Related papers: Mapping on the HEALPix grid
HEALPix is a Hierarchical, Equal Area, and iso-Latitude Pixelisation of the sphere designed to support efficiently - local operations on the pixel set, - a hierarchical tree structure for multi-resolution applications, and - the global Fast…
HEALPix -- the Hierarchical Equal Area iso-Latitude Pixelization -- is a versatile data structure with an associated library of computational algorithms and visualization software that supports fast scientific applications executable…
HEALPix -- the Hierarchical Equal Area isoLatitude Pixelization -- has become a standard in high-energy and gravitational wave astronomy. Originally developed to improve the efficiency of all-sky Fourier analyses, it is now also utilized to…
HEALPix (Hierarchical Equal Area isoLatitude Pixelization) is a widely adopted spherical grid system in astrophysics, cosmology, and Earth sciences. Its equal-area, iso-latitude structure makes it particularly well-suited for large-scale…
Motivated by the desire for a new kind of approximation, we define a type of localization called pixelation. We present how pixelation manifests in representation theory and in the study of sites and sheaves. A path category is constructed…
High-resolution wide-angle fisheye images are becoming more and more important for robotics applications such as autonomous driving. However, using ordinary convolutional neural networks or vision transformers on this data is problematic…
In this paper we show that the spherical cap discrepancy of the point set given by centers of pixels in the HEALPix tessellation (short for Hierarchical, Equal Area and iso-Latitude Pixelation) of unit $2$-sphere is lower and upper bounded…
The initial descriptions of the FITS format provided a simplified method for describing the physical coordinate values of the image pixels, but deliberately did not specify any of the detailed conventions required to convey the complexities…
Scientific exploitation of the ever increasing volumes of astronomical data requires efficient and practical methods for data access, visualisation, and analysis. Hierarchical sky tessellation techniques enable a multi-resolution approach…
Compressed sensing has reinvigorated the field of non-Cartesian sampling in magnetic resonance imaging (MRI). Until now there has been no 3D radial view-order which meets all the desired characteristics for simultaneous…
This document presents HiPS, a hierarchical scheme for the description, storage and access of sky survey data. The system is based on hierarchical tiling of sky regions at finer and finer spatial resolution which facilitates a progressive…
The increasing volumes of astronomical data require practical methods for data exploration, access and visualisation. The Hierarchical Progressive Survey (HiPS) is a HEALPix based scheme that enables a multi-resolution approach to astronomy…
In Paper I, Greisen & Calabretta (2002) describe a generalized method for assigning physical coordinates to FITS image pixels. This paper implements this method for all spherical map projections likely to be of interest in astronomy. The…
Let \pi : X -> S be a morphism of algebraic stacks that is locally of finite presentation with affine stabilizers. We prove that there is an algebraic S-stack, the Hilbert stack, parameterizing proper algebraic stacks mapping quasi-finitely…
By combining tools from different areas of mathematics, we obtain 3D visualizations of elliptic curves over different fields that faithfully capture the underlying algebra and geometry.
Traditional visualisations are designed to be shown on a flat surface (screen or page) but most data is not "flat". For example, the surface of the earth exists on a sphere, however, when that surface is presented on a flat map, key…
As the most common representation for 3D shapes, mesh is often stored discretely with arrays of vertices and faces. However, 3D shapes in the real world are presented continuously. In this paper, we propose to learn a continuous…
Robots have the capability to collect large amounts of data autonomously by interacting with objects in the world. However, it is often not obvious \emph{how} to learning from autonomously collected data without human-labeled supervision.…
Superpixels have long been used in image simplification to enable more efficient data processing and storage. However, despite their computational potential, their irregular spatial distribution has often forced deep learning approaches to…
Let $K$ be a finite extension of the $p$-adic numbers $\mathbb Q_p$ with ring of integers $\mathcal O_K$, $\mathcal X$ a regular scheme, proper, flat, and geometrically irreducible over $\mathcal O_K$ of dimension $d$, and $\mathcal X_K$…