@inproceedings{18390,
  abstract     = {Symmetry and self-similarity is the cornerstone of Nature, exhibiting itself through the shapes of natural creations and ubiquitous laws of physics. Since many natural objects are symmetric, the absence of symmetry can often be an indication of some anomaly or abnormal behavior. Therefore, detection of asymmetries is important in numerous practical applications, including crystallography, medical imaging, and face recognition, to mention a few. Conversely, the assumption of underlying shape symmetry can facilitate solutions to many problems in shape reconstruction and analysis. Traditionally, symmetries are described as extrinsic geometric properties of the shape. While being adequate for rigid shapes, such a description is inappropriate for non-rigid ones. Extrinsic symmetry can be broken as a result of shape deformations, while its intrinsic symmetry is preserved. In this paper, we pose the problem of finding intrinsic symmetries of non-rigid shapes and propose an efficient method for their computation.},
  author       = {Raviv, Dan and Bronstein, Alexander and Bronstein, Michael M. and Kimmel, Ron},
  booktitle    = {11th International Conference on Computer Vision},
  isbn         = {9781424416301},
  issn         = {2380-7504},
  location     = {Rio de Janeiro, Brazil},
  publisher    = {IEEE},
  title        = {{Symmetries of non-rigid shapes}},
  doi          = {10.1109/iccv.2007.4409181},
  volume       = {72},
  year         = {2007},
}

@inproceedings{3182,
  abstract     = {In the work of the authors (2003), we showed that graph cuts can find hypersurfaces of globally minimal length (or area) under any Riemannian metric. Here we show that graph cuts on directed regular grids can approximate a significantly more general class of continuous non-symmetric metrics. Using submodularity condition (Boros and Hammer, 2002 and Kolmogorov and Zabih, 2004), we obtain a tight characterization of graph-representable metrics. Such "submodular" metrics have an elegant geometric interpretation via hypersurface functionals combining length/area and flux. Practically speaking, we attend 'geo-cuts' algorithm to a wider class of geometrically motivated hypersurface functionals and show how to globally optimize any combination of length/area and flux of a given vector field. The concept of flux was recently introduced into computer vision by Vasilevskiy and Siddiqi (2002) but it was mainly studied within variational framework so far. We are first to show that flux can be integrated into graph cuts as well. Combining geometric concepts of flux and length/area within the global optimization framework of graph cuts allows principled discrete segmentation models and advances the slate of the art for the graph cuts methods in vision. In particular we address the "shrinking" problem of graph cuts, improve segmentation of long thin objects, and introduce useful shape constraints.},
  author       = {Kolmogorov, Vladimir and Boykov, Yuri},
  booktitle    = {Proceedings of the Tenth IEEE International Conference on Computer Vision Volume 1},
  issn         = {2380-7504},
  location     = {NW Washington, DC, United States},
  pages        = {564 -- 571},
  publisher    = {IEEE},
  title        = {{What metrics can be approximated by geo cuts or global optimization of length area and flux}},
  doi          = {10.1109/ICCV.2005.252},
  volume       = {1},
  year         = {2005},
}