2024/02/21 by Brittany Terese Fasy, Fasy, Brittany Terese, David L. Millman +3 · 1 citation
Computer Science · #Computational Geometry (cs.CG) #Constraint Satisfaction and Optimization #FOS: Computer and information sciences #Image Retrieval and Classification Techniques #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2402.13632
openalex publication_date 2024/02/21 · openalex created_date 2024/02/23 · openalex updated_date 2026/07/28
Recent developments in shape reconstruction and comparison call for the use of many different (topological) descriptor types, such as persistence diagrams and Euler characteristic functions. We establish a framework to quantitatively compare the strength of different descriptor types, setting up a theory that allows for future comparisons and analysis of descriptor types and that can inform choices made in applications. We use this framework to partially order a set of six common descriptor types. We then give lower bounds on the size of sets of descriptors that uniquely correspond to simplicial complexes, giving insight into the advantages of using verbose rather than concise topological descriptors.