TY - JOUR

T1 - Higher-order momentum distributions and locally affine LDDMM registration

AU - Sommer, Stefan Horst

AU - Nielsen, Mads

AU - Darkner, Sune

AU - Pennec, Xavier

PY - 2013

Y1 - 2013

N2 - To achieve sparse parametrizations that allow intuitive analysis, we aim to represent deformation with a basis containing interpretable elements, and we wish to use elements that have the description capacity to represent the deformation compactly. To accomplish this, we introduce in this paper higher-order momentum distributions in the large deformation diffeomorphic metric mapping (LDDMM) registration framework. While the zeroth-order moments previously used in LDDMM only describe local displacement, the first-order momenta that are proposed here represent a basis that allows local description of affine transformations and subsequent compact description of non-translational movement in a globally nonrigid deformation. The resulting representation contains directly interpretable information from both mathematical and modeling perspectives. We develop the mathematical construction of the registration framework with higher-order momenta, we show the implications for sparse image registration and deformation description, and we provide examples of how the parametrization enables registration with a very low number of parameters. The capacity and interpretability of the parametrization using higher-order momenta lead to natural modeling of articulated movement, and the method promises to be useful for quantifying ventricle expansion and progressing atrophy during Alzheimer's disease.

AB - To achieve sparse parametrizations that allow intuitive analysis, we aim to represent deformation with a basis containing interpretable elements, and we wish to use elements that have the description capacity to represent the deformation compactly. To accomplish this, we introduce in this paper higher-order momentum distributions in the large deformation diffeomorphic metric mapping (LDDMM) registration framework. While the zeroth-order moments previously used in LDDMM only describe local displacement, the first-order momenta that are proposed here represent a basis that allows local description of affine transformations and subsequent compact description of non-translational movement in a globally nonrigid deformation. The resulting representation contains directly interpretable information from both mathematical and modeling perspectives. We develop the mathematical construction of the registration framework with higher-order momenta, we show the implications for sparse image registration and deformation description, and we provide examples of how the parametrization enables registration with a very low number of parameters. The capacity and interpretability of the parametrization using higher-order momenta lead to natural modeling of articulated movement, and the method promises to be useful for quantifying ventricle expansion and progressing atrophy during Alzheimer's disease.

KW - large deformation diffeomorphic metric mapping

KW - diffeomorphic registration

KW - reproducing kernel Hilbert space

KW - kernels

KW - momentum

KW - computational anatomy

U2 - 10.1137/110859002

DO - 10.1137/110859002

M3 - Journal article

VL - 6

SP - 341

EP - 367

JO - SIAM Journal on Imaging Sciences

JF - SIAM Journal on Imaging Sciences

SN - 1936-4954

IS - 1

ER -