based setups. Traditionally, we have a rich toolbox of geometry processing algorithms designed for polygonal meshes to analyze and operate on surface geometry. Without an analogous toolbox, neural representations are typically discretized and converted into a mesh, before applying any geometry processing algorithm. This is unsatisfactory and, as we demonstrate, unnecessary. In this work, we propose a spherical neural surface representation for genus‐0 surfaces and demonstrate how to compute core geometric operators directly on this representation. Namely, we estimate surface normals and first and second fundamental forms of the surface, as well as compute surface gradient, surface divergence and Laplace Beltrami operator on scalar/vector fields defined on the surface. Our representation is fully seamless, overcoming a key limitation of similar explicit representations such as Neural Surface Maps [MAKM21]. These operators, in turn, enable geometry processing directly on the neural representations without any unnecessary meshing. We demonstrate illustrative applications in (neural) spectral analysis, heat flow and mean curvature flow, and evaluate robustness to isometric shape variations. We propose theoretical formulations and validate their numerical estimates, against analytical estimates, mesh‐based baselines, and neural alternatives, where available. By systematically linking neural surface representations with classical geometry processing algorithms, we believe this work can become a key ingredient in enabling neural geometry processing. Code is available via the project webpage. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Computer Graphics Forum is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1111/cgf.70021 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 14 StartPage: 1 Subjects: – SubjectFull: Computational geometry Type: general – SubjectFull: Spherical geometry Type: general – SubjectFull: Geometric shapes Type: general – SubjectFull: Directional derivatives Type: general – SubjectFull: Geometric analysis Type: general – SubjectFull: Spectral theory Type: general Titles: – TitleFull: Neural Geometry Processing via Spherical Neural Surfaces. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Williamson, Romy – PersonEntity: Name: NameFull: Mitra, Niloy J. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 05 Text: May2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 01677055 Numbering: – Type: volume Value: 44 – Type: issue Value: 2 Titles: – TitleFull: Computer Graphics Forum Type: main |
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