Tensorial spin-s harmonics

Fast Spin ±2 Spherical Harmonics Transforms

An exact fast algorithm is developed for the direct spin-weighted spherical harmonics transforms of bandlimited spin ±2 functions on the sphere. First, we define spin functions on the sphere and their decomposition in an orthonormal basis of spin-weighted spherical harmonics. Second, we discuss the a priori O(L4) asymptotic complexity of the spin ±2 spherical harmonics transforms, where 2L stan...

Increasing the Dimension of Creativity in Rotation Invariant Feature Design Using 3D Tensorial Harmonics

Spherical harmonics are widely used in 3D image processing due to their compactness and rotation properties. For example, it is quite easy to obtain rotation invariance by taking the magnitudes of the representation, similar to the power spectrum known from Fourier analysis. We propose a novel approach extending the spherical harmonic representation to tensors of higher order in a very efficien...

Fluid Simulation on S using Spherical Harmonics

Fast spin ±2 spherical harmonics transforms and application in cosmology

An exact fast algorithm is developed for the spin-weighted spherical harmonics transforms of band-limited spin ±2 functions on the sphere. First, we recall the notion of spin functions on the sphere and their decomposition in an orthonormal basis of spin-weighted spherical harmonics. Second, we discuss the a priori O(L4) asymptotic complexity of the spin ±2 spherical harmonics transforms, where...

Tensorial Mixture Models

We introduce a generative model, we call Tensorial Mixture Models (TMMs) based on mixtures of basic component distributions over local structures (e.g. patches in an image) where the dependencies between the local-structures are represented by a ”priors tensor” holding the prior probabilities of assigning a component distribution to each local-structure. In their general form, TMMs are intracta...