文章基本信息

标题：The Discrete Morse Complex of Images: Algorithms, Modeling and Applications
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作者：da Silva, Ricardo Dutra ; Pedrini, Helio ; Hamann, Bernd 等
期刊名称：OASIcs : OpenAccess Series in Informatics
电子版ISSN：2190-6807
出版年度：2021
卷号：89
页码：18:1-18:19
DOI：10.4230/OASIcs.iPMVM.2020.18
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：The Morse complex can be used for studying the topology of a function, e.g., an image or terrain height field when understood as bivariate functions. We present an algorithm for the computation of the discrete Morse complex of two-dimensional images using an edge-based data structure. By using this data structure, it is possible to perform local operations efficiently, which is important to construct the complex and make the structure useful for areas like visualization, persistent homology computation, or construction of a topological hierarchy. We present theoretical and applied results to demonstrate benefits and use of our method.
关键词：Discrete Morse Complex; Image Topology; Cell Complexes