1,594 research outputs found
A novel variational model for image registration using Gaussian curvature
Image registration is one important task in many image processing
applications. It aims to align two or more images so that useful information
can be extracted through comparison, combination or superposition. This is
achieved by constructing an optimal trans- formation which ensures that the
template image becomes similar to a given reference image. Although many models
exist, designing a model capable of modelling large and smooth deformation
field continues to pose a challenge. This paper proposes a novel variational
model for image registration using the Gaussian curvature as a regulariser. The
model is motivated by the surface restoration work in geometric processing
[Elsey and Esedoglu, Multiscale Model. Simul., (2009), pp. 1549-1573]. An
effective numerical solver is provided for the model using an augmented
Lagrangian method. Numerical experiments can show that the new model
outperforms three competing models based on, respectively, a linear curvature
[Fischer and Modersitzki, J. Math. Imaging Vis., (2003), pp. 81- 85], the mean
curvature [Chumchob, Chen and Brito, Multiscale Model. Simul., (2011), pp.
89-128] and the diffeomorphic demon model [Vercauteren at al., NeuroImage,
(2009), pp. 61-72] in terms of robustness and accuracy.Comment: 23 pages, 5 figures. Key words: Image registration, Non-parametric
image registration, Regularisation, Gaussian curvature, surface mappin
A Bayesian analysis of regularised source inversions in gravitational lensing
Strong gravitational lens systems with extended sources are of special
interest because they provide additional constraints on the models of the lens
systems. To use a gravitational lens system for measuring the Hubble constant,
one would need to determine the lens potential and the source intensity
distribution simultaneously. A linear inversion method to reconstruct a
pixellated source brightness distribution of a given lens potential model was
introduced by Warren & Dye. In the inversion process, a regularisation on the
source intensity is often needed to ensure a successful inversion with a
faithful resulting source. In this paper, we use Bayesian analysis to determine
the optimal regularisation constant (strength of regularisation) of a given
form of regularisation and to objectively choose the optimal form of
regularisation given a selection of regularisations. We consider and compare
quantitatively three different forms of regularisation previously described in
the literature for source inversions in gravitational lensing: zeroth-order,
gradient and curvature. We use simulated data with the exact lens potential to
demonstrate the method. We find that the preferred form of regularisation
depends on the nature of the source distribution.Comment: 18 pages, 10 figures; Revisions based on referee's comments after
initial submission to MNRA
Numerical Study of c>1 Matter Coupled to Quantum Gravity
We present the results of a numerical simulation aimed at understanding the
nature of the `c = 1 barrier' in two dimensional quantum gravity. We study
multiple Ising models living on dynamical graphs and analyse the
behaviour of moments of the graph loop distribution. We notice a universality
at work as the average properties of typical graphs from the ensemble are
determined only by the central charge. We further argue that the qualitative
nature of these results can be understood from considering the effect of
fluctuations about a mean field solution in the Ising sector.Comment: 12 page
On the Effective Action of Noncommutative Yang-Mills Theory
We compute here the Yang-Mills effective action on Moyal space by integrating
over the scalar fields in a noncommutative scalar field theory with harmonic
term, minimally coupled to an external gauge potential. We also explain the
special regularisation scheme chosen here and give some links to the Schwinger
parametric representation. Finally, we discuss the results obtained: a
noncommutative possibly renormalisable Yang-Mills theory.Comment: 19 pages, 6 figures. At the occasion of the "International Conference
on Noncommutative Geometry and Physics", April 2007, Orsay (France). To
appear in J. Phys. Conf. Se
The jump set under geometric regularisation. Part 1: Basic technique and first-order denoising
Let u \in \mbox{BV}(\Omega) solve the total variation denoising problem
with -squared fidelity and data . Caselles et al. [Multiscale Model.
Simul. 6 (2008), 879--894] have shown the containment of the jump set of in that of . Their proof
unfortunately depends heavily on the co-area formula, as do many results in
this area, and as such is not directly extensible to higher-order,
curvature-based, and other advanced geometric regularisers, such as total
generalised variation (TGV) and Euler's elastica. These have received increased
attention in recent times due to their better practical regularisation
properties compared to conventional total variation or wavelets. We prove
analogous jump set containment properties for a general class of regularisers.
We do this with novel Lipschitz transformation techniques, and do not require
the co-area formula. In the present Part 1 we demonstrate the general technique
on first-order regularisers, while in Part 2 we will extend it to higher-order
regularisers. In particular, we concentrate in this part on TV and, as a
novelty, Huber-regularised TV. We also demonstrate that the technique would
apply to non-convex TV models as well as the Perona-Malik anisotropic
diffusion, if these approaches were well-posed to begin with
Semiclassical quantisation of space-times with apparent horizons
Coherent or semiclassical states in canonical quantum gravity describe the
classical Schwarzschild space-time. By tracing over the coherent state
wavefunction inside the horizon, a density matrix is derived.
Bekenstein-Hawking entropy is obtained from the density matrix, modulo the
Immirzi parameter. The expectation value of the area and curvature operator is
evaluated in these states. The behaviour near the singularity of the curvature
operator shows that the singularity is resolved. We then generalise the results
to space-times with spherically symmetric apparent horizons.Comment: 52 pages, 4 figure
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