Related papers: Determining Sphere Radius through Pairwise Distanc…
There is a growing interest in developing covariance functions for processes on the surface of a sphere due to wide availability of data on the globe. Utilizing the one-to-one mapping between the Euclidean distance and the great circle…
We consider the deconvolution problem for densities supported on a $(d-1)$-dimensional sphere with unknown center and unknown radius, in the situation where the distribution of the noise is unknown and without any other observations. We…
A new gridding technique for the solution of partial differential equations in cubical geometry is presented. The method is based on volume penalization, allowing for the imposition of a cubical geometry inside of its circumscribing sphere.…
This paper provides a survey of spherical designs and their applications, with a particular emphasis on the perspective of ``numerical analysis''. A set \(X_N\) of \(N\) points on the unit sphere \(\mathbb{S}^d\) is called a…
The Gromov-Hausdorff distance between two metric spaces measures how far the spaces are from being isometric. It has played an important and longstanding role in geometry and shape comparison. More recently, it has been discovered that the…
Mass and radius measurements of stars are important inputs for models of stellar structure. Binary stars are of particular interest in this regard, because astrometry and spectroscopy of a binary together provide the masses of both stars as…
We construct constraints from consistency between estimated parameters from different spheres, termed inter-sphere consistency. It facilitates more flexible calibration using only two spheres, which has been considered a challenging and not…
We propose new parameters to describe the geometry of a warped disc when viewed edge-on, a global warp parameter $w$, and a family of three parameters $A$, $B$ and $C$ that describe, independently, the shape of the warp. These parameters…
The numerical radius of a matrix is a scalar quantity that has many applications in the study of matrix analysis. Due to the difficulty in computing the numerical radius, inequalities bounding it have received a considerable attention in…
This paper presents a novel technique for camera calibration using a single view that incorporates a spherical mirror. Leveraging the distinct characteristics of the sphere's contour visible in the image and its reflections, we showcase the…
In this paper, we give a survey of various sphere theorems in geometry. These include the topological sphere theorem of Berger and Klingenberg as well as the differentiable version obtained by the authors. These theorems employ a variety of…
The transform considered in the paper averages a function supported in a ball in $\RR^n$ over all spheres centered at the boundary of the ball. This Radon type transform arises in several contemporary applications, e.g. in thermoacoustic…
Detection of circular objects in digital images is an important problem in several vision applications. Circle detection using randomized sampling has been developed in recent years to reduce the computational intensity. Randomized…
For millenia, sailors have used the empirical rule that the elevation angle of Polaris, the North Star, as measured by sextant, quadrant or astrolabe, is approximately equal to latitude. Here, we show using elementary trigonometry that…
Predicting the pose of objects from a single image is an important but difficult computer vision problem. Methods that predict a single point estimate do not predict the pose of objects with symmetries well and cannot represent uncertainty.…
We propose a new class of space-filling designs called rotated sphere packing designs for computer experiments. The approach starts from the asymptotically optimal positioning of identical balls that covers the unit cube. Properly scaled,…
We prove that the least-perimeter partition of the sphere into four regions of equal area is a tetrahedral partition.
We present a novel empirical method for correcting asteroid phase curves for rotational and geometrical effects using precomputed spin-and-shape models. Our approach normalizes sparse photometric data to a pole-on geometry, enabling…
Surveillance and surveying are two important applications of empirical research. A major part of terrain modelling is supported by photographic surveys which are used for capturing expansive natural surfaces using a wide range of sensors --…
This paper introduces a new analytical method for the determination of the coverage area modeling the Earth as an oblate ellipsoid of rotation. Starting from the knowledge of the satellite's position vector and the direction of the…