Authors: Corcoran, Padraig
Žunić, Joviša 
Rosin, Paul L.
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: A multi-scale topological shape model for single and multiple component shapes
Journal: Journal of Visual Communication and Image Representation
Volume: 64
First page: 102617
Issue Date: 2019
Rank: M21
ISSN: 1047-3203
DOI: 10.1016/j.jvcir.2019.102617
Abstract: 
A novel shape model of multi-scale topological features is proposed which considers those features relating to connected components and holes. This is achieved by considering the persistent homology of a pair of sublevel set functions corresponding to a pair of distance functions defined on the ambient space. The model is applicable to both single and multiple component shapes and, to the authors knowledge, is the first shape model to consider multi-scale topological features of multiple component shapes. It is demonstrated, both qualitatively and quantitatively, that the proposed model models useful multi-scale topological features and outperforms a commonly used benchmark models with respect to the task of multiple component shape retrieval.
Keywords: Multi-scale | Multiple component shapes | Persistent homology | Topology
Publisher: Elsevier

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