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.
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Germany (DE)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://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.
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