🍩 Database of Original & Non-Theoretical Uses of Topology

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The Topology of the Cosmic Web in Terms of Persistent Betti Numbers (2017)

Pratyush Pranav, Herbert Edelsbrunner, Rien van de Weygaert, Gert Vegter, Michael Kerber, Bernard J. T. Jones, Mathijs Wintraecken

Abstract
Abstract. We introduce a multiscale topological description of the Megaparsec web-like cosmic matter distribution. Betti numbers and topological persistence of
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The Persistent Cosmic Web and Its Filamentary Structure – II. Illustrations (2011)

T. Sousbie, C. Pichon, H. Kawahara

Abstract
Abstract. The recently introduced discrete persistent structure extractor (DisPerSE, Sousbie, Paper I) is implemented on realistic 3D cosmological simulations
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Persistent Betti Numbers for a Noise Tolerant Shape-Based Approach to Image Retrieval (2011)

Patrizio Frosini, Claudia Landi

Abstract
In content-based image retrieval a major problem is the presence of noisy shapes. It is well known that persistent Betti numbers are a shape descriptor that admits a dissimilarity distance, the matching distance, stable under continuous shape deformations. In this paper we focus on the problem of dealing with noise that changes the topology of the studied objects. We present a general method to turn persistent Betti numbers into stable descriptors also in the presence of topological changes. Retrieval tests on the Kimia-99 database show the effectiveness of the method.
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