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Higher-order momentum distributions and locally affine LDDMM registration

Abstract : 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 nontranslational 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.
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https://hal.inria.fr/hal-00813869
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Submitted on : Tuesday, April 16, 2013 - 11:21:17 AM
Last modification on : Monday, August 31, 2020 - 1:06:02 PM

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Stefan Sommer, Mads Nielsen, Sune Darkner, Xavier Pennec. Higher-order momentum distributions and locally affine LDDMM registration. SIAM Journal on Imaging Sciences, Society for Industrial and Applied Mathematics, 2013, 6 (1), pp.341-367. ⟨10.1137/110859002⟩. ⟨hal-00813869⟩

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