A Relaxation Result for an Inhomogeneous Functional Preserving Point-Like and Curve-Like Singularities in Image Processing

Aubert, Gilles; Graziani, Daniele

doi:10.1142/s0129167x12501200

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2014

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“…In this paper, we have decided to use a variational model. Such models have been investigated by Aubert and al [7,8,9,10,14] especially in the detection of points in 2D images. One important tool is the capacity theory [1].…”

Section: Introductionmentioning

confidence: 99%

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

Bergounioux

Vicente

2014

Acta Appl Math

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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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