Journal of Mathematical Imaging and Vision

, Volume 35, Issue 1, pp 1–22 | Cite as

Multiphase Image Segmentation and Modulation Recovery Based on Shape and Topological Sensitivity

  • M. Hintermüller
  • A. Laurain


Topological sensitivity analysis is performed for the piecewise constant Mumford-Shah functional. Topological and shape derivatives are combined in order to derive an algorithm for image segmentation with fully automatized initialization. Segmentation of 2D and 3D data is presented. Further, a generalized Mumford-Shah functional is proposed and numerically investigated for the segmentation of images modulated due to, e.g., coil sensitivities.


Image processing k-means clustering Modulation recovery Mumford-Shah functional Piecewise constant reconstruction Segmentation Shape and topological sensitivity 


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© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Humboldt-Universität zu BerlinBerlinGermany
  2. 2.Department of Mathematics and Scientific ComputingUniversity of GrazGrazAustria

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