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Image segmentation with a finite element method. (English) Zbl 0947.65075

The author presents a discretized version of the Mumford-Shah functional for image segmentation [cf. D. Mumford and J. Shah, Commun. Pure Appl. Math. 42, No. 5, 577-685 (1989; Zbl 0691.49036)] based on the finite element method and proves the \(\Gamma\)-convergence. He proves also the convergence of the minimum value and minimizers of the discretized functional to that of the original functional, respectively. Finally, he presents some numerial results computed from both artificial and real images.

MSC:

65K10 Numerical optimization and variational techniques
68U10 Computing methodologies for image processing
49J45 Methods involving semicontinuity and convergence; relaxation
49M15 Newton-type methods

Citations:

Zbl 0691.49036
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