Spherical Harmonics arise on the sphere S in the same way that the (Fourier) exponential functions {e}k∈Z arise on the circle. Spherical Harmonic series have many of the same wonderful properties as Fourier series, but have lacked one important thing: a numerically stable fast transform analogous to the Fast Fourier Transform. Without a fast transform, evaluating (or expanding in) Spherical Har...

Illumination can have a significant impact on the appearance of surfaces, as the patterns of shading, specularities and shadows change. For instance, some images of a face under different lighting conditions are shown in figure 1. Differences in lighting can often play a much greater role in image variability of human faces than differences between individual people. Lighting designers in movie...

A sharp upper bound for the number of nodal domains of spherical harmonics for the rst six eigenvalues is deduced.

We construct classes of nonstationary wavelets generated by what we call spherical basis functions (SBFs), which comprise a subclass of Schoen-berg's positive deenite functions on the m-sphere. The wavelets are intrinsically deened on the m-sphere, and are independent of the choice of coordinate system. In addition, they may be orthogonalized easily, if desired. We will discuss decomposition, r...

In this paper, we have proposed a method for 2D image retrieval based on object shapes. The method relies on transforming the 2D images into 3D space based on distance transform. Spherical harmonics are obtained for the 3D data and used as descriptors for the underlying 2D images. The proposed method is compared against two existing methods which use spherical harmonics for shape based retrieva...

We investigate the numerics behind the numerical solution of the Boltzmann transport equation using an expansion of the distribution function in spherical harmonics for the purpose of electronic device simulation. Traditional implementations of higher order spherical harmonics expansions suffer from huge memory requirements especially for two and three dimensional devices. To overcome these com...

The SO(5)⊃ SO(3) spherical harmonics form a natural basis for expansion of nuclear collective model angular wave functions. They underlie the recently-proposed algebraic method for diagonalization of the nuclear collective model Hamiltonian in an SU(1, 1)× SO(5) basis. We present a computer code for explicit construction of the SO(5)⊃ SO(3) spherical harmonics and use them to compute the Clebsc...

An approach to real-valued time-domain implementation of modal beamformer for spherical microphone arrays is proposed. The advantage of the time-domain implementation is that we can update the beamformer when each new snapshot arrives. Our technique is based on a modified filter-and-sum spherical harmonics domain (SHD) beamforming structure. The time series received at the microphones are conve...

The inherent complexity of the radiative transfer equation makes the exact treatment of radiative heat transfer impossible even for idealized situations and simple boundary conditions. Therefore, a wide variety of efficient solution methods have been developed for the RTE. Among these solution methods the spherical harmonics method, the moment method, and the discrete ordinates method provide m...