@inproceedings{3170,
  abstract     = {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.},
  author       = {Boykov, Yuri and Kolmogorov, Vladimir},
  isbn         = {0769519504},
  location     = {Nice, France},
  pages        = {26 -- 33},
  publisher    = {IEEE},
  title        = {{Computing geodesics and minimal surfaces via graph cuts}},
  doi          = {10.1109/ICCV.2003.1238310},
  volume       = {1},
  year         = {2008},
}

@inproceedings{3174,
  abstract     = {We address visual correspondence problems without assuming that scene points have similar intensities in different views. This situation is common, usually due to non-lambertian scenes or to differences between cameras. We use maximization of mutual information, a powerful technique for registering images that requires no a priori model of the relationship between scene intensities in different views. However, it has proven difficult to use mutual information to compute dense visual correspondence. Comparing fixed-size windows via mutual information suffers from the well-known problems of fixed windows, namely poor performance at discontinuities and in low-texture regions. In this paper, we show how to compute visual correspondence using mutual information without suffering from these problems. Using 'a simple approximation, mutual information can be incorporated into the standard energy minimization framework used in early vision. The energy can then be efficiently minimized using graph cuts, which preserve discontinuities and handle low-texture regions. The resulting algorithm combines the accurate disparity maps that come from graph cuts with the tolerance for intensity changes that comes from mutual information.},
  author       = {Kim, Junhwan and Kolmogorov, Vladimir and Zabih, Ramin},
  booktitle    = {Proceedings Ninth International Conference on Computer Vision},
  isbn         = {0769519504},
  location     = {Nice, France},
  pages        = {1033 -- 1040},
  publisher    = {IEEE},
  title        = {{Visual correspondence using energy minimization and mutual information}},
  doi          = {10.1109/ICCV.2003.1238463},
  volume       = {2},
  year         = {2008},
}