2,895 research outputs found
Higher-Order Momentum Distributions and Locally Affine LDDMM Registration
To achieve sparse parametrizations that allows 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 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 non-rigid 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
Indirect Image Registration with Large Diffeomorphic Deformations
The paper adapts the large deformation diffeomorphic metric mapping framework
for image registration to the indirect setting where a template is registered
against a target that is given through indirect noisy observations. The
registration uses diffeomorphisms that transform the template through a (group)
action. These diffeomorphisms are generated by solving a flow equation that is
defined by a velocity field with certain regularity. The theoretical analysis
includes a proof that indirect image registration has solutions (existence)
that are stable and that converge as the data error tends so zero, so it
becomes a well-defined regularization method. The paper concludes with examples
of indirect image registration in 2D tomography with very sparse and/or highly
noisy data.Comment: 43 pages, 4 figures, 1 table; revise
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