Computational anatomy: an emerging discipline
Quarterly of Applied Mathematics - Special issue on current and future challenges in the applications of mathematics
Intrinsic Statistics on Riemannian Manifolds: Basic Tools for Geometric Measurements
Journal of Mathematical Imaging and Vision
Symmetric Log-Domain Diffeomorphic Registration: A Demons-Based Approach
MICCAI '08 Proceedings of the 11th international conference on Medical Image Computing and Computer-Assisted Intervention - Part I
Log-domain diffeomorphic registration of diffusion tensor images
WBIR'10 Proceedings of the 4th international conference on Biomedical image registration
Endowing canonical geometries to cardiac structures
STACOM'10/CESC'10 Proceedings of the First international conference on Statistical atlases and computational models of the heart, and international conference on Cardiac electrophysiological simulation challenge
MICCAI'10 Proceedings of the 2010 international conference on Prostate cancer imaging: computer-aided diagnosis, prognosis, and intervention
MICCAI'10 Proceedings of the 13th international conference on Medical image computing and computer-assisted intervention: Part II
International Journal of Computer Vision
Schild's Ladder for the parallel transport of deformations in time series of images
IPMI'11 Proceedings of the 22nd international conference on Information processing in medical imaging
Spectral demons --- image registration via global spectral correspondence
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part II
An implicit inter-subject shape driven image deformation model for prostate motion estimation
MICCAI'12 Proceedings of the 4th international conference on Abdominal Imaging: computational and clinical applications
Groupwise spectral log-demons framework for atlas construction
MCV'12 Proceedings of the Second international conference on Medical Computer Vision: recognition techniques and applications in medical imaging
Geodesics, Parallel Transport & One-Parameter Subgroups for Diffeomorphic Image Registration
International Journal of Computer Vision
Spectral Log-Demons: Diffeomorphic Image Registration with Very Large Deformations
International Journal of Computer Vision
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This paper focuses on the estimation of statistical atlases of 3D images by means of diffeomorphic transformations. Within a Log-Euclidean framework, the exponential and logarithm maps of diffeomorphisms need to be computed. In this framework, the Inverse Scaling and Squaring (ISS) method has been recently extended for the computation of the logarithm map, which is one of the most time demanding stages. In this work we propose to apply the Baker-Campbell-Hausdorff (BCH) formula instead. In a 3D simulation study, BCH formula and ISS method obtained similar accuracy but BCH formula was more than 100 times faster. This approach allowed us to estimate a 3D statistical brain atlas in a reasonable time, including the average and the modes of variation. Details for the computation of the modes of variation in the Sobolev tangent space of diffeomorphisms are also provided.