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Journal of Mathematical Imaging and Vision

, Volume 59, Issue 3, pp 432–455 | Cite as

A Non-local Topology-Preserving Segmentation-Guided Registration Model

  • Noémie Debroux
  • Solène Ozeré
  • Carole Le Guyader
Article

Abstract

In this paper, we address the issue of designing a theoretically well-motivated segmentation-guided registration method capable of handling large and smooth deformations. The shapes to be matched are viewed as hyperelastic materials and more precisely as Saint Venant–Kirchhoff ones and are implicitly modeled by level set functions. These are driven in order to minimize a functional containing both a nonlinear-elasticity-based regularizer prescribing the nature of the deformation, and a criterion that forces the evolving shape to match intermediate topology-preserving segmentation results. Theoretical results encompassing existence of minimizers, existence of a weak viscosity solution of the related evolution problem and asymptotic results are given. The study is then complemented by the derivation of the discrete counterparts of the asymptotic results provided in the continuous domain. Both a pure quadratic penalization method and an augmented Lagrangian technique (involving a related dual problem) are investigated with convergence results.

Keywords

Topology-preserving segmentation Registration Nonlinear elasticity Saint Venant–Kirchhoff material Quasi-convexity Relaxed problem Asymptotic behavior Weak viscosity solutions Nonconvex programming Augmented Lagrangian Duality with zero gap Supergradient method 

Notes

Acknowledgements

The project is co-financed by the European Union with the European regional development fund (ERDF, HN0002137) and by the Normandie Regional Council via the M2NUM project. The authors would like to thank Dr. Caroline Petitjean (LITIS, Université de Rouen, France) for providing the cardiac cycle MRI images.

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Laboratoire de MathématiquesNormandie Université, INSA de RouenSaint-Etienne-du-Rouvray CedexFrance

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