Home
Uni-Logo
 

On the Statistical Interpretation of the Piecewise Smooth Mumford-Shah Functional

Thomas Brox, D. Cremers
International Conference on Scale Space and Variational Methods in Computer Vision (SSVM), Springer, LNCS, Vol.4485: 203-213, May 2007
Abstract: In region-based image segmentation, two models dominate the field: the Mumford-Shah functional and statistical approaches based on Bayesian inference. Whereas the latter allow for numerous ways to describe the statistics of intensities in regions, the first includes spatially smooth approximations. In this paper, we show that the piecewise smooth Mumford-Shah functional is a first order approximation of Bayesian a-posteriori maximization where region statistics are computed in local windows. This equivalence not only allows for a statistical interpretation of the full Mumford-Shah functional. Inspired by the Bayesian model, it also offers to formulate an extended Mumford-Shah functional that takes the variance of the data into account.


Other associated files : brox_ssvm07_seg.pdf [331KB]  

Images and movies

 

BibTex reference

@InProceedings{Bro07i,
  author       = "T. Brox and D. Cremers",
  title        = "On the Statistical Interpretation of the Piecewise Smooth Mumford-Shah Functional",
  booktitle    = "International Conference on Scale Space and Variational Methods in Computer Vision (SSVM)",
  series       = "Lecture Notes in Computer Science",
  volume       = "4485",
  pages        = "203-213",
  month        = "May",
  year         = "2007",
  publisher    = "Springer",
  url          = "http://lmbweb.informatik.uni-freiburg.de/Publications/2007/Bro07i"
}

Other publications in the database