We study Sobolev type estimates for the approximation order resulting from using strictly positive definite kernels to do interpolation on the n-sphere. The interpolation knots are scattered. Our approach partly follows the general theory of Golomb and Weinberger and related estimates. These error estimates are then based on series expansions of smooth functions in terms of spherical harmonics....

Biological rhythms such as circadian rhythms, biochemical rhythms and neural oscillators are based on the mathematical model of the theory of harmonic oscillators. These are solutions of certain second-order differential equations. They can also be viewed as spherical harmonics on the circle in the two-dimensional Euclidean space. The spherical harmonics on (n-1)-spheres and, more generally, th...

This paper presents a new set of hemispherical basis functions dedicated to hemispherical data representation. These functions are derived from associated Legendre polynomials. We demonstrate the usefulness of this basis for representation of surface reflectance functions, rendering using environment maps and for efficient global illumination computation using radiance caching. We show that our...

Experimental investigation of a speech enhancement algorithm is presented. The algorithm is designed for a spherical microphone array, and formulated in the spherical harmonics domain, based on a plane-wave model that is also formulated in the spherical harmonics domain. The proposed algorithm facilitates dereverberation by employing DOA estimation, rather that room impulse response identificat...

The real spherical harmonics have been used extensively in computer graphics, but the conventional representation is in terms of spherical coordinates and involves expensive trigonometric functions. While the polynomial form is often listed for low orders, directly evaluating the basis functions independently is inefficient. This paper will describe in detail how recurrence relations can be use...

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 provide some simple characterizations for the spherical harmonics coefficients of an isotropic random field on the sphere. The main result is a characterization of isotropic gaussian fields through independence of the coefficients of their development in spherical harmonics.

A brain surface reconstruction allows advanced analysis of structural and functional brain data that is not possible using volumetric data alone. However, the generation of a brain surface mesh from MRI data often introduces topological defects and artifacts that must be corrected. We show that it is possible to accurately correct these errors using spherical harmonics. Our results clearly demo...