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