Images contain various types of useful information that should be extracted whenever required and this information may be in the form of text present in image. Extraction of this information involves detection, localization, extraction, enhancement and recognition of the text from the given image. Mathematical morphology is the foundation of morphological image processing, which consists of a s...

We establish a hierarchy of weighted majorization relations for the singularities of generalized Lamé equations and the zeros of their Van Vleck and Heine-Stieltjes polynomials as well as for multiparameter spectral polynomials of higher Lamé operators. These relations translate into natural dilation and subordination properties in the Choquet order for certain probability measures associated w...

In this paper we discuss how biresiduations provide a unifying paradigm for fuzzy formal concept analysis and mathematical morphology. In particular we provide constructions of morphological operators such as dilation and erosion within the framework of convolution algebras of action networks (also known as small covariant categories) over join complete semirings. This unifies and generalizes p...

Several tasks in artificial intelligence require to be able to find models about knowledge dynamics. They include belief revision, fusion and belief merging, and abduction. In this paper we exploit the algebraic framework of mathematical morphology in the context of propositional logic, and define operations such as dilation or erosion of a set of formulas. We derive concrete operators, based o...

In this paper we consider the conformal group of the unit sphere S, the proper Lorentz group Spin(1, n), for the study of spherical continuous wavelet transforms. The parameter space is determined by the factorization of the gyrogroup of the unit ball by an appropriate gyro-subgroup. We study two families of sections that give rise to anisotropic conformal dilation operators for the unit sphere...

Abstract Using probabilistic tools, we prove that any weak* continuous semigroup $(T_t)_{t \geqslant 0}$ of self-adjoint unital completely positive measurable Schur multipliers acting on the space $\mathrm {B}({\mathrm {L}}^2(X))$ bounded operators Hilbert ${\mathrm {L}}^2(X)$ , where X is a suitable measure space, can be dilated by group Markov $*$ -automorphisms bigger von Neumann algebra. We...

A numerical index is introduced for semigroups of completely positive maps of B(H) which generalizes the index of E0-semigroups. It is shown that the index of a unital completely positive semigroup agrees with the index of its dilation to an E0-semigroup, provided that the dilation is minimal. Introduction. We introduce a numerical index for semigroups P = {Pt : t ≥ 0} of normal completely posi...

This paper is devoted to the multivariable $$H^\infty $$ functional calculus associated with a finite commuting family of sectorial operators on Banach space. First we prove that if $$(A_1,\ldots , A_d)$$ such family, $$A_k$$ R-sectorial R-type $$\omega _k\in (0,\pi )$$ $$k=1,\ldots ,d$$ and admits bounded (\Sigma _{\theta _1}\times \cdots \times \Sigma _d})$$ joint for some $$\theta (\omega _k...