Acta Applicandae Mathematicae

, Volume 141, Issue 1, pp 17–47 | Cite as

Parameter Selection in a Mumford–Shah Geometrical Model for the Detection of Thin Structures

  • Maïtine BergouniouxEmail author
  • David Vicente


We present a variational model to perform the segmentation of thin structures in MRI images (namely codimension 1 objects). It is based on the classical Mumford–Shah functional and we have added geometrical priors as constraints. We precisely describe the structure model (that we call tubes). We give existence, uniqueness and regularity results for the solution to the optimization problem. The keypoint is the fact that 2D/3D problems are equivalent to 1D ones. This gives hints to perform an automatic parameter tuning for numerical purpose.


Variational method Segmentation Thin structures Mumford–Shah 


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Laboratory MAPMO, CNRS, UMR 7349, Fédération Denis Poisson, FR 2964, Bâtiment de Mathématiques, BP 6759University of OrléansOrléans Cedex 2France

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