Bourdin, Blaise Image segmentation with a finite element method. (English) Zbl 0947.65075 M2AN, Math. Model. Numer. Anal. 33, No. 2, 229-244 (1999). 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. Reviewer: Dinh Nho Hào (Frankfurt) Cited in 34 Documents MSC: 65K10 Numerical optimization and variational techniques 68U10 Computing methodologies for image processing 49J45 Methods involving semicontinuity and convergence; relaxation 49M15 Newton-type methods Keywords:Mumford-Shah functional; image segmentation; finite element method; convergence; numerial results Citations:Zbl 0691.49036 PDFBibTeX XMLCite \textit{B. Bourdin}, M2AN, Math. Model. Numer. Anal. 33, No. 2, 229--244 (1999; Zbl 0947.65075) Full Text: DOI EuDML Link