Efficient Computation of Image Persistence.
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| Title: | Efficient Computation of Image Persistence. |
|---|---|
| Authors: | Bauer, Ulrich1 (AUTHOR) ulrich.bauer@tum.de, Schmahl, Maximilian2 (AUTHOR) maximilian.schmahl@web.de |
| Source: | Discrete & Computational Geometry. Dec2025, Vol. 74 Issue 4, p999-1019. 21p. |
| Subjects: | Optimization algorithms, Mathematical complexes, Image representation, Algorithms, Computer software |
| Abstract: | We present an algorithm for computing the barcode of the image of a morphism in persistent homology induced by an inclusion of filtered finite-dimensional chain complexes. The algorithm makes use of the clearing optimization and can be applied to inclusion-induced maps in persistent absolute homology and persistent relative cohomology for filtrations of pairs of simplicial complexes. The clearing optimization works particularly well in the context of relative cohomology, and using previous duality results we can translate the barcodes of images in relative cohomology to those in absolute homology. This forms the basis for an implementation of image persistence computations for inclusions of filtrations of Vietoris–Rips complexes in the framework of the software Ripser. [ABSTRACT FROM AUTHOR] |
| Copyright of Discrete & Computational Geometry is the property of Springer Nature 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 |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 189681741 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Efficient Computation of Image Persistence. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Bauer%2C+Ulrich%22">Bauer, Ulrich</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> ulrich.bauer@tum.de</i><br /><searchLink fieldCode="AR" term="%22Schmahl%2C+Maximilian%22">Schmahl, Maximilian</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> maximilian.schmahl@web.de</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Discrete+%26+Computational+Geometry%22">Discrete & Computational Geometry</searchLink>. Dec2025, Vol. 74 Issue 4, p999-1019. 21p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Optimization+algorithms%22">Optimization algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+complexes%22">Mathematical complexes</searchLink><br /><searchLink fieldCode="DE" term="%22Image+representation%22">Image representation</searchLink><br /><searchLink fieldCode="DE" term="%22Algorithms%22">Algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Computer+software%22">Computer software</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: We present an algorithm for computing the barcode of the image of a morphism in persistent homology induced by an inclusion of filtered finite-dimensional chain complexes. The algorithm makes use of the clearing optimization and can be applied to inclusion-induced maps in persistent absolute homology and persistent relative cohomology for filtrations of pairs of simplicial complexes. The clearing optimization works particularly well in the context of relative cohomology, and using previous duality results we can translate the barcodes of images in relative cohomology to those in absolute homology. This forms the basis for an implementation of image persistence computations for inclusions of filtrations of Vietoris–Rips complexes in the framework of the software Ripser. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Discrete & Computational Geometry is the property of Springer Nature 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: 10.1007/s00454-025-00769-8 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 21 StartPage: 999 Subjects: – SubjectFull: Optimization algorithms Type: general – SubjectFull: Mathematical complexes Type: general – SubjectFull: Image representation Type: general – SubjectFull: Algorithms Type: general – SubjectFull: Computer software Type: general Titles: – TitleFull: Efficient Computation of Image Persistence. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Bauer, Ulrich – PersonEntity: Name: NameFull: Schmahl, Maximilian IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 12 Text: Dec2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 01795376 Numbering: – Type: volume Value: 74 – Type: issue Value: 4 Titles: – TitleFull: Discrete & Computational Geometry Type: main |
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