Related papers: The Spherical Mean Transform with Data on a Parabo…

Many computer vision challenges require continuous outputs, but tend to be solved by discrete classification. The reason is classification's natural containment within a probability $n$-simplex, as defined by the popular softmax activation…

We establish injectivity results for three different spherical means on an $H$-type group, $G$. First is the standard spherical means which is defined to be the average of a function over the spheres in the complement of the center, second…

We investigate discrete spin transformations, a geometric framework to manipulate surface meshes by controlling mean curvature. Applications include surface fairing -- flowing a mesh onto say, a reference sphere -- and mesh extrusion --…

Using reduction of spherical functions, we obtain generators of the algebra and the field of invariants for the coadjoint representation of Borel and maximal nilpotent subalgebras of simple Lie algebras.

In the present paper, we consider two applications of the pentagon equation. The first deals with actions of flips on edges of triangulations labelled by rational functions in some variables. The second can be formulated as a system of…

Spatial stochastic processes that are modeled over the entire Earth's surface require statistical approaches that directly consider the spherical domain. Here, we extend the notion of intrinsic random functions (IRF) to model non-stationary…

We present a novel method for reconstructing the shape of an object from measured gradient data. A certain class of optical sensors does not measure the shape of an object, but its local slope. These sensors display several advantages,…

It was shown by E. Gluskin and V.D. Milman in [GAFA Lecture Notes in Math. 1807, 2003] that the classical arithmetic-geometric mean inequality can be reversed (up to a multiplicative constant) with high probability, when applied to…

Spherical regression explores relationships between variables on spherical domains. We develop a nonparametric model that uses a diffeomorphic map from a sphere to itself. The restriction of this mapping to diffeomorphisms is natural in…

This paper presents some results on a well-known problem in Algebraic Signal Sampling and in other areas of applied mathematics: reconstruction of piecewise-smooth functions from their integral measurements (like moments, Fourier…

We prove surface and volume mean value formulas for classical solutions to uniformly elliptic equations in divergence form with H\"{o}lder continuous coefficients. The kernels appearing in the integrals are supported on the level and…

We consider in the plane the problem of reconstructing a domain from the normal derivative of its Green's function with pole at a fixed point in the domain. By means of the theory of conformal mappings, we obtain existence, uniqueness,…

Let $\mathcal{O}$ be a set of $k$ orientations in the plane, and let $P$ be a simple polygon in the plane. Given two points $p,q$ inside $P$, we say that $p$ $\mathcal{O}$-\emph{sees} $q$ if there is an $\mathcal{O}$-\emph{staircase}…

The mean center of a geographical region, including continents and countries, has been mostly determined to study the trend of population migration, the shift of economic hubs, and the spatial change of extreme climate events. However, the…

In order to produce high dynamic range images in radio interferometry, bright extended sources need to be removed with minimal error. However, this is not a trivial task because the Fourier plane is sampled only at a finite number of…

We introduce a statistical extension of the classic Poisson Surface Reconstruction algorithm for recovering shapes from 3D point clouds. Instead of outputting an implicit function, we represent the reconstructed shape as a modified Gaussian…

The concept of turnaround surface in an accelerating universe is generalized to arbitrarily large deviations from spherical symmetry, to close the gap between the idealized theoretical literature and the real world observed by astronomers.…

Any function from a round $n$-dimensional sphere of radius $r$ into $n$-dimensional Euclidean space must distort the metric additively by at least $\displaystyle \frac{\pi r}{1 + \sqrt{1 - \frac{2}{n+2}}}$ if $n$ is even and $\displaystyle…

Basis functions which are invariant under the operations of a rotational point group $G$ are able to describe any 3-D object which exhibits the rotational point group symmetry. However, in order to characterize the spatial statistics of an…

This letter considers the problem of recovering a positive stream of Diracs on a sphere from its projection onto the space of low-degree spherical harmonics, namely, from its low-resolution version. We suggest recovering the Diracs via a…