Non-commutative versions of Arveson’s curvature invariant and Euler characteristic for a commuting n-tuple of operators are introduced. The noncommutative curvature invariant is sensitive enough to determine if an ntuple is free. In general both invariants can be thought of as measuring the freeness or curvature of an n-tuple. The connection with dilation theory provides motivation and exhibits...

Junior Barrera Departamento de Ciência da Computação Instituto de Matemática e Estatı́stica— Universidade de São Paulo Rua do Matão, 1010 05508-900 São Paulo, Brazil E-mail: [email protected] Abstract. Iterating (composing) a sequence of window operators results in an operator defined over the window determined by the dilation of the component windows. Although a statistically designed iterative ope...

there are many different ways to subdivide the spectrum of a bounded linear operator; some of them aremotivated by applications to physics (in particular, quantum mechanics). in this study, the relationship betweenthe subdivisions of spectrum which are not required to be disjoint and goldberg's classification are given.moreover, these subdivisions for some summability methods are studied.

A new construction of a directional continuous wavelet analysis on the sphere is derived herein. We adopt the harmonic scaling idea for the spherical dilation operator recently proposed by Sanz et al. [1] but extend the analysis to a more general directional framework. Directional wavelets are a powerful extension that allow one to also probe oriented structure in the analysed function. Our sph...

Wavelets, known to be useful in non-linear multi-scale processes and in multi-resolution analysis, are shown to have a q-deformed algebraic structure. The translation and dilation operators of the theory associate with any scaling equation a non-linear, two parameter algebra. This structure can be mapped onto the quantum group suq(2) in one limit, and approaches a Fourier series generating alge...

This paper proposes an approach for mathematical morphology operators whose structuring element can locally adapt its orientation across the pixels of the image. The orientation at each pixel is extracted by means of a diffusion process of the average squared gradient field. The resulting vector field, the average squared gradient vector flow, extends the orientation information from the edges ...

The transition method for image binarization is based on the concept of t-transition pixels, a generalization of edge pixels, and t-transition sets. We introduce a novel unsupervised thresholding for unimodal histograms to estimate the transition sets. We also present dilation and incidence transition operators to refine the transition set. Afterward, we propose the simple edge transition opera...

The smoothness property of refinable functions is an important issue in all multiresolution analysis and has a strong impact on applications of wavelets to image processing, geometric and numerical solutions of elliptic partial differential equations. The purpose of this paper is to characterize the smoothness properties of refinable functions with exponentially decaying masks and an isotropic ...

Medieval stained glass windows are a stylized artform that has not previously been thoroughly treated in the computer graphics literature. In this paper, we present an automated method for transforming an arbitrary image into a stained-glass version of that image. The key issues in designing a stained glass window are the tile boundaries and tile colors. We use erosion and dilation operators to...

Morphological operations are simple mathematical constructs, which have led to effective solution for many problems in image processing and computer vision. These solutions employ discrete operators and are applied to digitized images. The mathematics behind the morphological operators also exists in the continuous domain, the domain where the images came from. We observed that the discrete ope...