Morphological image processing filters preserve shapes related to the structuring element shape of the operator. The basic morphological operators are minimum (erosion) and maximum (dilation) operations performed on the pixels within a structuring element. Although these operators (and the compound operators formed from them) are able to smooth noise, they also introduce a statistical and deter...

Path openings and closings are algebraic morphological operators using families of thin and oriented structuring elements that are not necessarily perfectly straight. These operators can typically be used in filtering applications in lieu of operators based on the more standard families of straight line structuring elements. They yield results which are less constrained than filters based on st...

This document describes morphological operators designed for partition images. Two approaches are addressed. In the first one, each cell of the partition is considered independently of the others and various anti-extensive operators can be defined on it. However, these operators can be applied directly on the whole partition. There is no need to extract each cell to transform it. The second app...

This paper presents a comprehensive discussion on connected morphological operators for binary images. Introducing a connectivity on the underlying space, every image induces a partition of the space in foreground and background components. A connected operator is an operator that coarsens this partition for every input image. A connected operator is called a grain operator if it has the follow...

Mathematical Morphology is a nonlinear image processing theory, which is currently based on complete lattices. This work extends its scope to complete semilattices, which are more general. Speci c morphological operators de ned in complete semilattices are shown, by means of simulations, to be potentially useful in some video processing applications, like detection of fast motion, extraction of...

Multiscale signal analysis has been used since the early 1990s as a powerful tool for image processing. Nonlinear PDEs and multiscale morphological filters can be used to create nonlinear operators that have advantages over linear operators, notably preserving important features such as edges in images. In this report, we present the nonlinear Hamilton-Jacobi PDEs commonly used as filters for i...

Originally, mathematical morphology was a theory of signal transformations which are invariant under Euclidean translations. An interest in the extension of mathematical morphology to spatially-variant (SV) operators has emerged due to the requirements imposed by numerous applications in adaptive signal (image) processing. This paper presents a general theory of spatially-variant mathematical m...