Abstract. We study some factorisation and dilation properties of completely positive maps on noncommutative L-spaces. We show that Akcoglu’s dilation theorem for positive contractions on classical (= commutative) L-spaces has no reasonable analog in the noncommutative setting. Our study relies on non symmetric analogs of Pisier’s operator space valued noncommutative L-spaces that we investigate...

We present a novel framework for learning morphological operators using counter-harmonic mean. It combines concepts from morphology and convolutional neural networks. A thorough experimental validation analyzes basic morphological operators dilation and erosion, opening and closing, as well as the much more complex top-hat transform, for which we report a real-world application from the steel i...

In this paper, classified and comparative study of edge detection algorithms are presented. Experimental results prove that Boie-Cox, ShenCastan and Canny operators are better than Laplacian of Gaussian (LOG), while LOG is better than Prewitt and Sobel in case of noisy image. Subjective and objective methods are used to evaluate the different edge operators. The morphological filter is more imp...

and the corresponding inversion formula analyze the frequency content of f . Underlying many finer decompositions into simpler pieces are the fundamental invariance properties of R and the corresponding operators. For harmonic analysis on R these are the translations t → t+x and the dilations t → at, where t, x ∈ R and a ∈ R. The corresponding operators are the translation operator Tx (2) Txf(t...

We propose a feasible laboratory interferometry experiment with matter waves in a gravitational potential caused by a pair of artificial field-generating masses. It will demonstrate that the presence of these masses (and, for moving atoms, time dilation) induces a phase shift, even if it does not cause any classical force. The phase shift is identical to that produced by the gravitational redsh...

Abstract. This article introduces the notion of consistent families (⇤)n 1 of Quantum Channels. These families correspond to simultaneous observation of di↵erent copies of a given quantum system. Here, we are primarily interested in the analysis of measurements connected with them. As usual, the measurement of a quantum system requires the construction of a classical dilation of the correspondi...

Mathematical morphology (MM) is a theory for spatial structure analysis that was established by introducing fundamental operators applied to two sets [1]. A set is processed by another one having a carefully selected shape and size, known as the structuring element (SE). In the context of image processing, the SE acts as a probe for extracting or suppressing specific structures of the image obj...

Bartovský, J. Hardware Architectures for Morphological Filters with Large Structuring Elements. University Paris-Est, University of West Bohemia. Directors: Mohamed Akil, Vjačeslav Georgiev. This thesis is focused on implementation of fundamental morphological filters in the dedicated hardware. The main objective of this thesis is to provide a programmable and efficient implementation of basic ...

We give here some of the basic properties of the classes ¡4>^|, {♦ !, 1 < r < 1, of dilation operators acting in rearrangement-invariant spaces I on the circle It is shown that to each space 3E there correspond two numbers i, V, called indices, which satisfy 0 < r¡ < g < 1; these numbers represent the rate of growth or decay of ||* || as r — + 1. By using the operators + to obtain estimates for...