2020/12/24 by Chuan-Shen Hu, Yu-Min Chung, Hu, Chuan-Shen +5
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Algorithm #Artificial intelligence #Closing (real estate) #Computer science #Construct (python library) #Decomposition #Digital Image Processing Techniques #Domain (mathematical analysis) #Epistemology #Image (mathematics) #Image Retrieval and Classification Techniques #Inclusion (mineral) #Mathematical analysis #Mathematics #Physics #Programming language #Property (philosophy) #Pure mathematics #Structuring #Theoretical computer science
paper · pdf · doi:10.48550/arxiv.2012.13132
openalex publication_date 2020/12/24 · openalex created_date 2021/01/05 · openalex updated_date 2026/08/05
Persistent homology (PH), a key tool in topological data analysis (TDA), captures global topological features of digital images through topological filtrations. Alternatively, mathematical morphology (MM), rooted in set theory and lattice theory, provides operations such as opening and closing to modify local geometric structures in digital images. This motivates incorporating local geometric information into a PH framework via morphological filtrations, yielding an MM-based PH framework. However, the validity of such filtrations depends on the absorption property of MM operations, which may fail for arbitrary structuring elements, the components defining MM operators. To address this issue, we introduce shift inclusion as a sufficient condition for ensuring absorption, provide a formal proof, and demonstrate its utility in pore-structure analysis, highlighting the synergy between MM and PH for image and scientific data analysis.