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Recent Development of the DML-CZ and Its Current State

Rákosník, Jiří (2011)

Towards a Digital Mathematics Library. Bertinoro, Italy, July 20-21st, 2011

The project DML-CZ: The Czech Digital Mathematics Library has been implemented since 2005 and in 2010 switched over to routine operation. This report describes progress, growth and usage of the DML-CZ, the experience from cooperation with content providers in the designed editorial workflow, some newly implemented features, adjustments of the workflow following from both the ongoing practical experience and the requirements of the advancing EuDML project, the general public acceptance and attendance...

Recognition of atherosclerotic plaques and their extended dimensioning with computerized tomography angiography imaging

Tomasz Markiewicz, Mirosław Dziekiewicz, Marek Maruszyński, Romana Bogusławska-Walecka, Wojciech Kozłowski (2014)

International Journal of Applied Mathematics and Computer Science

In this paper the authors raise the issue of automatic discrimination of atherosclerotic plaques within an artery lumen based on numerical and statistical thresholding of Computerized Tomography Angiographic (CTA) images and their advanced dimensioning as a support for preoperative vessel assessment. For the study, a set of tomograms of the aorta, as well as the ilio-femoral and femoral arteries were examined. In each case a sequence of about 130-480 images of the artery cutoff planes were analyzed...

Region of interest contrast measures

Václav Remeš, Michal Haindl (2018)

Kybernetika

A survey of local image contrast measures is presented and a new contrast measure for measuring the local contrast of regions of interest is proposed. The measures validation is based on the gradual objective contrast decreasing on medical test images in both grayscale and color. The performance of the eleven most frequented contrast measures is mutually compared and their robustness to different types of image degradation is analyzed. Since the contrast measures can be both global, regional and...

Segmentation of MRI data by means of nonlinear diffusion

Radomír Chabiniok, Radek Máca, Michal Beneš, Jaroslav Tintěra (2013)

Kybernetika

The article focuses on the application of the segmentation algorithm based on the numerical solution of the Allen-Cahn non-linear diffusion partial differential equation. This equation is related to the motion of curves by mean curvature. It exhibits several suitable mathematical properties including stable solution profile. This allows the user to follow accurately the position of the segmentation curve by bringing it quickly to the vicinity of the segmented object and by approaching the details...

Segmenting colour images on the basis of a fuzzy hierarchical approach.

Jesús Chamorro-Martínez, Daniel Sánchez, Belén Prados-Suárez, Elena Galán-Perales, M.ª Amparo Vila (2003)

Mathware and Soft Computing

In this paper we deal with two problems related to imprecision in colour image segmentation processes: to decide whether a set of pixels verify the property to be homogeneously coloured, and to represent the set of possible segmentations of an image at different precision levels. In order to solve the first problem we introduce a measure of distance between colours in the CIE L*a*b* space, that allows us to measure the degree of homogeneity of two pixels p and q on the basis of the maximum distance...

Self-avoiding walks on the lattice ℤ² with the 8-neighbourhood system

Andrzej Chydziński, Bogdan Smołka (2001)

Applicationes Mathematicae

This paper deals with the properties of self-avoiding walks defined on the lattice with the 8-neighbourhood system. We compute the number of walks, bridges and mean-square displacement for N=1 through 13 (N is the number of steps of the self-avoiding walk). We also estimate the connective constant and critical exponents, and study finite memory and generating functions. We show applications of this kind of walk. In addition, we compute upper bounds for the number of walks and the connective constant....

Stability and consistency of the semi-implicit co-volume scheme for regularized mean curvature flow equation in level set formulation

Angela Handlovičová, Karol Mikula (2008)

Applications of Mathematics

We show stability and consistency of the linear semi-implicit complementary volume numerical scheme for solving the regularized, in the sense of Evans and Spruck, mean curvature flow equation in the level set formulation. The numerical method is based on the finite volume methodology using the so-called complementary volumes to a finite element triangulation. The scheme gives the solution in an efficient and unconditionally stable way.

Symbol Declarations in Mathematical Writing

Wolska, Magdalena, Grigore, Mihai (2010)

Towards a Digital Mathematics Library. Paris, France, July 7-8th, 2010

We present three corpus-based studies on symbol declaration in mathematical writing. We focus on simple object denoting symbols which may be part of larger expressions. We look into whether the symbols are explicitly introduced into the discourse and whether the information on once interpreted symbols can be used to interpret structurally related symbols. Our goal is to support fine-grained semantic interpretation of simple and complex mathematical expressions. The results of our analysis empirically...

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