Zigzag persistence for image processing: New software and applications

Topological image analysis is a powerful tool for understanding the structure and topology of images, being persistent homology one of its most popular methods. However, persistent homology requires a chain of inclusions of topological spaces, which can be challenging for digital images. In this art...

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Detalhes bibliográficos
Autores: Divasón, Jose, Romero, Ana, Santolaria, Pilar, Yániz, Jesús L.
Formato: artículo
Estado:Versión publicada
Fecha de publicación:2024
País:España
Recursos:Universidad de Zaragoza
Repositorio:Zaguán. Repositorio Digital de la Universidad de Zaragoza
OAI Identifier:oai:zaguan.unizar.es:136204
Acesso em linha:http://zaguan.unizar.es/record/136204
Access Level:acceso abierto
Descrição
Resumo:Topological image analysis is a powerful tool for understanding the structure and topology of images, being persistent homology one of its most popular methods. However, persistent homology requires a chain of inclusions of topological spaces, which can be challenging for digital images. In this article, we explore the use of zigzag persistence, a recent variant of traditional persistence, for digital image processing. To this end, new algorithms are developed to build a simplicial complex associated to a digital image and to compute the relationships between homology classes of a sequence of binary images via zigzag persistence. Additionally, we provide a simple software to use them. We demonstrate its effectiveness by applying it to a real-world problem of analyzing honey bee sperm videos.