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Inter and Intra-modal Deformable Registration: Continuous Deformations Meet Efficient Optimal Linear Programming

  • Ben Glocker
  • Nikos Komodakis
  • Nikos Paragios
  • Georgios Tziritas
  • Nassir Navab
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4584)

Abstract

In this paper we propose a novel non-rigid volume registration based on discrete labeling and linear programming. The proposed framework reformulates registration as a minimal path extraction in a weighted graph. The space of solutions is represented using a set of a labels which are assigned to predefined displacements. The graph topology corresponds to a superimposed regular grid onto the volume. Links between neighborhood control points introduce smoothness, while links between the graph nodes and the labels (end-nodes) measure the cost induced to the objective function through the selection of a particular deformation for a given control point once projected to the entire volume domain. Higher order polynomials are used to express the volume deformation from the ones of the control points. Efficient linear programming that can guarantee the optimal solution up to (a user-defined) bound is considered to recover the optimal registration parameters. Therefore, the method is gradient free, can encode various similarity metrics (simple changes on the graph construction), can guarantee a globally sub-optimal solution and is computational tractable. Experimental validation using simulated data with known deformation, as well as manually segmented data demonstrate the extreme potentials of our approach.

Keywords

Discrete Optimization Deformable Registration Linear Programming 

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Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Ben Glocker
    • 1
    • 2
  • Nikos Komodakis
    • 1
    • 3
  • Nikos Paragios
    • 1
  • Georgios Tziritas
    • 3
  • Nassir Navab
    • 2
  1. 1.GALEN Group, Laboratoire de Mathématiques Appliquées aux Systèmes, Ecole Centrale de Paris 
  2. 2.Chair for Computer Aided Medical Procedures & Augmented Reality, Technische Universität München 
  3. 3.Computer Science Department, University of Crete 

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