Diffeomorphic Metric Landmark Mapping Using Stationary Velocity Field Parameterization

Yang, Xianfeng, Li, Yonghui, Reutens, David and Jiang, Tianzi (2015) Diffeomorphic Metric Landmark Mapping Using Stationary Velocity Field Parameterization. International Journal of Computer Vision, 115 2: 69-86. doi:10.1007/s11263-015-0802-4


Author Yang, Xianfeng
Li, Yonghui
Reutens, David
Jiang, Tianzi
Title Diffeomorphic Metric Landmark Mapping Using Stationary Velocity Field Parameterization
Journal name International Journal of Computer Vision   Check publisher's open access policy
ISSN 0920-5691
1573-1405
Publication date 2015-02-14
Year available 2015
Sub-type Article (original research)
DOI 10.1007/s11263-015-0802-4
Open Access Status
Volume 115
Issue 2
Start page 69
End page 86
Total pages 18
Place of publication New York, NY United States
Publisher Springer New York LLC
Collection year 2015
Language eng
Formatted 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.
Keyword Computational anatomy
Diffeomorphic metric mapping
Landmark matching
Metric approximation
Stationary parameterization
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: Queensland Brain Institute Publications
Official 2016 Collection
Centre for Advanced Imaging Publications
 
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