A direct implementation of the bilateral filter requires O(σs) operations per pixel, where σs is the (effective) width of the spatial kernel. A fast implementation of the bilateral filter was recently proposed that require O(1) operations per pixel with respect to σs. This is done by using trigonometric functions for the range kernel of the bilateral filter, and by exploiting their so-called sh...

Abstract. In this paper we study the orthogonality conditions satisfied by Jacobi polynomials P (α,β) n when the parameters α and β are not necessarily > −1. We establish orthogonality on a generic closed contour on a Riemann surface. Depending on the parameters, this leads to either full orthogonality conditions on a single contour in the plane, or to multiple orthogonality conditions on a num...

A direct implementation of the bilateral filter requires O(σ(s)(2)) operations per pixel, where σ(s) is the (effective) width of the spatial kernel. A fast implementation of the bilateral filter that required O(1) operations per pixel with respect to σ(s) was recently proposed. This was done by using trigonometric functions for the range kernel of the bilateral filter, and by exploiting t...

We are building a system that can automatically acquire 3D range scans and 2D images to build geometrically correct, texture mapped 3D models of urban environments. This paper deals with the problem of automatically registering the 3D range scans with images acquired at other times and with unknown camera calibration and location. The method involves the utilization of parallelism and orthogona...

We describe a perceptual space for timbre, define an objective metric that takes into account perceptual orthogonality and measure the quality of timbre interpolation. We discuss two timbre representations and measure perceptual judgments on an equivalent range of timbre variety. We determine that a timbre space based on Mel-frequency cepstral coefficients (MFCC) is a good model for a perceptua...

Recent work by Kilmer and Martin, [10] and Braman [2] provides a setting in which the familiar tools of linear algebra can be extended to better understand third-order tensors. Continuing along this vein, this paper investigates further implications including: 1) a bilinear operator on the matrices which is nearly an inner product and which leads to definitions for length of matrices, angle bet...

We invert the Fredholm equation representing the light scattered by a single spherical particle or a distribution of spherical particles to obtain the particle size distribution function and refractive index. We obtain the solution by expanding the distribution function as a linear combination of a set of orthonormal basis functions. The set of orthonormal basis functions is composed of Schmidt...

Sampling a finite stream of filtered pulses violates the bandlimited assumption of the Nyquist-Shannon sampling theory. However, recent low rate sampling schemes have shown that these sparse signals can be sampled with perfect reconstruction at their rate of innovation. To reach this goal in the presence of noise, an estimation procedure is needed to estimate the time-delay and the amplitudes o...