The focus of this article is to develop computationally efficient mathematical morphology operators on hypergraphs. To this aim we consider lattice structures on hypergraphs on which we build morphological operators. We develop a pair of dual adjunctions between the vertex set and the hyper edge set of a hypergraph H , by defining a vertex-hyperedge correspondence. This allows us to recover the...

In this paper we introduce a class of morphological operators with applications to sharpening digitized grey valued images. We introduce t.he underlying partial differential equation (PDE) that governs this class of operators. For discrete implementations of the operator class! we show that instances utilizing a parabolic structuring function, have special properties that lead to an efficient i...

This article presents the use of anisotropic dynamic structuring elements, or amoebas, in order to build content-aware noise reduction filters. The amoeba is the ball defined by a special geodesic distance computed for each pixel, and can be used as a kernel for many kinds of filters and morphological operators.

Filtering is one of the core post-processing steps for airborne LiDAR point cloud. In recent years, the morphology-based filtering algorithms have proven to be a powerful and efficient tool for filtering airborne LiDAR point cloud. However, most traditional morphology-based algorithms have difficulties in preserving abrupt terrain features, especially when using larger filtering windows. In ord...

A new technique for the realisation of soft morphological filters based on the majority gate algorithm is presented in this paper. A pipelined systolic array architecture suitable to perform soft morphological filtering is also presented. The processing times of the proposed hardware structure do not depend on the data window size and the required silicon area is linearly related to the number ...