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Zigzag persistence for image processing: New software and applications
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DOI：10.1016/j.patrec.2024.06.010.png)
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Abstract
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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.
Keywords:
Zigzag persistence
Image processing
Topological data analysis
Mathematical morphology
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