Gaussian convolutions are perhaps the most often used image operators in low-level computer vision tasks. Surprisingly though, there are precious few articles that describe efficient and accurate implementations of these operators. In this paper we describe numerical approximations of Gaussian convolutions based on interpolation. We start with the continuous convolution integral and use an inte...

We introduce a new method of constructing kernels on sets whose elements are discrete structures like strings, trees and graphs. The method can be applied iteratively to build a kernel on a innnite set from kernels involving generators of the set. The family of kernels generated generalizes the family of radial basis kernels. It can also be used to deene kernels in the form of joint Gibbs proba...

Cellular automata have been used to model the formation and dynamics of patterns in a variety of chemical, biological and ecological systems. However, for patterns in which sharp interfaces form and propagate, automata simulations can exhibit undesirable properties, including spurious anisotropy and poor representation of interface curvature eeects. These simulations are also prohibitively slow...

We present an intrinsically defined algebra of operators containing the right and left invariant Calderón-Zygmund operators on a stratified group. The operators in our algebra are pseudolocal and bounded on Lp (1 < p <∞). This algebra provides an example of an algebra of singular integrals that falls outside of the classical Calderón-Zygmund theory.

We primarily consider here the L mapping properties of a class of strongly singular Radon transforms on the Heisenberg group H; these are convolution operators on H with kernels of the form M(z, t) = K(z)δ0(t) where K is a strongly singular kernel on C . Our results are obtained by utilizing the group Fourier transform and uniform asymptotic forms for Laguerre functions due to Erdélyi. We also ...

In this paper, we connect rectangular free probability theory and spherical integrals. We prove the analogue, for rectangular or square non-Hermitian matrices, of a result that Guionnet and Mäıda proved for Hermitian matrices in [12]. More specifically, we study the limit, as n,m tend to infinity, of 1 n logE{exp[nmθXn]}, where θ ∈ R, Xn is the real part of an entry of UnMnVm, Mn is a certain n...

We prove that the free additive convolution of two Borel probability measures supported on the real line can have a component that is singular continuous with respect to the Lebesgue measure on R only if one of the two measures is a point mass. The density of the absolutely continuous part with respect to the Lebesgue measure is shown to be analytic wherever positive and finite. The atoms of th...