Related papers: On Invariance, Equivariance, Correlation and Convo…
Designing a convolution for a spherical neural network requires a delicate tradeoff between efficiency and rotation equivariance. DeepSphere, a method based on a graph representation of the sampled sphere, strikes a controllable balance…
Self-supervised learning (SSL) methods have achieved remarkable success in learning image representations allowing invariances in them - but therefore discarding transformation information that some computer vision tasks actually require.…
Many flexible parameterizations exist to represent data on the sphere. In addition to the venerable spherical harmonics, we have the Slepian basis, harmonic splines, wavelets and wavelet-like Slepian frames. In this paper we focus on the…
Deep learning based on deep neural networks of various structures and architectures has been powerful in many practical applications, but it lacks enough theoretical verifications. In this paper, we consider a family of deep convolutional…
Multivariate spatial data plays an important role in computational science and engineering simulations. The potential features and hidden relationships in multivariate data can assist scientists to gain an in-depth understanding of a…
State-of-the-art 2D image compression schemes rely on the power of convolutional neural networks (CNNs). Although CNNs offer promising perspectives for 2D image compression, extending such models to omnidirectional images is not…
The spherical harmonics $Y_{\ell m}(\theta,\varphi)$ are complex-valued functions on the surface of a sphere, and have found widespread application in physics and astronomy. Every physics students knows them from quantum mechanics and…
The dynamics in the photosphere is governed by the multi-scale turbulent convection termed as granulation and supergranulation. It is important to derive 3-dimensional velocity vectors to understand the nature of the turbulent convection.…
This paper presents a general form of the covariance matrix structure for a vector random field that is axially symmetric and mean square continuous on the sphere and provides a series representation for a longitudinally reversible one. The…
We propose a transform for signals defined on the sphere that reveals their localized directional content in the spatio-spectral domain when used in conjunction with an asymmetric window function. We call this transform the directional…
Hyperspectral imaging provides detailed information about the scanned objects, as it captures their spectral characteristics within a large number of wavelength bands. Classification of such data has become an active research topic due to…
Head-related transfer functions (HRTFs) are crucial for spatial soundfield reproduction in virtual reality applications. However, obtaining personalized, high-resolution HRTFs is a time-consuming and costly task. Recently, deep…
Spatial data display correlation between observations collected at neighboring locations. Generally, machine and deep learning methods either do not account for this correlation or do so indirectly through correlated features and thereby…
Variables adapted to the quantum dynamics of spherically symmetric models are introduced, which further simplify the spherically symmetric volume operator and allow an explicit computation of all matrix elements of the Euclidean and…
In many applications data are measured or defined on a spherical manifold; spherical harmonic transforms are then required to access the frequency content of the data. We derive algorithms to perform forward and inverse spin spherical…
Spatial field correlation functions represent a key quantity for the description of mesoscopic phenomena in disordered media and the optical characterization of complex materials. Yet many aspects related to the vector nature of light waves…
A fast algorithm is developed for the directional correlation of scalar band-limited signals and band-limited steerable filters on the sphere. The asymptotic complexity associated to it through simple quadrature is of order O(L^5), where 2L…
Graph-structured data is ubiquitous in scientific domains, where models often face imbalanced learning settings. In imbalanced regression, domain preferences focus on specific target value ranges that represent the most scientifically…
Coherent state theory is shown to reproduce three categories of representations of the spectrum generating algebra for an algebraic model: (i) classical realizations which are the starting point for geometric quantization; (ii) induced…
A simple derivation of the classical solutions of a nonlinear model describing a harmonic oscillator on the sphere and the hyperbolic plane is presented in polar coordinates. These solutions are then related to those in cartesian…