Abstract
This paper deals with finite-difference approximations of Euler equations arising in the variational formulation of image segmentation problems. We illustrate how they can be defined by the following steps: (a) definition of the minimization problem for the Mumford–Shah functional (MSf), (b) definition of a sequence of functionals Γ-convergent to the MSf, and (c) definition and numerical solution of the Euler equations associated to the kth functional of the sequence. We define finite difference approximations of the Euler equations, the related solution algorithms, and we present applications to segmentation problems by using synthetic images. We discuss application results, and we mainly analyze computed discontinuity contours and convergence histories of method executions.
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Spitaleri, R.M., March, R. & Arena, D. Finite difference solution of Euler equations arising in variational image segmentation. Numerical Algorithms 21, 353–365 (1999). https://doi.org/10.1023/A:1019184724430
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DOI: https://doi.org/10.1023/A:1019184724430