With inputs from RGB-D camera, industrial camera and wheel odometer, in this letter, we propose a geometry-based detecting method, by which the 3-D modulated LED map can be acquired with the aid of visual odometry algorithm from ORB-SLAM2 system when...
This paper presents relevant modern mathematical formulations for (classical) gauge field theories, namely, ordinary differential geometry, noncommutative geometry, and transitive Lie algebroids. They provide rigorous frameworks to describe Yang-Mill...
We give an intrinsic definition of the special geometry which arises in global N=2 supersymmetry in four dimensions. The base of an algebraic integrable system exhibits this geometry, and with an integrality hypothesis any special Kahler manifold i...
We define and investigate extension groups in the context of Arakelov geometry. The 'arithmetic extension groups' we introduce are extensions by groups of analytic types of the usual extension groups attached to $Ø_X$-modules over an arithmetic sc...
We interpret the log-Brunn-Minkowski conjecture of Böröczky-Lutwak-Yang-Zhang as a spectral problem in centro-affine differential geometry. In particular, we show that the Hilbert-Brunn-Minkowski operator coincides with the centro-affine Laplacian,...
In this paper, we study the differential invariants and the invariant heat flow in centro-affine geometry, proving that the latter is equivalent to the inviscid Burgers' equation. Furthermore, we apply the centro-affine invariants to develop an invar...
In this paper, the isoperimetric inequality in centro-affine plane geometry is obtained. We also investigate the long-term behavior of an invariant plane curve flow, whose evolution process can be expressed as a second-order nonlinear parabolic equat...
In geometry, a vertex (pl.: vertices or vertexes), also called a corner, is a point where two or more curves, lines, or line segments meet or intersect
It seems to be very unlikely that all relevant information in the stock market could be fully encoded in a geometrical shape. Still,the present paper will reveal the geometry behind the stock market transactions. The prices of market index (DJIA) sto...
We present StreamNet, an autoencoder architecture for the analysis of the highly heterogeneous geometry of large collections of white matter streamlines. This proposed framework takes advantage of geometry-preserving properties of the Wasserstein-1 m...
A lot of attention has been drawn over the last few years by the investigation of the geometry of spherical random eigenfunctions (random spherical harmonics) in the high frequency regime, i.e ., for diverging eigenvalues. In this paper, we present a...
We define a jet-space analog of the BV-Laplacian, avoiding delta-functions and infinite constants; instead we show that the main properties of the BV-Laplacian and its relation to the Schouten bracket originate from the underlying jet-space geometry....
In geometry, direction, also known as spatial direction, vector direction or relative direction, is the common characteristic of all rays which coincide
We study various information-theoretic measures and the information geometry of the Poincaré distributions and the related hyperboloid distributions, and prove that their statistical mixture models are universal density estimators of smooth densitie...
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 reliably recog...
We present a 3D face reconstruction system that aims at recovering the 3D facial geometry of babies from uncalibrated photographs, BabyNet. Since the 3D facial geometry of babies differs substantially from that of adults, baby-specific facial reconst...
We report on a project to use a theorem prover to find proofs of the theorems in Tarskian geometry. These theorems start with fundamental properties of betweenness, proceed through the derivations of several famous theorems due to Gupta and end with...
The subject of this PhD thesis is noncommutative geometry - more specifically spectral triples - and how it can be generalized to semi-Riemannian manifolds generally, and Lorentzian manifolds in particular. The first half of this thesis will thus be...
We propose a new description of the (4+N)-dimensional Arkani-Hamed-Dimopoulos-Dvali (ADD) model in a (4+1)-dimensional warped geometry to solve the gauge hierarchy problem. It has the same KK spectrum as in the ADD model and recovers its phenomenons...
This is an expository paper. We prove the Cannon-Thurston property for bounded geometry surface groups with or without punctures. We prove three theorems, due to Cannon-Thurston, Minsky and Bowditch. The proofs are culled out of earlier work of the...