Geometrical-based algorithm for variational segmentation and smoothing of vector-valued images

An optimisation method based on a nonlinear functional is considered for segmentation and smoothing of vector-valued images. An edge-based approach is proposed to initially segment the image using geometrical properties such as metric tensor of the linearly smoothed image. The nonlinear functional is then minimised for each segmented region to yield the smoothed image. The functional is characterised with a unique solution in contrast with the Mumford–Shah functional for vector-valued images. An operator for edge detection is introduced as a result of this unique solution. This operator is analytically calculated and its detection performance and localisation are then compared with those of the DroGoperator. The implementations are applied on colour images as examples of vector-valued images, and the results demonstrate robust performance in noisy environments

A new Edge Detector Based on Parametric Surface Model: Regression Surface Descriptor

In this paper we present a new methodology for edge detection in digital images. The first originality of the proposed method is to consider image content as a parametric surface. Then, an original parametric local model of this surface representing image content is proposed. The few parameters involved in the proposed model are shown to be very sensitive to discontinuities in surface which correspond to edges in image content. This naturally leads to the design of an efficient edge detector. Moreover, a thorough analysis of the proposed model also allows us to explain how these parameters can be used to obtain edge descriptors such as orientations and curvatures. In practice, the proposed methodology offers two main advantages. First, it has high customization possibilities in order to be adjusted to a wide range of different problems, from coarse to fine scale edge detection. Second, it is very robust to blurring process and additive noise. Numerical results are presented to emphasis these properties and to confirm efficiency of the proposed method through a comparative study with other edge detectors.Comment: 21 pages, 13 figures and 2 table

Aspherical Supernova Shock Breakout and the Observations of Supernova 2008D

Shock breakout is the earliest, readily-observable emission from a core-collapse supernova explosion. Observing supernova shock breakout may yield information about the nature of the supernova shock prior to exiting the progenitor and, in turn, about the core-collapse supernova mechanism itself. X-ray Outburst 080109, later associated with SN 2008D, is a very well-observed example of shock breakout from a core-collapse supernova. Despite excellent observational coverage and detailed modeling, fundamental information about the shock breakout, such as the radius of breakout and driver of the light curve time scale, is still uncertain. The models constructed for explaining the shock breakout emission from SN 2008D all assume spherical symmetry. We present a study of the observational characteristics of {\it aspherical} shock breakout from stripped-envelope core-collapse supernovae. We conduct two-dimensional, jet-driven supernova simulations from stripped-envelope progenitors and calculate the resulting shock breakout X-ray spectra and light curves. The X-ray spectra evolve significantly in time as the shocks expand outward and are not well-fit by single-temperature and radius black bodies. The time scale of the X-ray burst light curve of the shock breakout is related to the shock crossing time of the progenitor, not the much shorter light crossing time that sets the light curve time scale in spherical breakouts. This could explain the long shock breakout light curve time scale observed for XRO 080109/SN 2008D.Comment: 16 pages, 29 figures. Accepted to Ap

Methods for Detection and Correction of Sudden Pixel Sensitivity Drops

PDC 8.0 includes implementation of a new algorithm to detect and correct step discontinuities appearing in roughly one of every twenty stellar light curves during a given quarter. An example of such a discontinuity in an actual light curve is shown in fig. 1. The majority of such discontinuities are believed to result from high-energy particles (either cosmic or solar in origin) striking the photometer and causing permanent local changes (typically -0.5% in summed apertures) in quantum efficiency, though a partial exponential recovery is often observed. Since these features, dubbed sudden pixel sensitivity dropouts (SPSDs), are uncorrelated across targets they cannot be properly accounted for by the current detrending algorithm. PDC de-trending is based on the assumption that features in flux time series are due either to intrinsic stellar phenomena or to systematic errors and that systematics will exhibit measurable correlations across targets. SPSD events violate these assumptions and their successful removal not only rectifies the flux values of affected targets, but demonstrably improves the overall performance of PDC de-trending

Analysis of energy- and time-dependence of supernova shock effects on neutrino crossing probabilities

It has recently been realized that supernova neutrino signals may be affected by shock propagation over a time interval of a few seconds after bounce. In the standard three-neutrino oscillation scenario, such effects crucially depend on the neutrino level crossing probability P_H in the 1-3 sector. By using a simplified parametrization of the time-dependent supernova radial density profile, we explicitly show that simple analytical expressions for P_H accurately reproduce the phase-averaged results of numerical calculations in the relevant parameter space. Such expressions are then used to study the structure of P_H as a function of energy and time, with particular attention to cases involving multiple crossing along the shock profile. Illustrative applications are given in terms of positron spectra generated by supernova electron antineutrinos through inverse beta decay.Comment: Major changes both in the text and in the figures in order to include the effect of a step-like shock front density profile; final version to appear in Physical Review

Time dependence of evanescent quantum waves

The time dependence of quantum evanescent waves generated by a point source with an infinite or a limited frequency band is analyzed. The evanescent wave is characterized by a forerunner (transient) related to the precise way the source is switched on. It is followed by an asymptotic, monochromatic wave which at long times reveals the oscillation frequency of the source. For a source with a sharp onset the forerunner is exponentially larger than the monochromatic solution and a transition from the transient regime to the asymtotic regime occurs only at asymptotically large times. In this case, the traversal time for tunneling plays already a role only in the transient regime. To enhance the monochromatic solution compared to the forerunner we investigate (a) frequency band limited sources and (b) the short time Fourier analysis (the spectrogram) corresponding to a detector which is frequency band limited. Neither of these two methods leads to a precise determination of the traversal time. However, if they are limited to determine the traversal time only with a precision of the traversal time itself both methods are successful: In this case the transient behavior of the evanescent waves is at a time of the order of the traversal time followed by a monochromatic wave which reveals the frequency of the source.Comment: 16 text pages and 9 postscript figure