This paper presents a new application of mathematical morphology (MM) operators for low speed slew bearing condition monitoring. The MM operators were used as a signal processing step and feature extraction method for bearing vibration signals. Four basic MM operators; erosion, dilation, closing and opening, were studied. This paper also investigates another potential MM operator, namely gradie...

Paul Halmos’ work in dilation theory began with a question and its answer: Which operators on a Hilbert space H can be extended to normal operators on a larger Hilbert space K ⊇ H? The answer is interesting and subtle. The idea of representing operator-theoretic structures in terms of conceptually simpler structures acting on larger Hilbert spaces has become a central one in the development of ...

This paper presents a simple yet efficient algorithm for multifocus image fusion, using a multiresolution signal decomposition scheme. The decomposition scheme is based on a nonlinear wavelet constructed with morphological operations. The analysis operators are constructed by morphological dilation combined with quadratic downsampling and the synthesis operators are constructed by morphological...

The hyperbolic algebra A h , studied recently by Katavolos and Power [5], is the weak star closed operator algebra on L 2 (R) generated by H ∞ (R), as multiplication operators, and by the dilation operators V t , t ≥ 0, given by V t f (x) = e t/2 f (e t x). We show that A h is a reflexive operator algebra and that the four dimensional manifold Lat A h (with the natural topology) is the reflexiv...

on utilizing the spectral representation of selfadjoint operators in hilbert spaces, some error bounds in approximating $n$-time differentiable functions of selfadjoint operators in hilbert spaces via a taylor's type expansion are given.

The main result of this paper gives criteria for extendibility of mappings defined on symmetric subsets of ∗-semigroups to positive definite ones. By specifying the mappings in question we obtain new solutions of relevant issues in harmonic analysis concerning truncations of some important multivariate moment problems, like complex, two-sided complex and multidimensional trigonometric moment pr...

In classical mathematical morphology for scalar images, the natural ordering of grey levels is used to define the erosion/dilation and the derived operators. Various operators can be sequentially applied to the resulting images always using the same ordering. In this paper we propose to consider the result of a prior transformation to define the imaginary part of a complex image, where the real...

There is a well-recognised need in diverse applications for reasoning with multiple, potentially inconsistent sources of information. One approach is to represent each source of information by a set of formulae and then use a merging operator to produce a set of formulae as output. A valuable range of model-based operators have been proposed that conform to interesting and intuitive properties....

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...

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...