Spherical Harmonic Transforms (SHTs) which are essentially Fourier transforms on the sphere are critical in global geopotential and related applications. Discrete SHTs are more complex to optimize computationally than Fourier transforms in the sense of the well-known Fast Fourier Transforms (FFTs). Furthermore, for analysis purposes, discrete SHTs are difficult to formulate for an optimal discr...

The description of 3D shapes using features that possess descriptive power and are invariant under similarity transformations is one of the most challenging issues in contentbased 3D model retrieval. Spherical harmonics-based descriptors have been proposed for obtaining rotation invariant representations. However, spherical harmonic analysis is based on a latitude-longitude parameterization of ...

We show that sparse spherical harmonic expansions can be recovered from a small number of randomly chosen samples on the sphere using `1-minimization. To this end, we establish the restricted isometry property of an associated preconditioned random measurement matrix.

In diffusion magnetic resonance imaging (dMRI), the diffusion signal can be reconstructed from measurements collected on single or multiple spheres in q-space using a spherical harmonic expansion. The number of measurements that can be acquired is severely limited and should be as small as possible. Previous sampling schemes have focused on using antipodal symmetry to reduce the number of sampl...

sectionHarmonic Volumetric Parameterization using MFS After the decomposition of a given object M , we get a set of star shapes {Mi}, each region being guarded by a point gi. Then we can parameterize each subregion onto a solid sphere. A key property that we will show shortly is that such a harmonic map is guaranteed to be bijective. The harmonic map can be computed using the method of fundamen...

The Earth’s gravitational field is represented by its multipole moments. Multipole moments have two kinds of equivalent forms, that is, the Cartesian symmetric and tracefree tensors and the spherical harmonic coefficients. The relation between these two forms is interesting and useful for some practical problems. Under Newtonian approximation, there exists a simple relation between the aforesai...

Spectral methods using spherical harmonic basis functions have proven to be very eeective in geophysical and astrophysical simulations. It is an unfortunate fact, however , that spurious oscillations, known as the Gibbs phenomenon, contaminate these spectral solutions, particularly in regions where discontinuities or steep gradients occur. They are also apparent in the polar regions even when c...

Environment-mapped rendering of Lambertian isotropic surfaces is common, and a popular technique is to use a quadratic spherical harmonic expansion. This compact irradiance map representation is widely adopted in interactive applications like video games. However, many materials are anisotropic, and shading is determined by the local tangent direction, rather than the surface normal. Even for v...

Satellite gradiometry and its instrumentation is an ultra-sensitive detection technique of the space gravitational gradient (i.e. the Hesse tensor of the gravitational potential). Gradiometry will be of great signiicance in inertial navigation, gravity survey, geodynamics and earthquake prediction research. In this paper, satellite gradiometry formulated as an inverse problem of satellite geode...

Surface registration between cortical surfaces is crucial in medical imaging for performing systematic comparisons between brains. Landmark-matching registration that matches anatomical features, called the sulcal landmarks, is often required to obtain a meaningful 1-1 correspondence between brain surfaces. This is commonly done by parameterizing the surface onto a simple parameter domain, such...