Convergence results for critical points of the one-dimensional Ambrosio-Tortorelli functional with fidelity term. (English) Zbl 1190.49048

Le, Nam Q.

Adv. Differ. Equ. 15, No. 3-4, 255-282 (2010).

Summary: We show that critical points of the one-dimensional Ambrosio-Tortorelli functional with fidelity term converge to those of the corresponding Mumford-Shah functional, a famous model for image segmentation. Equipartition and convergence of the energy-density are also derived.

MSC:

49Q20	Variational problems in a geometric measure-theoretic setting
49J45	Methods involving semicontinuity and convergence; relaxation
35B38	Critical points of functionals in context of PDEs (e.g., energy functionals)
35J60	Nonlinear elliptic equations
94A08	Image processing (compression, reconstruction, etc.) in information and communication theory

Keywords:

one-dimensional Ambrosio-Tortorelli functional; Mumford-Shah functional; image segmentation; energy-density