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Pré-Publication, Document De Travail Année : 2013

Parameter selection in a Mumford-Shah geometrical model for the detection of thin structures

Résumé

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) and write the problem as a bilevel problem. We focus on the lower level optimization problem and give existence, uniqueness and regularity results for the solution. 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.
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Dates et versions

hal-00918723 , version 1 (14-12-2013)
hal-00918723 , version 2 (07-07-2014)

Identifiants

  • HAL Id : hal-00918723 , version 1

Citer

Maïtine Bergounioux, David Vicente. Parameter selection in a Mumford-Shah geometrical model for the detection of thin structures. 2013. ⟨hal-00918723v1⟩
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