20,542 research outputs found
Computing Topology Preservation of RBF Transformations for Landmark-Based Image Registration
In image registration, a proper transformation should be topology preserving.
Especially for landmark-based image registration, if the displacement of one
landmark is larger enough than those of neighbourhood landmarks, topology
violation will be occurred. This paper aim to analyse the topology preservation
of some Radial Basis Functions (RBFs) which are used to model deformations in
image registration. Mat\'{e}rn functions are quite common in the statistic
literature (see, e.g. \cite{Matern86,Stein99}). In this paper, we use them to
solve the landmark-based image registration problem. We present the topology
preservation properties of RBFs in one landmark and four landmarks model
respectively. Numerical results of three kinds of Mat\'{e}rn transformations
are compared with results of Gaussian, Wendland's, and Wu's functions
Local interpolation schemes for landmark-based image registration: a comparison
In this paper we focus, from a mathematical point of view, on properties and
performances of some local interpolation schemes for landmark-based image
registration. Precisely, we consider modified Shepard's interpolants,
Wendland's functions, and Lobachevsky splines. They are quite unlike each
other, but all of them are compactly supported and enjoy interesting
theoretical and computational properties. In particular, we point out some
unusual forms of the considered functions. Finally, detailed numerical
comparisons are given, considering also Gaussians and thin plate splines, which
are really globally supported but widely used in applications
The optical system of the H.E.S.S. imaging atmospheric Cherenkov telescopes, Part II: mirror alignment and point spread function
Mirror facets of the H.E.S.S. imaging atmospheric Cherenkov telescopes are
aligned using stars imaged onto the closed lid of the PMT camera, viewed by a
CCD camera. The alignment procedure works reliably and includes the automatic
analysis of CCD images and control of the facet alignment actuators. On-axis,
80% of the reflected light is contained in a circle of less than 1 mrad
diameter. The spot widens with increasing angle to the telescope axis. In
accordance with simulations, the spot size has roughly doubled at an angle of
1.4 degr. from the axis. The expected variation of spot size with elevation due
to deformations of the support structure is visible, but is completely
non-critical over the usual working range. Overall, the optical quality of the
telescope exceeds the specifications.Comment: 23 pages, 13 figure
Marginal and Relevant Deformations of N=4 Field Theories and Non-Commutative Moduli Spaces of Vacua
We study marginal and relevant supersymmetric deformations of the N=4
super-Yang-Mills theory in four dimensions. Our primary innovation is the
interpretation of the moduli spaces of vacua of these theories as
non-commutative spaces. The construction of these spaces relies on the
representation theory of the related quantum algebras, which are obtained from
F-term constraints. These field theories are dual to superstring theories
propagating on deformations of the AdS_5xS^5 geometry. We study D-branes
propagating in these vacua and introduce the appropriate notion of algebraic
geometry for non-commutative spaces. The resulting moduli spaces of D-branes
have several novel features. In particular, they may be interpreted as
symmetric products of non-commutative spaces. We show how mirror symmetry
between these deformed geometries and orbifold theories follows from T-duality.
Many features of the dual closed string theory may be identified within the
non-commutative algebra. In particular, we make progress towards understanding
the K-theory necessary for backgrounds where the Neveu-Schwarz antisymmetric
tensor of the string is turned on, and we shed light on some aspects of
discrete anomalies based on the non-commutative geometry.Comment: 60 pages, 4 figures, JHEP format, amsfonts, amssymb, amsmat
Robust Cardiac Motion Estimation using Ultrafast Ultrasound Data: A Low-Rank-Topology-Preserving Approach
Cardiac motion estimation is an important diagnostic tool to detect heart
diseases and it has been explored with modalities such as MRI and conventional
ultrasound (US) sequences. US cardiac motion estimation still presents
challenges because of the complex motion patterns and the presence of noise. In
this work, we propose a novel approach to estimate the cardiac motion using
ultrafast ultrasound data. -- Our solution is based on a variational
formulation characterized by the L2-regularized class. The displacement is
represented by a lattice of b-splines and we ensure robustness by applying a
maximum likelihood type estimator. While this is an important part of our
solution, the main highlight of this paper is to combine a low-rank data
representation with topology preservation. Low-rank data representation
(achieved by finding the k-dominant singular values of a Casorati Matrix
arranged from the data sequence) speeds up the global solution and achieves
noise reduction. On the other hand, topology preservation (achieved by
monitoring the Jacobian determinant) allows to radically rule out distortions
while carefully controlling the size of allowed expansions and contractions.
Our variational approach is carried out on a realistic dataset as well as on a
simulated one. We demonstrate how our proposed variational solution deals with
complex deformations through careful numerical experiments. While maintaining
the accuracy of the solution, the low-rank preprocessing is shown to speed up
the convergence of the variational problem. Beyond cardiac motion estimation,
our approach is promising for the analysis of other organs that experience
motion.Comment: 15 pages, 10 figures, Physics in Medicine and Biology, 201
Nonlinear Morphoelastic Plates I: Genesis of Residual Stress
Volumetric growth of an elastic body may give rise to residual stress. Here a rigorous analysis of the residual strains and stresses generated by growth in the axisymmetric Kirchhoff plate is given. Balance equations are derived via the global constraint principle, growth is incorporated via a multiplicative decomposition of the deformation gradient, and the system is closed by a response function. The particular case of a compressible neo-Hookean material is analyzed and the existence of residually stressed states is established
- …