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We propose a new edge detection method that is effective on multivariate irregular data in any domain. The method is based on a local polynomial annihilation technique and can be characterized by its convergence to zero for any value away from discontinuities. The method is numerically cost efficient and entirely independent of any specific shape or(More)
We discuss a general framework for recovering edges in piecewise smooth functions with finitely many jump discontinuities, where [f ](x) := f (x+) − f (x−) = 0. Our approach is based on two main aspects—localization using appropriate concentration kernels and separation of scales by nonlinear enhancement. To detect such edges, one employs concentration(More)
Gibbs ringing is a well known artifact that effects reconstruction of images having discontinuities. This is a problem in the reconstruction of magnetic resonance imaging (MRI) data due to the many different tissues normally present in each scan. The Gibbs ringing artifact manifests itself at the boundaries of the tissues, making it difficult to determine(More)
The Gegenbauer image reconstruction method, previously shown to improve the quality of magnetic resonance images, is utilized in this study as a segmentation preprocessing step. It is demonstrated that, for all simulated and real magnetic resonance images used in this study, the Gegenbauer reconstruction method improves the accuracy of segmentation.(More)
Computational fluid dynamics simulations using the WENO-LF method are applied to high Mach number nonrelativistic astrophysical jets, including the effects of radiative cooling. Our numerical methods have allowed us to simulate astrophysical jets at much higher Mach numbers than have been attained (Mach 20) in the literature. Our simulations of the HH 1-2(More)
We present a novel deconvolution approach to accurately restore piecewise smooth signals from blurred data. The first stage uses Higher Order Total Variation restorations to obtain an estimate of the location of jump discontinuities from the blurred data. In the second stage the estimated jump locations are used to determine the local orders of a Variable(More)
We are concerned with the detection of edges—the location and amplitudes of jump discontinuities of piecewise smooth data realized in terms of its discrete grid values. We discuss the interplay between two approaches. One approach, realized in the physical space, is based on local differences and is typically limited to low-order of accuracy. and realized(More)
Keywords: Stochastic partial differential equations Multivariate edge detection Generalized polynomial chaos method a b s t r a c t Edge detection has traditionally been associated with detecting physical space jump dis-continuities in one dimension, e.g. seismic signals, and two dimensions, e.g. digital images. Hence most of the research on edge detection(More)