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Analysis of gradient flow of a regularized Mumford-Shah functional for image segmentation and image inpainting

Xiaobing Feng, Andreas Prohl (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

This paper studies the gradient flow of a regularized Mumford-Shah functional proposed by Ambrosio and Tortorelli (1990, 1992) for image segmentation, and adopted by Esedoglu and Shen (2002) for image inpainting. It is shown that the gradient flow with L2 x L∞ initial data possesses a global weak solution, and it has a unique global in time strong solution, which has at most finite number of point singularities in the space-time, when the initial data are in H1 x H1 ∩ L∞. A family of fully...

Constructions of interpolation curves from given supporting elements. II

Josef Matušů, Josef Novák (1986)

Aplikace matematiky

This paper deals with the constructions of interpolation curves which pass through given supporting points (nodes) and touch supporting tangent vectors given at only some of these points or, as the case may be, at all these points. The mathematical kernel of these constructions is based on the Lienhard's interpolation method. Formulae for the curvature of plane and space interpolation curves are derived.

Data approximation using polyharmonic radial basis functions

Segeth, Karel (2021)

Programs and Algorithms of Numerical Mathematics

The paper is concerned with the approximation and interpolation employing polyharmonic splines in multivariate problems. The properties of approximants and interpolants based on these radial basis functions are shown. The methods of such data fitting are applied in practice to treat the problems of, e.g., geographic information systems, signal processing, etc. A simple 1D computational example is presented.

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