Geodesic active contours and graph cuts are two standard image segmentation techniques. We introduce a new segmentation method combining some of their benefits. Our main intuition is that any cut on a graph embedded in some continuous space can be interpreted as a contour (in 2D) or a surface (in 3D). We show how to build a grid graph and set its edge weights so that the cost of cuts is arbitrarily close to the length (area) of the corresponding contours (surfaces) for any anisotropic Riemannian metric. There are two interesting consequences of this technical result. First, graph cut algorithms can be used to find globally minimum geodesic contours (minimal surfaces in 3D) under arbitrary Riemannian metric for a given set of boundary conditions. Second, we show how to minimize metrication artifacts in existing graph-cut based methods in vision. Theoretically speaking, our work provides an interesting link between several branches of mathematics -differential geometry, integral geometry, and combinatorial optimization. The main technical problem is solved using Cauchy-Crofton formula from integral geometry.


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    Title :

    Computing geodesics and minimal surfaces via graph cuts


    Contributors:
    Boykov, (author) / Kolmogorov, (author)


    Publication date :

    2003-01-01


    Size :

    509813 byte




    Type of media :

    Conference paper


    Type of material :

    Electronic Resource


    Language :

    English



    Computing Geodesics and Minimal Surfaces via Graph Cuts

    Boykov, Y. / Kolmogorov, V. / IEEE | British Library Conference Proceedings | 2003



    Computing Visual Correspondence with Occlusions via Graph Cuts

    Kolmogorov, V. / Zabih, R. / IEEE | British Library Conference Proceedings | 2001