15,896 research outputs found
Finite element surface registration incorporating curvature, volume preservation, and statistical model information
We present a novel method for nonrigid registration of 3D surfaces and images. The method can be used to register surfaces by means of their distance images, or to register medical images directly. It is formulated as a minimization problem of a sum of several terms representing the desired properties of a registration result: smoothness, volume preservation, matching of the surface, its curvature, and possible other feature images, as well as consistency with previous registration results of similar objects, represented by a statistical deformation model. While most of these concepts are already known, we present a coherent continuous formulation of these constraints, including the statistical deformation model. This continuous formulation renders the registration method independent of its discretization. The finite element discretization we present is, while independent of the registration functional, the second main contribution of this paper. The local discontinuous Galerkin method has not previously been used in image registration, and it provides an efficient and general framework to discretize each of the terms of our functional. Computational efficiency and modest memory consumption are achieved thanks to parallelization and locally adaptive mesh refinement. This allows for the first time the use of otherwise prohibitively large 3D statistical deformation models
Information-Theoretic Registration with Explicit Reorientation of Diffusion-Weighted Images
We present an information-theoretic approach to the registration of images
with directional information, and especially for diffusion-Weighted Images
(DWI), with explicit optimization over the directional scale. We call it
Locally Orderless Registration with Directions (LORD). We focus on normalized
mutual information as a robust information-theoretic similarity measure for
DWI. The framework is an extension of the LOR-DWI density-based hierarchical
scale-space model that varies and optimizes the integration, spatial,
directional, and intensity scales. As affine transformations are insufficient
for inter-subject registration, we extend the model to non-rigid deformations.
We illustrate that the proposed model deforms orientation distribution
functions (ODFs) correctly and is capable of handling the classic complex
challenges in DWI-registrations, such as the registration of fiber-crossings
along with kissing, fanning, and interleaving fibers. Our experimental results
clearly illustrate a novel promising regularizing effect, that comes from the
nonlinear orientation-based cost function. We show the properties of the
different image scales and, we show that including orientational information in
our model makes the model better at retrieving deformations in contrast to
standard scalar-based registration.Comment: 16 pages, 19 figure
An Eulerian projection method for quasi-static elastoplasticity
A well-established numerical approach to solve the Navier--Stokes equations
for incompressible fluids is Chorin's projection method, whereby the fluid
velocity is explicitly updated, and then an elliptic problem for the pressure
is solved, which is used to orthogonally project the velocity field to maintain
the incompressibility constraint. In this paper, we develop a mathematical
correspondence between Newtonian fluids in the incompressible limit and
hypo-elastoplastic solids in the slow, quasi-static limit. Using this
correspondence, we formulate a new fixed-grid, Eulerian numerical method for
simulating quasi-static hypo-elastoplastic solids, whereby the stress is
explicitly updated, and then an elliptic problem for the velocity is solved,
which is used to orthogonally project the stress to maintain the
quasi-staticity constraint. We develop a finite-difference implementation of
the method and apply it to an elasto-viscoplastic model of a bulk metallic
glass based on the shear transformation zone theory. We show that in a
two-dimensional plane strain simple shear simulation, the method is in
quantitative agreement with an explicit method. Like the fluid projection
method, it is efficient and numerically robust, making it practical for a wide
variety of applications. We also demonstrate that the method can be extended to
simulate objects with evolving boundaries. We highlight a number of
correspondences between incompressible fluid mechanics and quasi-static
elastoplasticity, creating possibilities for translating other numerical
methods between the two classes of physical problems.Comment: 49 pages, 20 figure
Conformal Janus on Euclidean Sphere
We interpret Janus as an interface in a conformal field theory and study its
properties. The Janus is created by an exactly marginal operator and we study
its effect on the interface conformal field theory on the Janus. We do this by
utilizing the AdS/CFT correspondence. We compute the interface free energy both
from leading correction to the Euclidean action in the dual gravity description
and from conformal perturbation theory in the conformal field theory. We find
that the two results agree each other and that the interface free energy scales
precisely as expected from the conformal invariance of the Janus interface.Comment: 37 pages, 5 figures, references added, section 2 and references
added, published versio
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