Second-order edge-penalization in the ambrosio-tortorelli functional

Burger M, Esposito T, Zeppieri CI (2015)


Publication Language: English

Publication Type: Journal article

Publication year: 2015

Journal

Publisher: Society for Industrial and Applied Mathematics Publications

Book Volume: 13

Pages Range: 1354-1389

Issue: 4

DOI: 10.1137/15M1020848

Abstract

We propose and study two variants of the Ambrosio-Tortorelli functional where the first-order penalization of the edge variable v is replaced by a second-order term depending on the Hessian or on the Laplacian of v, respectively. We show that both the variants above provide an elliptic approximation of the Mumford-Shah functional in the sense of A-convergence. In particular the variant with the Laplacian penalization can be implemented numerically without any difficulties compared to the standard Ambrosio-Tortorelli functional. The computational results indicate several additional advantages. First of all, the diffuse approximation of the edge contours appears smoother and clearer for the minimizers of the second-order functional. Moreover, the convergence of alternating minimization algorithms seems improved for the new functional. We also illustrate the findings with several computational results.

Authors with CRIS profile

Involved external institutions

How to cite

APA:

Burger, M., Esposito, T., & Zeppieri, C.I. (2015). Second-order edge-penalization in the ambrosio-tortorelli functional. Multiscale Modeling & Simulation, 13, 1354-1389. https://dx.doi.org/10.1137/15M1020848

MLA:

Burger, Martin, T. Esposito, and C. I. Zeppieri. "Second-order edge-penalization in the ambrosio-tortorelli functional." Multiscale Modeling & Simulation 13 (2015): 1354-1389.

BibTeX: Download