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

Journal article

Publication Details

Author(s): Burger M, Esposito T, Zeppieri CI
Journal: Multiscale Modeling & Simulation
Publisher: Society for Industrial and Applied Mathematics Publications
Publication year: 2015
Volume: 13
Pages range: 1354-1389
ISSN: 1540-3459
Language: English


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.

External institutions with authors

Westfälische Wilhelms-Universität (WWU) Münster

How to cite

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.


Last updated on 2019-22-08 at 14:50