Abstract
In this paper, we propose a geometry-aware topological analysis of a segmentation of an image into regions which might correspond, for example, to a geographical map or to segmented cells in a microscopic image of a biological packed tissue. The regions must satisfy that the centroid of each one lies inside the region itself. We propose a novel simplicial complex modeling such data, for persistent homology computation, that better respects the geometry of the regions than existing techniques. More specifically, our approach joins benefits from previous models by encoding both neighbouring relations between the regions, as well as spatial distribution of the set of centroids. In addition, we introduce geometric information regarding distances between centroids and boundaries delimiting each region.
This research was funded by Ministerio de Ciencia e Innovación - Agencia Estatal de Investigación/10.13039/501100011033, grant PID2019-107339GB-I00 and Agencia Andaluza del Conocimiento, grant PAIDI-2020 P20-01145. Authors listed in alphabetical order.
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Jimenez, MJ., Medrano, B. (2022). Topological Analysis of Simple Segmentation Maps. In: Baudrier, É., Naegel, B., Krähenbühl, A., Tajine, M. (eds) Discrete Geometry and Mathematical Morphology. DGMM 2022. Lecture Notes in Computer Science, vol 13493. Springer, Cham. https://doi.org/10.1007/978-3-031-19897-7_11
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DOI: https://doi.org/10.1007/978-3-031-19897-7_11
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