Image Segmentation by Variational Methods: Mumford and Shah Functional and the Discrete Approximations

@article{Chambolle1995ImageSB,
  title={Image Segmentation by Variational Methods: Mumford and Shah Functional and the Discrete Approximations},
  author={Antonin Chambolle},
  journal={SIAM Journal of Applied Mathematics},
  year={1995},
  volume={55},
  pages={827-863}
}
Abstract. In this paper we discuss the links between Mumford and Shah’s variational problem for (signal and) image segmentation, based on an energy functional of a continuous grey-level function, and the numerical algorithms proposed to solve it. These numerical approaches are based on a discrete functional. We recall that, in one dimension, this discrete functional is asymptotically equivalent to the continuous functional. This can be summarized in a F-convergence result. We show that the same… CONTINUE READING

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