Related papers: Ambiguities in a Problem in Planar Geodesy
The two-dimensional surface of a bi-axial ellipsoid is characterized by the lengths of its major and minor axes. Longitude and latitude span an angular coordinate system across. We consider the egg-shaped surface of constant altitude above…
Projective geometry provides the preferred framework for most implementations of Euclidean space in graphics applications. Translations and rotations are both linear transformations in projective geometry, which helps when it comes to…
A set $L$ of straight lines and a set $P$ of points in the Euclidean plane define an arrangement $\mathcal{A}$ = ($L$, $P$) of construction lines and registration marks, if and only if: (1) any point in $P$ is a point of intersection of at…
Two averaging algorithms are considered which are intended for choosing an optimal plane and an optimal circle approximating a group of points in three-dimensional Euclidean space.
There are two problems Analytical Geometry with facing anyone who studies this discipline: define the nature of the locus represented by the general equation 2do degree in two or three variables: That curve represents the plane? What…
Extracting planes from a 3D scene is useful for downstream tasks in robotics and augmented reality. In this paper we tackle the problem of estimating the planar surfaces in a scene from posed images. Our first finding is that a surprisingly…
In this paper, we consider the rectilinear one-center problem on uncertain points in the plane. In this problem, we are given a set $P$ of $n$ (weighted) uncertain points in the plane and each uncertain point has $m$ possible locations each…
Algorithms for the computation of the forward and inverse geodesic problems for an ellipsoid of revolution are derived. These are accurate to better than 15 nm when applied to the terrestrial ellipsoids. The solutions of other problems…
An important problem in analytic and geometric combinatorics is estimating the number of lattice points in a compact convex set in a Euclidean space. Such estimates have numerous applications throughout mathematics. In this note, we exhibit…
We study some methods of subgradient projections for solving a convex feasibility problem with general (not necessarily hyperplanes or half-spaces) convex sets in the inconsistent case and propose a strategy that controls the relaxation…
Algebraic statistics is concerned with the study of probabilistic models and techniques for statistical inference using methods from algebra and geometry. This article presents a list of open mathematical problems in this emerging field,…
A basic problem in computer vision is to understand the structure of a real-world scene given several images of it. Here we study several theoretical aspects of the intra multi-view geometry of calibrated cameras when all that they can…
This paper presents a new method to recover the relative pose between two images, using three points and the vertical direction information. The vertical direction can be determined in two ways: 1- using direct physical measurement like IMU…
We study the understanding of deep neural networks from the scope in which they are trained on. While the accuracy of these models is usually impressive on the aggregate level, they still make mistakes, sometimes on cases that appear to be…
This paper investigates the relationship between a system of differential equations and the underlying geometry associated with it. The geometry of a surface determines shortest paths, or geodesics connecting nearby points, which are…
We discuss the interpretation of the angles in the Geodesic Light-Cone (GLC) coordinates. In particular, we clarify the way in which these angles can be identified with the observed ones. We show that, although this identification is always…
Goals for planning problems are typically conceived of as subsets of the state space. However, for many practical planning problems in robotics, we expect the robot to predict goals, e.g. from noisy sensors or by generalizing learned models…
We provide a new algebraic solution procedure for the global positioning problem in $n$ dimensions using $m$ satellites. We also give a geometric characterization of the situations in which the problem does not have a unique solution. This…
We geometrically analyze the problem of estimating parameters related to the shape and size of a two-dimensional target object on the plane by using randomly distributed distance sensors whose locations are unknown. Based on the analysis…
In multiview geometry when correspondences among multiple views are unknown the image points can be understood as being unlabeled. This is a common problem in computer vision. We give a novel approach to handle such a situation by regarding…