This paper explores the use of Spherical Harmonics to represent the reflectance function of a 3D surface with known geometry. It is shown that reflectance can be conceived of as a convolution in the angular domain. Spherical Harmonics are used to define a frequency domain in which convolution in the angular domain is equivalent to multiplication in the spherical harmonic frequency domain. This ...

In this paper we discuss a special class of regularization methods for solving the satellite gravity gradiometry problem in a spherical framework based on band-limited spherical regularization wavelets. Considering such wavelets as a result of a combination of some regu-larization methods with Galerkin discretization based on the spherical harmonic system we obtain the error estimates of regula...

In this paper we present a new scheme for the representation of object surfaces. The purpose is to model a surface efficiently in a coarse to fine hierarchy. Our scheme is based on the combination of spherical harmonic functions and wavelet networks on the sphere. The coefficients can be estimated from scattered data sampled from a star-shaped object’s surface. Spherical harmonic functions are ...

In this study we address the question of whether regional gravity field modeling techniques of GRACE data can offer improved resolution over traditional global spherical harmonic solutions. Earlier studies into large, equatorial river basins such as the Amazon, Zambezi and others showed no obvious distinction between regional and global techniques, but this may have been limited by the fact tha...

M. S. Mills,1,* G. A. Siviloglou,2 N. Efremidis,3 T. Graf,4 E. M. Wright,4 J. V. Moloney,4 and D. N. Christodoulides1 1CREOL School of Optics, University of Central Florida, Orlando, Florida 32816, USA 2MIT-Harvard Center for Ultracold Atoms, Research Laboratory of Electronics, and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA 3Department of A...

The spherical harmonic equations for radiative transport are a linear, hyperbolic set of balance laws that describe the state of a system of particles as they advect through and collide with a material medium. For regimes in which the collisionality of the system is light to moderate, significant qualitative differences have been observed between solutions, based on whether the angular approxim...

Accounting for uncertainty in three-dimensional (3D) shapes is important in a large number of scientific and engineering areas including: biometrics, biomedical imaging, and multimodality image registration. It is well known that 3D star-shaped objects can be represented by Fourier descriptors such as spherical harmonics and double Fourier series. However, the statistics of these spectral shape...

In this short note we propose a new method for construction new nice arrangement on the sphere Sd using the spaces of spherical harmonic.

We show a numerical evidence that a tethered surface model with extrinsic curvature undergoes a first-order crumpling transition between the smooth phase and a nonsmooth phase on triangulated tori. The results obtained in this Letter together with the previous ones on spherical surfaces lead us to conclude that the tethered surface model undergoes a first-order transition on compact surfaces.