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We improve the previously best known upper bounds on the sizes of $\theta$-spherical codes for every $\theta<\theta^*\approx 62.997^{\circ}$ at least by a factor of $0.4325$, in sufficiently high dimensions. Furthermore, for sphere packing…
Astronomical data does not always use Cartesian coordinates. Both all-sky observational data and simulations of rotationally symmetric systems, such as accretion and protoplanetary discs, may use spherical polar or other coordinate systems.…
Recent microscopy imaging techniques allow to precisely analyze cell morphology in 3D image data. To process the vast amount of image data generated by current digitized imaging techniques, automated approaches are demanded more than ever.…
Hyperspectral images often have hundreds of spectral bands of different wavelengths captured by aircraft or satellites that record land coverage. Identifying detailed classes of pixels becomes feasible due to the enhancement in spectral and…
The mathematical representations of data in the Spherical Harmonic (SH) domain has recently regained increasing interest in the machine learning community. This technical report gives an in-depth introduction to the theoretical foundation…
Whitening, or sphering, is a common preprocessing step in statistical analysis to transform random variables to orthogonality. However, due to rotational freedom there are infinitely many possible whitening procedures. Consequently, there…
We introduce a new method of symmetrization of mappings on the $n$-sphere ($n\geq 2$). They are applied to estimate solutions of quasilinear elliptic partial differential equations of $p$-Laplacian type, with combinations of Dirac measures…
A fast and exact algorithm is developed for the spin +-2 spherical harmonics transforms on equi-angular pixelizations on the sphere. It is based on the Driscoll and Healy fast scalar spherical harmonics transform. The theoretical exactness…
Most of existing superpixel methods are designed to segment standard planar images as pre-processing for computer vision pipelines. Nevertheless, the increasing number of applications based on wide angle capture devices, mainly generating…
Satellites mapping the spatial variations of the gravitational or magnetic fields of the Earth or other planets ideally fly on polar orbits, uniformly covering the entire globe. Thus, potential fields on the sphere are usually expressed in…
In polarization optics, various topological constructs, namely Poincar\'e spheres of different orders, are used to represent uniform and structured polarization distributions. Similarly, there are also structured polarization optical…
We extend our framework for 3D radiative transfer calculations with a non-local operator splitting methods along (full) characteristics to spherical and cylindrical coordinate systems. These coordinate systems are better suited to a number…
We present a general method for accelerating by more than an order of magnitude the convolution of pixelated function on the sphere with a radially-symmetric kernel. Our method splits the kernel into a compact real-space, and a compact…
The natural spherical projection associated with the Hierarchical Equal Area and isoLatitude Pixelisation, HEALPix, is described and shown to be one of an infinite class not previously documented in the cartographic literature. Projection…
We use group theoretic ideas and coset space methods to deal with problems in polarization optics of a global nature. These include the possibility of a globally smooth phase convention for electric fields for all points on the Poincar\'{e}…
A sphere is a fundamental geometric object widely used in (computer aided) geometric design. It possesses rational parameterizations but no parametric polynomial parameterization exists. The present study provides an approach to the optimal…
A generalization of the polar coding scheme called mixed-kernels is introduced. This generalization exploits several homogeneous kernels over alphabets of different sizes. An asymptotic analysis of the proposed scheme shows that its…
We present a formalism for analyzing a full-sky temperature and polarization map of the cosmic microwave background. Temperature maps are analyzed by expanding over the set of spherical harmonics to give multipole moments of the two-point…
Various integrals over elliptic integrals are evaluated as couplings on spheres, resulting in some integral and series representations for the mathematical constants $\pi$, $G$ and $\zeta(3)$.
The Poincar\'e sphere is a graphical representation in a three-dimensional space for the polarization of light. Similarly, an optical element with spatially varying birefringence can be represented by a surface on a four-dimensional…