Non-linearity and Non-Gaussianity through Phase Information

In the standard picture of structure formation, initially random-phase fluctuations are amplified by non-linear gravitational instability to produce a final distribution of mass which is highly non-Gaussian and has highly coupled Fourier phases. Second-order statistics, such as the power spectrum, are blind to this kind of phase association. We discuss the information contained in the phases of cosmological density fluctuations and their possible use in statistical analysis tools. In particular, we show how the bispectrum measures a particular form of phase association called quadratic phase coupling, show how to visualise phase association using colour models. These techniques offer the prospect of more complete tests of initial non-Gaussianity than those available at present.Comment: 7 pages, 1 figure (two parts). To appear in the proceedings of The MPA/ESO/MPE Joint Astronomy Conference "Mining the Sky" held in Garching, Germany, July 31 - August 4 2000. To be published in the Springer-Verlag series "ESO Astrophysics Symposia

A fast Bayesian approach to discrete object detection in astronomical datasets - PowellSnakes I

A new fast Bayesian approach is introduced for the detection of discrete objects immersed in a diffuse background. This new method, called PowellSnakes, speeds up traditional Bayesian techniques by: i) replacing the standard form of the likelihood for the parameters characterizing the discrete objects by an alternative exact form that is much quicker to evaluate; ii) using a simultaneous multiple minimization code based on Powell's direction set algorithm to locate rapidly the local maxima in the posterior; and iii) deciding whether each located posterior peak corresponds to a real object by performing a Bayesian model selection using an approximate evidence value based on a local Gaussian approximation to the peak. The construction of this Gaussian approximation also provides the covariance matrix of the uncertainties in the derived parameter values for the object in question. This new approach provides a speed up in performance by a factor of `hundreds' as compared to existing Bayesian source extraction methods that use MCMC to explore the parameter space, such as that presented by Hobson & McLachlan. We illustrate the capabilities of the method by applying to some simplified toy models. Furthermore PowellSnakes has the advantage of consistently defining the threshold for acceptance/rejection based on priors which cannot be said of the frequentist methods. We present here the first implementation of this technique (Version-I). Further improvements to this implementation are currently under investigation and will be published shortly. The application of the method to realistic simulated Planck observations will be presented in a forthcoming publication.Comment: 30 pages, 15 figures, revised version with minor changes, accepted for publication in MNRA

Image processing for plastic surgery planning

This thesis presents some image processing tools for plastic surgery planning. In particular, it presents a novel method that combines local and global context in a probabilistic relaxation framework to identify cephalometric landmarks used in Maxillofacial plastic surgery. It also uses a method that utilises global and local symmetry to identify abnormalities in CT frontal images of the human body. The proposed methodologies are evaluated with the help of several clinical data supplied by collaborating plastic surgeons

Observation of surface wave patterns modified by sub-surface shear currents

We report experimental observations of two canonical surface wave patterns --- ship waves and ring waves --- skewed by sub-surface shear, thus confirming effects predicted by recent theory. Observed ring waves on a still surface with sub-surface shear current are strikingly asymmetric, an effect of strongly anisotropic wave dispersion. Ship waves for motion across a sub--surface current on a still surface exhibit striking asymmetry about the ship's line of motion, and large differences in wake angle and transverse wavelength for upstream vs downstream motion are demonstrated, all of which in good agreement with theoretical predictions. Neither of these phenomena can occur on a depth-uniform current. A quantitative comparison of measured vs predicted average phase shift for a ring wave is grossly mispredicted by no-shear theory, but in good agreement with predictions for the measured shear current. A clear difference in wave frequency within the ring wave packet is observed in the upstream vs downstream direction for all shear flows, while it conforms with theory for quiescent water for propagation normal to the shear current, as expected. Peak values of the measured 2-dimensional Fourier spectrum for ship waves are shown to agree well with the predicted criterion of stationary ship waves, with the exception of some cases where results are imperfect due to the limited wave-number resolution, transient effects and/or experimental noise. Experiments were performed on controlled shear currents created in two different ways, with a curved mesh, and beneath a blocked stagnant-surface flow. Velocity profiles were measured with particle image velocimetry, and surface waves with a synthetic schlieren method. Our observations lend strong empirical support to recent predictions that wave forces on vessels and structures can be greatly affected by shear in estuarine and tidal waters.Comment: 21 pages, 11 figure

A General Geometric Fourier Transform Convolution Theorem

The large variety of Fourier transforms in geometric algebras inspired the straight forward definition of ``A General Geometric Fourier Transform`` in Bujack et al., Proc. of ICCA9, covering most versions in the literature. We showed which constraints are additionally necessary to obtain certain features like linearity, a scaling, or a shift theorem. In this paper we extend the former results by a convolution theorem