In this work we study the framework of mathematical morphology on simplicial complex spaces. Simplicial complexes are a versatile and widely used structure to represent multidimensional data, such as meshes, that are tridimensional complexes, or graphs, that can be interpreted as bidimensional complexes. Mathematical morphology is one of the most powerful frameworks for image processing, includ...

Abstract The subject of this paper is the semantically based postprocessing of color–coded images such as classification results. We outline why the classical definition of mathematical morphology suffers if it is used for processing of coded image data. Therefore we provide an extension for morphological operations such as dilation, erosion, opening, and closing. With a new understanding of mo...

Classical morphology is built up in such a way that all operators occur in pairs, e.g., dilation and erosion, opening and closing, etc. This phenomenon, which is a straightforward consequence of the duality principle, often prohibits the construction of tools that treat foreground and background of signals in exactly the same way. In this paper we discuss an alternative framework for morphologi...

The focus of this article is to develop mathematical morphology on hypergraphs. To this aim, we define lattice structures on hypergraphs on which we build mathematical morphology operators. We show some relations between these operators and the hypergraph structure, considering in particular transversals and duality notions. Then, as another contribution, we show how mathematical morphology can...