A novel diagonalized multilevel fast multipole method (MLFMM) for time harmonic Maxwell’s equations is proposed which realizes considerable memory savings without compromising accuracy and computational speed. The improvement is achieved by expanding the k-space integrals over the unit sphere in spherical harmonics. Since the spherical harmonics expansion is carried out for cartesian vector com...

This report reviews, in light of signal processing, the problem of relighting a Lambertian convex object with distant light source, whose crucial task is the decomposition of reflectance function into albedos (reflection coefficients) and lighting, based on a set of images and the 3-D geometry of the object from which the images were taken. A reflectance function is the result of filtering a li...

Spherical microphone arrays have been used for source localization in three-dimensional space recently. In this paper, a two-stage algorithm is developed to localize mixed far-field and near-field acoustic sources in free-field environment. In the first stage, an array signal model is constructed in the spherical harmonics domain. The recurrent relation of spherical harmonics is independent of ...

In contrast to the more common Diffusion Tensor Imaging (DTI), High Angular Resolution Diffusion Imaging (HARDI) allows superior delineation of angular microstructures of brain white matter, and makes possible multiple-fiber modeling of each voxel for better characterization of brain connectivity. However, in the context of image registration, the question of how much information is needed for ...

Near-field compensated higher order Ambisonics (HOA) is an approach to the physical synthesis of sound fields. The typical interpretation of the modern HOA approach is that the sound field to be synthesized and the spatio-temporal transfer function of the employed loudspeakers are expanded into series of spherical harmonics in order to determine the loudspeaker driving signals for spherical arr...

There is a lack of unified statistical modeling framework for cerebral shape asymmetry analysis in literature. Most previous approaches start with flipping the 3D magnetic resonance images (MRI). The anatomical correspondence across the hemispheres is then established by registering the original image to the flipped image. A difference of an anatomical index between these two images is used as ...

The spectral method with discrete spherical harmonics transform plays an important role in many applications. In spite of its advantages, the spherical harmonics transform has a drawback of high computational complexity, which is determined by that of the associated Legendre transform, and the direct computation requires time of O(N3) for cut-off frequency N . In this paper, we propose a fast a...

This pamphlet is intended for the scientist who is considering using Spherical Harmonics for some application. It is designed to introduce the Spherical Harmonics from a theoretical perspective and then discuss those practical issues necessary for their use in applications. I expect great variability in the backgrounds of the readers. In order to be informative to those who know less, without i...

The wave functions of a quantum isotropic harmonic oscillator in N-space modified by barriers at the coordinate hyperplanes can be expressed in terms of certain generalized spherical harmonics. These are associated with a product-type weight function on the sphere. Their analysis is carried out by means of differential-difference operators. The symmetries of this system involve the Weyl group o...

Image reconstruction from cone-beam projections is required for both x-ray computed tomography (CT) and single photon emission computed tomography (SPECT). Grangeat's algorithm accurately performs cone-beam reconstruction provided that Tuy's data sufficiency condition is satisfied and projections are complete. The algorithm consists of three stages: (a) Forming weighted plane integrals by calcu...