Path openings and closings are algebraic morphological operators using families of thin and oriented structuring elements that are not necessarily perfectly straight. These operators are naturally translation invariant and can be used in filtering applications instead of operators based on the more standard families of straight line structuring elements. They give similar results to area or att...

Today, the theoretical framework of mathematical morphology is phrased in terms of complete lattices and operators de ned on them. That means in particular that the choice of the underlying partial ordering is of eminent importance, as it determines the class of morphological operators that one ends up with. The duality principle for partially ordered sets, which says that the opposite of a par...

In this paper we propose a series of novel morphological operators that are anisotropic, and adapt themselves to the local orientation in the image. This new morphology is therefore rotation invariant; i.e. rotation of the image before or after the operation yields the same result. We present relevant properties required by morphology, as well as other properties shared with common morphologica...

A new morphological operator, namely RORPO (Ranking Orientation Responses of Path Operators), was recently introduced as a semi-global, morphological alternative to the local, Hessian-based operators for thin structure filtering in 3D images. In this context, a previous study has already provided experimental proof of its relevance by comparison to such differential operators. In this article, ...

— In this paper an adaptive hybrid morphological method is presented for designing translation invariant morphological operators via Matheron Decomposition and via Banon and Barrera Decomposition. It consists of a hybrid model composed of a Modular Morphological Neural Network (MMNN) and an evolutionary search mechanism: the adaptive Genetic Algorithm (GA) (adaptive rates in genetic operators)....

In this thesis, the limitations of the conventional morphological gradient (MG) as an edge detector are theoretically analyzed, and three new methods with improved performance are developed. The new methods are analyzed theoretically and demonstrated with both synthetic and real image data. The basic issues regarding edge detection, linear and nonlinear filtering, especially in morphological fi...

Two of G. Matheron’s seminal contributions have been his development of size distributions (else called ‘granulometries’) and his kernel representation theory. The first deals with semigroups of multiscale openings and closings of binary images (shapes) by compact convex sets, a basic ingredient of which are the multiscale Minkowski dilations and erosions. The second deals with representing inc...