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

Abstract : 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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https://hal.archives-ouvertes.fr/hal-00918723
Contributor : Maïtine Bergounioux Connect in order to contact the contributor
Submitted on : Monday, July 7, 2014 - 5:53:59 PM
Last modification on : Tuesday, October 12, 2021 - 5:20:12 PM
Long-term archiving on: : Tuesday, April 11, 2017 - 10:21:00 AM

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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, Springer Verlag, 2015, pp xx. ⟨10.1007/s10440-014-0002-1⟩. ⟨hal-00918723v2⟩

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