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

Maïtine Bergounioux (1) , David Vicente (1)

1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans

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.

Mots clés: Variational method; Mumford-Shah; segmentation

Domaines: Optimisation et contrôle [math.OC]

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⟩