具有非负空间相关参数的高阶Ambrosio–Tortorelli格式

IF 1.3 3区数学 Q1 MATHEMATICS

Advances in Calculus of Variations Pub Date : 2023-06-27 DOI:10.1515/acv-2021-0071

Irene Fonseca, Pan Liu, Xin Yang Lu

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引用次数: 0

摘要

摘要研究了具有加权底层度量的Ambrosio–Tortorelli近似格式。结果表明，它Γ-收敛于Mumford–Shah图像分割函数，这取决于权重ωd x｛\omega\，dx｝，其中ω是有界变化的特殊函数，以及它在跳跃处的值。

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

Abstract The 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 weight ω ⁢ d ⁢ x {\omega\,dx} , where ω is a special function of bounded variation, and on its values at the jumps.

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来源期刊

Advances in Calculus of Variations MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

3.90

自引率

5.90%

发文量

审稿时长

>12 weeks

期刊介绍： Advances in Calculus of Variations publishes high quality original research focusing on that part of calculus of variation and related applications which combines tools and methods from partial differential equations with geometrical techniques.