448 research outputs found
Numerical shadows: measures and densities on the numerical range
For any operator acting on an -dimensional Hilbert space we
introduce its numerical shadow, which is a probability measure on the complex
plane supported by the numerical range of . The shadow of at point
is defined as the probability that the inner product is equal to ,
where stands for a random complex vector from , satisfying .
In the case of N=2 the numerical shadow of a non-normal operator can be
interpreted as a shadow of a hollow sphere projected on a plane. A similar
interpretation is provided also for higher dimensions. For a hermitian its
numerical shadow forms a probability distribution on the real axis which is
shown to be a one dimensional -spline. In the case of a normal the
numerical shadow corresponds to a shadow of a transparent solid simplex in
onto the complex plane. Numerical shadow is found explicitly for
Jordan matrices , direct sums of matrices and in all cases where the
shadow is rotation invariant. Results concerning the moments of shadow measures
play an important role. A general technique to study numerical shadow via the
Cartesian decomposition is described, and a link of the numerical shadow of an
operator to its higher-rank numerical range is emphasized.Comment: 37 pages, 8 figure
Geometric and photometric affine invariant image registration
This thesis aims to present a solution to the correspondence problem for the registration
of wide-baseline images taken from uncalibrated cameras. We propose an affine
invariant descriptor that combines the geometry and photometry of the scene to find
correspondences between both views. The geometric affine invariant component of the
descriptor is based on the affine arc-length metric, whereas the photometry is analysed
by invariant colour moments. A graph structure represents the spatial distribution of the
primitive features; i.e. nodes correspond to detected high-curvature points, whereas arcs
represent connectivities by extracted contours. After matching, we refine the search for
correspondences by using a maximum likelihood robust algorithm. We have evaluated
the system over synthetic and real data. The method is endemic to propagation of errors
introduced by approximations in the system.BAE SystemsSelex Sensors and Airborne System
Wavelet-based numerical methods for the solution of the Nonuniform Multiconductor Transmission Lines
This work presents a new Time-Domain Space Expansion (TDSE) method for the numerical solution of the Nonuniform Multiconductor Transmission Lines (NMTL). This method is based on a weak formulation of the NMTL equations, which leads to a class of numerical schemes of different approximation order according to the particular choice of some trial and test functions. The core of this work is devoted to the definition of trial and test functions that can be used to produce accurate representations of the solution by keeping the computational effort as small as possible. It is shown that bases of wavelets are a good choice
Landmark-Matching Transformation with Large Deformation Via n-dimensional Quasi-conformal Maps
We propose a new method to obtain landmark-matching transformations between n-dimensional Euclidean spaces with large deformations. Given a set of feature correspondences, our algorithm searches for an optimal folding-free mapping that satisfies the prescribed landmark constraints. The standard conformality distortion defined for mappings between 2-dimensional spaces is first generalized to the n-dimensional conformality distortion K(f) for a mapping f between n-dimensional Euclidean spaces (n ≥ 3). We then propose a variational model involving K(f) to tackle the landmark-matching problem in higher dimensional spaces. The generalized conformality term K(f) enforces the bijectivity of the optimized mapping and minimizes its local geometric distortions even with large deformations. Another challenge is the high computational cost of the proposed model. To tackle this, we have also proposed a numerical method to solve the optimization problem more efficiently. Alternating direction method with multiplier is applied to split the optimization problem into two subproblems. Preconditioned conjugate gradient method with multi-grid preconditioner is applied to solve one of the sub-problems, while a fixed-point iteration is proposed to solve another subproblem. Experiments have been carried out on both synthetic examples and lung CT images to compute the diffeomorphic landmark-matching transformation with different landmark constraints. Results show the efficacy of our proposed model to obtain a folding-free landmark-matching transformation between n-dimensional spaces with large deformations
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