Higher-order momentum distributions and locally affine LDDMM registration
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Higher-order momentum distributions and locally affine LDDMM registration. / Sommer, Stefan Horst; Nielsen, Mads; Darkner, Sune; Pennec, Xavier.
In: S I A M Journal on Imaging Sciences, Vol. 6, No. 1, 2013, p. 341-367.Research output: Contribution to journal › Journal article › Research › peer-review
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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 -
ID: 118832329