A Sub-Riemannian Modular Approach for Diffeomorphic Deformations

We develop a generic framework to build large deformations from a combination of base modules. These modules constitute a dynamical dictionary to describe transformations. The method, built on a coherent sub-Riemannian framework, defines a metric on modular deformations and characterises optimal deformations as geodesics for this metric. We will present a generic way to build local affine transformations as deformation modules, and display examples.

[1]  Daniel Rueckert,et al.  Simultaneous Multi-scale Registration Using Large Deformation Diffeomorphic Metric Mapping , 2011, IEEE Transactions on Medical Imaging.

[2]  Nicholas Ayache,et al.  A Fast and Log-Euclidean Polyaffine Framework for Locally Linear Registration , 2009, Journal of Mathematical Imaging and Vision.

[3]  L. Younes,et al.  Statistics on diffeomorphisms via tangent space representations , 2004, NeuroImage.

[4]  Xavier Pennec,et al.  Higher-Order Momentum Distributions and Locally Affine LDDMM Registration , 2011, SIAM J. Imaging Sci..

[5]  Nicholas Ayache,et al.  Symmetric Log-Domain Diffeomorphic Registration: A Demons-Based Approach , 2008, MICCAI.

[6]  Daniel Rueckert,et al.  Diffeomorphic Registration Using B-Splines , 2006, MICCAI.

[7]  Andrei A. Agrachev,et al.  Two-dimensional almost-Riemannian structures with tangency points , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[8]  L. Younes,et al.  Diffeomorphometry and geodesic positioning systems for human anatomy. , 2014, Technology.

[9]  Sylvain Arguillere.  Géométrie sous-riemannienne en dimension infinie et applications à l'analyse mathématique des formes , 2014 .

[10]  Henry O. Jacobs.  Symmetries in LDDMM with higher order momentum distributions , 2013, ArXiv.

[11]  Guido Gerig,et al.  Optimal Data-Driven Sparse Parameterization of Diffeomorphisms for Population Analysis , 2011, IPMI.

[12]  U. Grenander.  Elements of Pattern Theory , 1996 .

[13]  Laurent Younes,et al.  Constrained Diffeomorphic Shape Evolution , 2012, Found. Comput. Math..

[14]  Peter Lorenzen,et al.  Structural and radiometric asymmetry in brain images , 2003, Medical Image Anal..

[15]  John Ashburner,et al.  A fast diffeomorphic image registration algorithm , 2007, NeuroImage.

[16]  L. Younes,et al.  On the metrics and euler-lagrange equations of computational anatomy. , 2002, Annual review of biomedical engineering.

[17]  Xavier Pennec,et al.  Capturing the multiscale anatomical shape variability with polyaffine transformation trees , 2012, Medical Image Anal..

[18]  Alain Trouvé,et al.  The Varifold Representation of Nonoriented Shapes for Diffeomorphic Registration , 2013, SIAM J. Imaging Sci..

[19]  Xavier Pennec,et al.  Sparse Multi-Scale Diffeomorphic Registration: The Kernel Bundle Framework , 2012, Journal of Mathematical Imaging and Vision.

[20]  Michael Brady,et al.  Adaptive Non-rigid Registration of Real Time 3D Ultrasound to Cardiovascular MR Images , 2007, IPMI.