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On Total Variation Minimization and Surface Evolution Using Parametric Maximum Flows

On Total Variation Minimization and Surface Evolution Using Parametric Maximum Flows,10.1007/s11263-009-0238-9,International Journal of Computer Visio

On Total Variation Minimization and Surface Evolution Using Parametric Maximum Flows   (Citations: 15)
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In a recent paper Boykov et al. (LNCS, Vol. 3953, pp. 409–422, 2006) propose an approach for computing curve and surface evolution using a variational approach and the geo-cuts method of Boykov and Kolmogorov (International conference on computer vision, pp. 26–33, 2003). We recall in this paper how this is related to well-known approaches for mean curvature motion, introduced by Almgren et al. (SIAM Journal on Control and Optimization 31(2):387–438, 1993) and Luckhaus and Sturzenhecker (Calculus of Variations and Partial Differential Equations 3(2):253–271, 1995), and show how the corresponding problems can be solved with sub-pixel accuracy using Parametric Maximum Flow techniques. This provides interesting algorithms for computing crystalline curvature motion, possibly with a forcing term.
Journal: International Journal of Computer Vision - IJCV , vol. 84, no. 3, pp. 288-307, 2009
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    • ...This is related to the work of [3] and [6], where gradient flows of interphases were studied in an integral framework,incasetheoriginalenergyfunctionalisgraphrepresentableinthediscretesetting.Thispaperdiffersintwomaindirections: we study images instead of interphases, and we do not require the original energy functional to be graph representable, i.e., we allow more complicated energy functionals involving ...

    Egil Baeet al. Graph Cuts for Curvature Based Image Denoising

    • ...We are of course aware of max-flow/min-cut type algorithms, for instance the one in [16]...

    Sylvain Durandet al. Multiplicative Noise Removal Using L1 Fidelity on Frame Coefficients

    • ...For these cases we refer to [36] for the associated graph constructions...
    • ...At this point we have to mention another paper on the subject which we came across during the resubmission phase of this paper. In [36], the priors of the form...
    • ...The authors of [36] also claim, without proof, that the approach described in [18] could be applied for minimization of energies with such priors...

    Mehmet Haydar Karcíet al. Minimization of Monotonically Levelable Higher Order MRF Energies via ...

    • ... approximation via locally quadratic functionals as in the work of Vese et al. [2,37]; (4) iterative thresholding algorithms based on projections onto convex sets as in the work of Chambolle [10] as well as in the work of Combettes and Wajs [15] and Daubechies et al. [19]; (5) iterative minimization of the Bregman distance as in the work of Osher et al. [32] (also notice the very recent Bregman split approach [27]); (6) graph cuts [11,16] ...
    • ...We expect that the use of other algorithms [11,16,27,32,39] may change quantitatively the results but not qualitatively...

    Massimo Fornasieret al. A convergent overlapping domain decomposition method for total variati...

    • ...Finally, such motions can be compared with others where the interplay between time and space discretization is crucial (as in [8, 10, 17])...

    Andrea Braideset al. Motion and Pinning of Discrete Interfaces

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