International Journal of Computer Vision

, Volume 115, Issue 2, pp 69–86 | Cite as

Diffeomorphic Metric Landmark Mapping Using Stationary Velocity Field Parameterization

  • Xianfeng Yang
  • Yonghui Li
  • David Reutens
  • Tianzi Jiang
Article
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Accepted:

Abstract

Large deformation diffeomorphic metric mapping (LDDMM) has been shown as an effective computational paradigm to measure anatomical variability. However, its time-varying vector field parameterization of diffeomorphism flow leads to computationally expensive implementation, as well as some theoretical issues in metric based shape analysis, e.g. high order metric approximation via Baker–Campbell–Hausdorff (BCH) formula. To address these problems, we study the role of stationary vector field parameterization in context of LDDMM. Under this setting registration is formulated as finding the Lie group exponential path with minimal energy in Riemannian manifold of diffeomorphisms bringing two shapes together. Accurate derivation of Euler–Lagrange equation shows that optimal vector field for landmark matching is associated with singular momenta at landmark trajectories in whole time domain, and a new momentum optimization scheme is proposed to solve the variational problem. Length of group exponential path is also proposed as an alternative shape metric to geodesic distance, and pair-wise metrics among a population are computed through an approximation method via BCH formula which only needs registrations to a template. The proposed methods have been tested on both synthesized data and real database. Compared to non-stationary parameterization, this method can achieve comparable registration accuracy in significantly reduced time. Second order metric approximation by this method also improves significantly over first order, which can not be achieved by non-stationary parameterization. Correlation between the two shape metrics is also investigated, and their statistical power in clinical study compared.

Keywords

Computational anatomy Diffeomorphic metric mapping  Stationary parameterization  Landmark matching Metric approximation 
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Notes

Acknowledgments

This work was partially supported by the National Key Basic Research and Development Program (973) (Grant No. 2011CB707800), the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB02030300), and the National Natural Science Foundation of China (Grant No. 91132301). We also thank Dr. Anqi Qiu for thoughtful discussions on LDDMM.

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Xianfeng Yang
    • 1
    • 2
  • Yonghui Li
    • 1
  • David Reutens
    • 2
  • Tianzi Jiang
    • 1
    • 2
    • 3
    • 4
    • 5
  1. 1.The Queensland Brain InstituteThe University of QueenslandBrisbaneAustralia
  2. 2.The Centre for Advanced ImagingThe University of QueenslandBrisbaneAustralia
  3. 3.CAS Center for Excellence in Brain Science, Institute of AutomationChinese Academy of SciencesBeijingChina
  4. 4.Brainnetome Center, Institute of AutomationChinese Academy of SciencesBeijingChina
  5. 5.National Laboratory of Pattern Recognition, Institute of AutomationChinese Academy of SciencesBeijingChina

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