Unified Heat Kernel Regression for Diffusion, Kernel Smoothing and Wavelets on Manifolds and Its Application to Mandible Growth Modeling in CT Images

We present a novel kernel regression framework for smoothing scalar surface data using the Laplace-Beltrami eigenfunctions. Starting with the heat kernel constructed from the eigenfunctions, we formulate a new bivariate kernel regression framework as a weighted eigenfunction expansion with the heat kernel as the weights. The new kernel regression is mathematically equivalent to isotropic heat diffusion, kernel smoothing and recently popular diffusion wavelets. Unlike many previous partial differential equation based approaches involving diffusion, our approach represents the solution of diffusion analytically, reducing numerical inaccuracy and slow convergence. The numerical implementation is validated on a unit sphere using spherical harmonics. As an illustration, we have applied the method in characterizing the localized growth pattern of mandible surfaces obtained in CT images from subjects between ages 0 and 20 years by regressing the length of displacement vectors with respect to the template surface.Comment: Accepted in Medical Image Analysi

Effects of sampling rate and type of anti-aliasing filter on linear-predictive estimates of formant frequencies in men, women, and children

The purpose of this study was to assess the effect of downsampling the acoustic signal on the accuracy of linear-predictive (LPC) formant estimation. Based on speech produced by men, women, and children, the first four formant frequencies were estimated at sampling rates of 48, 16, and 10 kHz using different anti-alias filtering. With proper selection of number of LPC coefficients, anti-alias filter and between-frame averaging, results suggest that accuracy is not improved by rates substantially below 48 kHz. Any downsampling should not go below 16 kHz with a filter cut-off centered at 8 kHz. (C) 2020 Acoustical Society of America6 month embargo; published online: 04 March 2020This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]