In recent work, we introduced 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 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 cross-section topology. In particular, the notion of (lambda) -destructible point allows us to selectively modify the topology, based on a local contrast parameter (lambda) . By combining homotopic and non-homotopic operators, we introduce new methods for filtering, thinning, segmenting and enhancing grayscale images.