Digital $n-$Manifolds With Or Without Boundaries
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913614375419904 |
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| author | İs, Melih Karaca, İsmet |
| author_facet | İs, Melih Karaca, İsmet |
| contents | This work aims to define the concept of manifold, which has a very important place in the topology, on digital images. So, a general perspective is provided for two and three-dimensional imaging studies on digital curves and digital surfaces. Throughout the study, the features present in topological manifolds but that are not satisfied in the discrete version are specifically underlined. In addition, other concepts closely related to manifolds such as submanifold, orientation, and partition of unity are also discussed in digital images. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_12008 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Digital $n-$Manifolds With Or Without Boundaries İs, Melih Karaca, İsmet Algebraic Topology 57N65, 58K65, 32Q55, 68U05 G.2.3 This work aims to define the concept of manifold, which has a very important place in the topology, on digital images. So, a general perspective is provided for two and three-dimensional imaging studies on digital curves and digital surfaces. Throughout the study, the features present in topological manifolds but that are not satisfied in the discrete version are specifically underlined. In addition, other concepts closely related to manifolds such as submanifold, orientation, and partition of unity are also discussed in digital images. |
| title | Digital $n-$Manifolds With Or Without Boundaries |
| topic | Algebraic Topology 57N65, 58K65, 32Q55, 68U05 G.2.3 |
| url | https://arxiv.org/abs/2412.12008 |