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

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Autorinnen und Autoren: Burger M, Esposito T, Zeppieri CI
Zeitschrift: Multiscale Modeling & Simulation
Verlag: Society for Industrial and Applied Mathematics Publications
Jahr der Veröffentlichung: 2015
Band: 13
Seitenbereich: 1354-1389
ISSN: 1540-3459
Sprache: Englisch


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.

Einrichtungen weiterer Autorinnen und Autoren

Westfälische Wilhelms-Universität (WWU) Münster


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

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


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