A multi-scale kernel bundle for LDDMM: towards sparse deformation description across space and scales

Authors:
Stefan Sommer;Mads Nielsen;François Lauze;Xavier Pennec
Affiliations:
Dept. of Computer Science, Univ. of Copenhagen, Denmark;Dept. of Computer Science, Univ. of Copenhagen, Denmark and Synarc Imaging Technologies, Rødovre, Denmark;Dept. of Computer Science, Univ. of Copenhagen, Denmark and Synarc Imaging Technologies, Rødovre, Denmark;INRIA Sophia-Antipolis, France
Venue:
IPMI'11 Proceedings of the 22nd international conference on Information processing in medical imaging
Year:
2011

Citing 8
Cited 4

Variational problems on flows of diffeomorphisms for image matching

Quarterly of Applied Mathematics
Computing Large Deformation Metric Mappings via Geodesic Flows of Diffeomorphisms

International Journal of Computer Vision
The differential geometry of landmark shape manifolds: metrics, geodesics, and curvature

The differential geometry of landmark shape manifolds: metrics, geodesics, and curvature
Registration of Anatomical Images Using Paths of Diffeomorphisms Parameterized with Stationary Vector Field Flows

International Journal of Computer Vision
Simultaneous fine and coarse diffeomorphic registration: application to atrophy measurement in alzheimer's disease

MICCAI'10 Proceedings of the 13th international conference on Medical image computing and computer-assisted intervention: Part II
Riemannian elasticity: a statistical regularization framework for non-linear registration

MICCAI'05 Proceedings of the 8th international conference on Medical image computing and computer-assisted intervention - Volume Part II
A log-euclidean framework for statistics on diffeomorphisms

MICCAI'06 Proceedings of the 9th international conference on Medical Image Computing and Computer-Assisted Intervention - Volume Part I
Deformable templates using large deformation kinematics

IEEE Transactions on Image Processing

Kernel bundle EPDiff: evolution equations for multi-scale diffeomorphic image registration

SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
Sparse Multi-Scale Diffeomorphic Registration: The Kernel Bundle Framework

Journal of Mathematical Imaging and Vision
Flexible Shape Matching with Finite Element Based LDDMM

International Journal of Computer Vision
Functional Currents: A New Mathematical Tool to Model and Analyse Functional Shapes

Journal of Mathematical Imaging and Vision

Quantified Score

Hi-index	0.00

Visualization

Abstract

The Large Deformation Diffeomorphic Metric Mapping framework constitutes a widely used and mathematically well-founded setup for registration in medical imaging. At its heart lies the notion of the regularization kernel, and the choice of kernel greatly affects the results of registrations. This paper presents an extension of the LDDMM framework allowing multiple kernels at multiple scales to be incorporated in each registration while preserving many of the mathematical properties of standard LDDMM. On a dataset of landmarks from lung CT images, we show by example the influence of the kernel size in standard LDDMM, and we demonstrate how our framework, LDDKBM, automatically incorporates the advantages of each scale to reach the same accuracy as the standard method optimally tuned with respect to scale. The framework, which is not limited to landmark data, thus removes the need for classical scale selection. Moreover, by decoupling the momentum across scales, it promises to provide better interpolation properties, to allow sparse descriptions of the total deformation, to remove the tradeoff between match quality and regularity, and to allow for momentum based statistics using scale information.