Invariant feature representations for 3D objects are one of the basic needs in 3D object retrieval and classification. One tool to obtain rotation invariance are Spherical Harmonics, which are an orthogonal basis for the functions defined on the 2-sphere. We show that the irreducible representations of the 3D rotation group, which acts on the Spherical Harmonic representation, can give more inf...

In this paper we demonstrate performance of several local and multi-resolution gravity models derived from existing spherical harmonic models. A model of this type was provided to USAFSC in 1997, and additional variants have been developed since then. We also begin to address the problem of estimating multi-resolution models directly from gravity measurements. We hope to demonstrate that it is ...

Utilizing the fact that solid-harmonic combinations of Cartesian and Hermite Gaussian atomic orbitals are identical, a new scheme for the evaluation of molecular integrals over solid-harmonic atomic orbitals is presented, where the integration is carried out over Hermite rather than Cartesian atomic orbitals. Since Hermite Gaussians are defined as derivatives of spherical Gaussians, the corresp...

A random climate field over the globe can be decomposed into a series of spherical harmonic functions. This paper shows that the mean square sampling error for a spherical harmonic coefficient is composed of aliased powers from other spherical harmonic omponents due to the spatial gaps in sampling networks. A general formula is given for calculating the aliased powers. On the basis of the spect...

A review is given of the geodetic concepts necessary for oceanographers to make use of satellite gravity data to define the geoid, and to interpret the resulting product. The geoid is defined, with particular attention to subtleties related to the representation of the permanent tide, and the way in which the geoid is represented in ocean models. 5 The usual spherical harmonic description of th...

Abstract We present a new, model-independent approach for measuring non-Gaussianity of the Cosmic Microwave Background (CMB) anisotropy pattern. Our approach is based on the empirical distribution function of the normalized spherical harmonic expansion coefficients alm of a nearly full-sky CMB map, like the ones expected from forthcoming satellite experiments. Using a set of Kolmogorov-Smirnov ...

Decomposition of a soundfield into spherical harmonics is a fundamental problem in acoustic signal processing. This paper shows how to design non-spherical microphone array structures in 3D space to decompose a soundfield into spherical harmonic components. We use the mode limiting property of the Bessel functions and zeros of the associated Legendre functions together with orthoganality of the...

We present a fast and accurate algorithm for evaluating singular integral operators on smooth surfaces that are globally parametrized by spherical coordinates. Problems of this type arise, for example, in simulating Stokes flows with particulate suspensions and in multi-particle scattering calculations. For smooth surfaces, spherical harmonic expansions are commonly used for geometry representa...

A new construction of a directional continuous wavelet analysis on the sphere is derived herein. We adopt the harmonic scaling idea for the spherical dilation operator recently proposed by Sanz et al. [1] but extend the analysis to a more general directional framework. Directional wavelets are a powerful extension that allow one to also probe oriented structure in the analysed function. Our sph...