Higher order Ambrosio–Tortorelli scheme with non-negative spatially dependent parameters-Reference-Cited by-同舟云学术

Higher order Ambrosio–Tortorelli scheme with non-negative spatially dependent parameters

Published:2023-06-27 Issue:4 Volume:16 Page:885-902
ISSN:1864-8258
Container-title:Advances in Calculus of Variations
language:en
Short-container-title:

Author:

Fonseca Irene¹,Liu Pan²,Lu Xin Yang³

Affiliation:

1. Department of Mathematics , Carnegie Mellon University , 5000 Forbes Avenue , Pittsburgh , PA 15213 , USA

2. Department of Radiology , First Medical Center of Chinese PLA General Hospital , Beijing 100853 , P. R. China

3. Department of Mathematical Sciences , Lakehead University , 955 Oliver Road , Thunder Bay , ON , Canada

Abstract

AbstractThe Ambrosio–Tortorelli approximation scheme with weighted underlying metric is investigated. It is shown that it Γ-converges to a Mumford–Shah image segmentation functional depending on the weightω⁢d⁢x

{\omega\,dx}

, where ω is a special function of bounded variation, and on its values at the jumps.

Funder

Division of Mathematical Sciences

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/acv-2021-0071/pdf

Reference19 articles.

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2. L. Ambrosio, On the lower semicontinuity of quasiconvex integrals in SBV ⁢ ( Ω , 𝐑 k ) {\rm SBV}(\Omega,{\mathbf{R}}^{k}) , Nonlinear Anal. 23 (1994), no. 3, 405–425.

3. L. Ambrosio, N. Fusco and D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems, Oxford Math. Monogr., The Clarendon, New York, 2000.

4. L. Ambrosio and V. M. Tortorelli, Approximation of functionals depending on jumps by elliptic functionals via Γ-convergence, Comm. Pure Appl. Math. 43 (1990), no. 8, 999–1036.

5. H. Attouch, Variational Convergence for Functions and Operators, Appl. Math. Ser. Pitman, Boston, 1984.