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Article Dans Une Revue Acta Applicandae Mathematicae Année : 2015

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)

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Maïtine Bergounioux, David Vicente. Parameter selection in a Mumford-Shah geometrical model for the detection of thin structures. Acta Applicandae Mathematicae, 2015, pp xx. ⟨10.1007/s10440-014-0002-1⟩. ⟨hal-00918723v2⟩
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