9 citations · 17 across the 11 of their papers we have counts for
11 papers
MMPersistence: A mathematical morphology-oriented software library for computing persistent homology on cubical complexes
Chuan-Shen Hu
Mathematical morphology (MM) is a powerful and widely used framework in image processing. Through set-theoretic and discrete geometric principles, MM operations such as erosion, di…
A Sheaf-Theoretic and Topological Perspective on Complex Network Modeling and Attention Mechanisms in Graph Neural Models
Chuan-Shen Hu
Combinatorial and topological structures, such as graphs, simplicial complexes, and cell complexes, form the foundation of geometric and topological deep learning (GDL and TDL) arc…
Verification Method for Graph Isomorphism Criteria
Chuanfu Hu, Aimin Hou
The criteria for determining graph isomorphism are crucial for solving graph isomorphism problems. The necessary condition is that two isomorphic graphs possess invariants, but the…
Identifying weak critical fluctuations of intermittency in heavy-ion collisions with topological machine learning
Rui Wang, Chengrui Qiu, Chuan-Shen Hu +2
Large density fluctuations of conserved charges have been proposed as a promising signature for exploring the QCD critical point in heavy-ion collisions. These fluctuations are exp…
Locating topological structures in digital images via local homology
Chuan-Shen Hu
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…
A Multi-parameter Persistence Framework for Mathematical Morphology
Yu-Min Chung, Sarah Day, Chuan-Shen Hu
The field of mathematical morphology offers well-studied techniques for image processing. In this work, we view morphological operations through the lens of persistent homology, a…
A Sheaf and Topology Approach to Generating Local Branch Numbers in Digital Images
Chuan-Shen Hu, Yu-Min Chung
This paper concerns a theoretical approach that combines topological data analysis (TDA) and sheaf theory. Topological data analysis, a rising field in mathematics and computer sci…
Conditions for Morphology-Based Topological Filtrations and Applications to Firn Data Analysis
Chuan-Shen Hu, Yu-Min Chung, Kaitlin Keegan +1
Persistent homology (PH), a key tool in topological data analysis (TDA), captures global topological features of digital images through \emph{topological filtrations}. Alternativel…
A Brief Note for Sheaf Structures on Posets
Chuan-Shen Hu
This note is a part of the lecture notes of a graduate student algebraic geometry seminar held at the department of mathematics in National Taiwan Normal University, 2020 Falls. It…
A persistent homology approach to heart rate variability analysis with an application to sleep-wake classification
Yu-Min Chung, Chuan-Shen Hu, Yu-Lun Lo +1
Persistent homology (PH) is a recently developed theory in the field of algebraic topology to study shapes of datasets. It is an effective data analysis tool that is robust to nois…
TopoResNet: A hybrid deep learning architecture and its application to skin lesion classification
Yu-Min Chung, Chuan-Shen Hu, Austin Lawson +1
Skin cancer is one of the most common cancers in the United States. As technological advancements are made, algorithmic diagnosis of skin lesions is becoming more important. In thi…