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- W4316830015 abstract "Topological data analysis (TDA) is a rising branch in modern applied mathematics. It extracts topological structures as features of a given space and uses these features to analyze digital data. Persistent homology, one of the central tools in TDA, defines persistence barcodes to measure the changes in local topologies among deformations of topological spaces. Although local spatial changes characterize barcodes, it is hard to detect the locations of corresponding structures of barcodes due to computational limitations. The paper provides an efficient and concise way to divide the underlying space and applies the local homology of the divided system to approximate the locations of local holes in the based space. We also demonstrate this local homology framework on digital images." @default.
- W4316830015 created "2023-01-17" @default.
- W4316830015 creator A5085356273 @default.
- W4316830015 date "2023-01-13" @default.
- W4316830015 modified "2023-09-26" @default.
- W4316830015 title "Locating topological structures in digital images via local homology" @default.
- W4316830015 doi "https://doi.org/10.48550/arxiv.2301.05474" @default.
- W4316830015 hasPublicationYear "2023" @default.
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