73 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
Quicksilver: Fast Predictive Image Registration - a Deep Learning Approach
This paper introduces Quicksilver, a fast deformable image registration
method. Quicksilver registration for image-pairs works by patch-wise prediction
of a deformation model based directly on image appearance. A deep
encoder-decoder network is used as the prediction model. While the prediction
strategy is general, we focus on predictions for the Large Deformation
Diffeomorphic Metric Mapping (LDDMM) model. Specifically, we predict the
momentum-parameterization of LDDMM, which facilitates a patch-wise prediction
strategy while maintaining the theoretical properties of LDDMM, such as
guaranteed diffeomorphic mappings for sufficiently strong regularization. We
also provide a probabilistic version of our prediction network which can be
sampled during the testing time to calculate uncertainties in the predicted
deformations. Finally, we introduce a new correction network which greatly
increases the prediction accuracy of an already existing prediction network. We
show experimental results for uni-modal atlas-to-image as well as uni- / multi-
modal image-to-image registrations. These experiments demonstrate that our
method accurately predicts registrations obtained by numerical optimization, is
very fast, achieves state-of-the-art registration results on four standard
validation datasets, and can jointly learn an image similarity measure.
Quicksilver is freely available as an open-source software.Comment: Add new discussion
Sliding at first order: Higher-order momentum distributions for discontinuous image registration
In this paper, we propose a new approach to deformable image registration
that captures sliding motions. The large deformation diffeomorphic metric
mapping (LDDMM) registration method faces challenges in representing sliding
motion since it per construction generates smooth warps. To address this issue,
we extend LDDMM by incorporating both zeroth- and first-order momenta with a
non-differentiable kernel. This allows to represent both discontinuous
deformation at switching boundaries and diffeomorphic deformation in
homogeneous regions. We provide a mathematical analysis of the proposed
deformation model from the viewpoint of discontinuous systems. To evaluate our
approach, we conduct experiments on both artificial images and the publicly
available DIR-Lab 4DCT dataset. Results show the effectiveness of our approach
in capturing plausible sliding motion
Reduction by Lie Group symmetries in diffeomorphic image registration and deformation modelling
We survey the role of reduction by symmetry in the large deformation diffeomorphic metric mapping framework for registration of a variety of data types (landmarks, curves, surfaces, images and higher-order derivative data). Particle relabelling symmetry allows the equations of motion to be reduced to the Lie algebra allowing the equations to be written purely in terms of the Eulerian velocity field. As a second use of symmetry, the infinite dimensional problem of finding correspondences between objects can be reduced for a range of concrete data types, resulting in compact representations of shape and spatial structure. Using reduction by symmetry, we describe these models in a common theoretical framework that draws on links between the registration problem and geometric mechanics. We outline these constructions and further cases where reduction by symmetry promises new approaches to the registration of complex data types
Unified Heat Kernel Regression for Diffusion, Kernel Smoothing and Wavelets on Manifolds and Its Application to Mandible Growth Modeling in CT Images
We present a novel kernel regression framework for smoothing scalar surface
data using the Laplace-Beltrami eigenfunctions. Starting with the heat kernel
constructed from the eigenfunctions, we formulate a new bivariate kernel
regression framework as a weighted eigenfunction expansion with the heat kernel
as the weights. The new kernel regression is mathematically equivalent to
isotropic heat diffusion, kernel smoothing and recently popular diffusion
wavelets. Unlike many previous partial differential equation based approaches
involving diffusion, our approach represents the solution of diffusion
analytically, reducing numerical inaccuracy and slow convergence. The numerical
implementation is validated on a unit sphere using spherical harmonics. As an
illustration, we have applied the method in characterizing the localized growth
pattern of mandible surfaces obtained in CT images from subjects between ages 0
and 20 years by regressing the length of displacement vectors with respect to
the template surface.Comment: Accepted in Medical Image Analysi
- …