Academic Journal
Quasi-conformal Convolution: A Learnable Convolution for Deep Learning on Simply Connected Open Surfaces.
| Τίτλος: | Quasi-conformal Convolution: A Learnable Convolution for Deep Learning on Simply Connected Open Surfaces. |
|---|---|
| Συγγραφείς: | Zhang, Han, Ip, Tsz Lok, Lui, Lok Ming |
| Πηγή: | SIAM Journal on Imaging Sciences; 2026, Vol. 19 Issue 1, p555-583, 29p |
| Θεματικοί όροι: | Quasiconformal mappings, Geometric surfaces, Riemannian manifolds, Convolutional neural networks, Deep learning, Geometric analysis, Computer-assisted image analysis (Medicine) |
| Περίληψη: | Deep learning on non-Euclidean domains is important for analyzing complex geometric data that lacks common coordinate systems and familiar Euclidean properties. A central challenge in this field is to define convolution on domains, which inherently possess irregular and non-Euclidean structures. In this work, we introduce quasi-conformal convolution (QCC), a novel framework for defining convolution on simply-connected open surfaces using quasi-conformal theories. Each QCC operator is linked to a specific quasi-conformal mapping, enabling the adjustment of the convolution operation through manipulation of this mapping. By utilizing trainable estimator modules that produce quasi-conformal mappings, QCC facilitates adaptive and learnable convolution operators that can be dynamically adjusted according to the underlying data structured on the surfaces. QCC unifies a broad range of spatially defined convolutions, facilitating the learning of tailored convolution operators on each underlying surface optimized for specific tasks. Building on this foundation, we develop the quasi-conformal convolutional neural network (QCCNN) to address a variety of tasks related to geometric data. We validate the efficacy of QCCNN through the classification of images defined on curvilinear simply-connected open Riemann surfaces, demonstrating superior performance in this context. Additionally, we explore its potential in medical applications, including craniofacial analysis using 3D facial data and lesion segmentation on 3D human faces, achieving enhanced accuracy and reliability. [ABSTRACT FROM AUTHOR] |
| Copyright of SIAM Journal on Imaging Sciences is the property of Society for Industrial & Applied Mathematics 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.) | |
| Βάση Δεδομένων: | Complementary Index |
| FullText | Text: Availability: 0 |
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| Header | DbId: edb DbLabel: Complementary Index An: 192769992 RelevancyScore: 1023 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 1023.34954833984 |
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| Items | – Name: Title Label: Title Group: Ti Data: Quasi-conformal Convolution: A Learnable Convolution for Deep Learning on Simply Connected Open Surfaces. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Zhang%2C+Han%22">Zhang, Han</searchLink><br /><searchLink fieldCode="AR" term="%22Ip%2C+Tsz+Lok%22">Ip, Tsz Lok</searchLink><br /><searchLink fieldCode="AR" term="%22Lui%2C+Lok+Ming%22">Lui, Lok Ming</searchLink> – Name: TitleSource Label: Source Group: Src Data: SIAM Journal on Imaging Sciences; 2026, Vol. 19 Issue 1, p555-583, 29p – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22Quasiconformal+mappings%22">Quasiconformal mappings</searchLink><br /><searchLink fieldCode="DE" term="%22Geometric+surfaces%22">Geometric surfaces</searchLink><br /><searchLink fieldCode="DE" term="%22Riemannian+manifolds%22">Riemannian manifolds</searchLink><br /><searchLink fieldCode="DE" term="%22Convolutional+neural+networks%22">Convolutional neural networks</searchLink><br /><searchLink fieldCode="DE" term="%22Deep+learning%22">Deep learning</searchLink><br /><searchLink fieldCode="DE" term="%22Geometric+analysis%22">Geometric analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Computer-assisted+image+analysis+%28Medicine%29%22">Computer-assisted image analysis (Medicine)</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Deep learning on non-Euclidean domains is important for analyzing complex geometric data that lacks common coordinate systems and familiar Euclidean properties. A central challenge in this field is to define convolution on domains, which inherently possess irregular and non-Euclidean structures. In this work, we introduce quasi-conformal convolution (QCC), a novel framework for defining convolution on simply-connected open surfaces using quasi-conformal theories. Each QCC operator is linked to a specific quasi-conformal mapping, enabling the adjustment of the convolution operation through manipulation of this mapping. By utilizing trainable estimator modules that produce quasi-conformal mappings, QCC facilitates adaptive and learnable convolution operators that can be dynamically adjusted according to the underlying data structured on the surfaces. QCC unifies a broad range of spatially defined convolutions, facilitating the learning of tailored convolution operators on each underlying surface optimized for specific tasks. Building on this foundation, we develop the quasi-conformal convolutional neural network (QCCNN) to address a variety of tasks related to geometric data. We validate the efficacy of QCCNN through the classification of images defined on curvilinear simply-connected open Riemann surfaces, demonstrating superior performance in this context. Additionally, we explore its potential in medical applications, including craniofacial analysis using 3D facial data and lesion segmentation on 3D human faces, achieving enhanced accuracy and reliability. [ABSTRACT FROM AUTHOR] – Name: Abstract Label: Group: Ab Data: <i>Copyright of SIAM Journal on Imaging Sciences is the property of Society for Industrial & Applied Mathematics 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: 10.1137/25M1731162 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 29 StartPage: 555 Subjects: – SubjectFull: Quasiconformal mappings Type: general – SubjectFull: Geometric surfaces Type: general – SubjectFull: Riemannian manifolds Type: general – SubjectFull: Convolutional neural networks Type: general – SubjectFull: Deep learning Type: general – SubjectFull: Geometric analysis Type: general – SubjectFull: Computer-assisted image analysis (Medicine) Type: general Titles: – TitleFull: Quasi-conformal Convolution: A Learnable Convolution for Deep Learning on Simply Connected Open Surfaces. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Zhang, Han – PersonEntity: Name: NameFull: Ip, Tsz Lok – PersonEntity: Name: NameFull: Lui, Lok Ming IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Text: 2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 19364954 Numbering: – Type: volume Value: 19 – Type: issue Value: 1 Titles: – TitleFull: SIAM Journal on Imaging Sciences Type: main |
| ResultId | 1 |