Topological operators for grayscale image processing

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.