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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)
The classical Gibbs phenomenon exhibited by global Fourier projections and interpolants can be resolved in smooth regions by reprojecting in a truncated Gegenbauer series, achieving high resolution recovery of the function up to the point of discontinuity. Unfortunately, due to the poor conditioning of the Gegenbauer polynomials, the method suffers both(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)
This paper addresses the recovery of piecewise smooth functions from their discrete data. Reconstruction methods using both pseudo-spectral coefficients and physical space interpolants have been discussed extensively in the literature, and it is clear that an a priori knowledge of the jump discontinuity location is essential for any reconstruction technique(More)
The Gegenbauer reconstruction method effectively eliminates the Gibbs phenomenon and restores exponential accuracy to the approximations of piecewise smooth functions. Recent investigations show that its success depends upon choosing parameters in such a way that the reg-ularization and the truncation error estimates are equally considered. This paper shows(More)
To David Gottlieb in honor of his 60th birthday for providing much wisdom, guidance, and encouragement over the years. Abstract. Although many techniques have been developed to resolve the classical Gibbs phenomenon , only Gegenbauer reconstruction achieves high resolution recovery of the function up to the points of discontinuity. Unfortunately, due to the(More)