The concept of strictness of morphological operators is discussed, and it is shown that the ordinary morphological operators have extreme strictness which leads to sensitivity to noise and digital artifacts. Based on this observation new morphological operators that generalize the ordinary morphological operators, are de ned. The generalized operators have controllable strictness and so excessi...

The aim of belief merging is to merge conflicting information while preserving as much of it as possible. Most proposals in the literature work with knowledge bases expressed in propositional logic. We propose a new framework for merging knowledge bases expressed in (subsets of) first-order logic. Dilation operators (a concept originally introduced by Bloch and Lang) are employed and developed,...

PURPOSE To evaluate the intra- and interobserver reproducibility of peripapillary retinal nerve fiber layer (RNFL) thickness measurements before and after pupil dilation using spectral-domain optical coherence tomography (SD-OCT). METHODS In this observational case series, 44 eyes of 44 healthy subjects were scanned by two trained operators on the same day, using Cirrus SD-OCT (Carl Zeiss Med...

Let E be a product system of C-correspondences over Nr 0 . Some sufficient conditions for the existence of a not necessarily regular isometric dilation of a completely contractive representation of E are established and difference between regular and -regular dilations discussed. It is in particular shown that a minimal isometric dilation is -regular if and only if it is doubly commuting. The c...

The classical paradigm of Calderon and Zygmund provides a set of techniques invariant under translations and dilations that allow to prove estimates for operators acting on function spaces on IR. We focus on the real line as underlying space and further concentrate on estimates for operators that are themselves invariant under translation and dilation. The only such operators bounded on L(R) ar...

In this paper, maximal dissipative fourth order operators with equal deficiency indices are investigated. We construct a self adjoint dilation of such operators. We also construct a functional model of the maximal dissipative operator which based on the method of Pavlov and define its characteristic function. We prove theorems on the completeness of the system of eigenvalues and eigenvectors of...

In some recent works on scattering theory [KR1, KR2, KR3, KR5], it was conjectured and then proved that, modulo a compact term, the wave operators for Schrödinger systems can be rewritten as a product of a function of the dilation operator A and a function of the Laplacian −∆. Furthermore, the functions of the dilation operator are rather insensitive to a particular choice of the perturbed oper...

The application of mathematical morphology to image processing and analysis has initiated a new approach for solving a number of problems in the image enhancement field. So, we have used morphological operators to detect and extract the background of images. Various operators used are erosion, dilation, opening and closing. After the background is extracted, contrast of bad lightning image is i...

We investigate how common binary mathematical morphology operators can be adapted so that the size of the structuring element can vary across the image pixels. We show that when the structuring elements are balls of a metric, locally adaptable erosion and dilation can be efficiently implemented as a variant of distance transformation algorithms. Opening and closing are obtained by a local thres...

A traditional wavelet is a special case of a vector in a separable Hilbert space that generates a basis under the action of a system of unitary operators defined in terms of translation and dilation operations. A Coxeter/fractal-surface wavelet is obtained by defining fractal surfaces on foldable figures, which tesselate the embedding space by reflections in their bounding hyperplanes instead o...