1 October 2001 Topological operators for grayscale image processing
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In recent work, we introduced some topological notions for grayscale images based on a cross-section topology. In particular, the notion of destructible point, which corresponds to the classical notion of simple point, allows us to build operators that simplify a grayscale image while preserving its topology. In this paper, we introduce new notions and operators in the framework of the crosssection topology. In particular, the notion of the l-destructible point allows us to selectively modify the topology, based on a local contrast parameter l. By combining homotopic and nonhomotopic operators, we introduce new methods for filtering, thinning, segmenting, and enhancing grayscale images.
Michel Couprie, Francisco-Nivando Bezerra, Gilles Bertrand, "Topological operators for grayscale image processing," Journal of Electronic Imaging 10(4), (1 October 2001). https://doi.org/10.1117/1.1408316

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