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

被引：3

作者：

Bergounioux, Maitine ^{[1
]}

Vicente, David ^{[1
]}

机构：

[1] Univ Orleans, CNRS, UMR 7349, Lab MAPMO,FR 2964, F-45067 Orleans 2, France

来源：

ACTA APPLICANDAE MATHEMATICAE | 2016年 / 141卷 / 01期

关键词：

Variational method; Segmentation; Thin structures; Mumford-Shah; POINTS;

D O I：

10.1007/s10440-014-0002-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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). We give existence, uniqueness and regularity results for the solution to the optimization problem. 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.

引用

页码：17 / 47

页数：31

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