Abstract
We propose the minimization of a nonquadratic functional or, equivalently, a nonlinear diffusion model to smooth noisy image functionsg:Ω ⊂R n →R while preserving significant transitions of the data. The model is chosen such that important properties of the conventional quadratic-functional approach still hold: (1) existence of a unique solution continuously depending on the datag and (2) stability of approximations using the standard finite-element method. Relations with other global approaches for the segmentation of image data are discussed. Numerical experiments with real data illustrate this approach.
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This work was supported by the ESPRIT project SUBSYM.
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Schnörr, C. Unique reconstruction of piecewise-smooth images by minimizing strictly convex nonquadratic functionals. J Math Imaging Vis 4, 189–198 (1994). https://doi.org/10.1007/BF01249896
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DOI: https://doi.org/10.1007/BF01249896