7,848 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
Weighted Mean Curvature
In image processing tasks, spatial priors are essential for robust
computations, regularization, algorithmic design and Bayesian inference. In
this paper, we introduce weighted mean curvature (WMC) as a novel image prior
and present an efficient computation scheme for its discretization in practical
image processing applications. We first demonstrate the favorable properties of
WMC, such as sampling invariance, scale invariance, and contrast invariance
with Gaussian noise model; and we show the relation of WMC to area
regularization. We further propose an efficient computation scheme for
discretized WMC, which is demonstrated herein to process over 33.2
giga-pixels/second on GPU. This scheme yields itself to a convolutional neural
network representation. Finally, WMC is evaluated on synthetic and real images,
showing its superiority quantitatively to total-variation and mean curvature.Comment: 12 page
CMB Anisotropy in Compact Hyperbolic Universes I: Computing Correlation Functions
CMB anisotropy measurements have brought the issue of global topology of the
universe from the realm of theoretical possibility to within the grasp of
observations. The global topology of the universe modifies the correlation
properties of cosmic fields. In particular, strong correlations are predicted
in CMB anisotropy patterns on the largest observable scales if the size of the
Universe is comparable to the distance to the CMB last scattering surface. We
describe in detail our completely general scheme using a regularized method of
images for calculating such correlation functions in models with nontrivial
topology, and apply it to the computationally challenging compact hyperbolic
spaces. Our procedure directly sums over images within a specified radius,
ideally many times the diameter of the space, effectively treats more distant
images in a continuous approximation, and uses Cesaro resummation to further
sharpen the results. At all levels of approximation the symmetries of the space
are preserved in the correlation function. This new technique eliminates the
need for the difficult task of spatial eigenmode decomposition on these spaces.
Although the eigenspectrum can be obtained by this method if desired, at a
given level of approximation the correlation functions are more accurately
determined. We use the 3-torus example to demonstrate that the method works
very well. We apply it to power spectrum as well as correlation function
evaluations in a number of compact hyperbolic (CH) spaces. Application to the
computation of CMB anisotropy correlations on CH spaces, and the observational
constraints following from them, are given in a companion paper.Comment: 27 pages, Latex, 11 figures, submitted to Phys. Rev. D, March 11,
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