Related papers: Spherical harmonics entropy for optimal 3D modelin…
Segmentation, a useful/powerful technique in pattern recognition, is the process of identifying object outlines within images. There are a number of efficient algorithms for segmentation in Euclidean space that depend on the variational…
P. Baird and the second author studied harmonic morphisms from a three-dimensional simply-connected space form to a surface and obtained a complete local and global classification of them. In this paper, we obtain a description of all…
Real-space refinement of atomic models in macromolecular crystallography or in cryo electron microscopy fits a model to a map obtained experimentally. This requires generating model maps of a limited resolution which moreover may vary from…
The transport of charged particles or photons in a scattering medium can be modelled with a Boltzmann equation. The mathematical treatment for scattering in such scenarios is often simplified if evaluated in a frame where the scattering…
Applying convolutional neural networks to spherical images requires particular considerations. We look to the millennia of work on cartographic map projections to provide the tools to define an optimal representation of spherical images for…
The Shannon entropy, the desequilibrium and their generalizations (R\'enyi and Tsallis entropies) of the three-dimensional single-particle systems in a spherically-symmetric potential $V(r)$ can be decomposed into angular and radial parts.…
Observations and theoretical calculations have shown the importance of non-spherically symmetric structures in supernovae. Thus, the interpretation of observed supernova spectra requires the ability to solve the transfer equation in 3-D…
Many problems across computer vision and the natural sciences require the analysis of spherical data, for which representations may be learned efficiently by encoding equivariance to rotational symmetries. We present a generalized spherical…
A method is described by which a function defined on a cubic grid (as from a finite difference solution of a partial differential equation) can be resolved into spherical harmonic components at some fixed radius. This has applications to…
Magnetic Resonance Imaging (MRI) is used in everyday clinical practice to assess brain tumors. Several automatic or semi-automatic segmentation algorithms have been introduced to segment brain tumors and achieve an expert-like accuracy.…
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…
In this paper, we present a robust spherical harmonics approach for the classification of point cloud-based objects. Spherical harmonics have been used for classification over the years, with several frameworks existing in the literature.…
Semantic segmentation for spherical data is a challenging problem in machine learning since conventional planar approaches require projecting the spherical image to the Euclidean plane. Representing the signal on a fundamentally different…
In the last decade diffusion MRI has become a powerful tool to non-invasively study white-matter integrity in the brain. Recently many research groups have focused their attention on multi-shell spherical acquisitions with the aim of…
In this paper we study the recurrence relations in the spin-weighted spheroidal harmonics (SWSHs) through super-symmetric quantum mechanics. We use the shape invariance property to solve the spin-weighted spheroidal wave equations. The…
We report an extension of the source imaging method for analyzing three-dimensional sources from three-dimensional correlations. Our technique consists of expanding the correlation data and the underlying source function in spherical…
3D Gaussian Splatting is emerging as a state-of-the-art technique in novel view synthesis, recognized for its impressive balance between visual quality, speed, and rendering efficiency. However, reliance on third-degree spherical harmonics…
We demonstrate a fast spin-s spherical harmonic transform algorithm, which is flexible and exact for band-limited functions. In contrast to previous work, where spin transforms are computed independently, our algorithm permits the…
We propose an image processing scheme based on reordering of its patches. For a given corrupted image, we extract all patches with overlaps, refer to these as coordinates in high-dimensional space, and order them such that they are chained…
Associated Legendre polynomials and spherical harmonics are central to calculations in many fields of science and mathematics - not only chemistry but computer graphics, magnetic, seismology and geodesy. There are a number of algorithms for…