@TechReport{Shekhovtsov-TR-2011-11,
  IS = { zkontrolovano 11 Jan 2012 },
  UPDATE  = { 2011-10-03 },
  author = {Alexander Shekhovtsov and Pushmeet Kohli and Carsten Rother},
  title = {Curvature Prior for {MRF}-based Segmentation and Shape Inpainting},
  institution = {Center for Machine Perception, K13133 FEE Czech Technical University},
  address = {Prague, Czech Republic},
  year = {2011},
  month = {September},
  type = {Research Report},
  number = {CTU--CMP--2011--11},
  issn = {1213-2365},
  pages = {17},
  figures = {16},
  psurl = {[curvature_patterns-2011-TR-ar.pdf]},
  project = {FP7-ICT-247870 NIFTi},
  annote = {Most image labeling problems such as segmentation and
    image reconstruction are fundamentally ill-posed and suffer from
    ambiguities and noise. Higher order image priors encode high level
    structural dependencies between pixels and are key to overcoming
    these problems. However, these priors in general lead to
    computationally intractable models. This paper addresses the
    problem of discovering compact representations of higher order
    priors which allow efficient inference. We propose a framework for
    solving this problem which uses a recently proposed representation
    of higher order functions where they are encoded as lower
    envelopes of linear functions. Maximum a Posterior inference on
    our learned models reduce to minimizing a pairwise function of
    discrete variables, which can be done approximately using standard
    methods. Although this is a primarily theoretical paper, we also
    demonstrate the practical effectiveness of our framework on the
    problem of learning a shape prior for image segmentation and
    reconstruction. We show that our framework can learn a compact
    representation that approximates a prior that encourages low
    curvature shapes. We evaluate the approximation accuracy, discuss
    properties of the trained model, and show various results for
    shape inpainting and image segmentation.},
  keywords = {curvature, segmentation, MRF, shape-inpainting, 
    higher order terms, patterns, field of experts},
}