相关论文: Global Illumination of non-Euclidean spaces
We propose a quantum metrology protocol for the localization of a non-cooperative point-like target in three-dimensional space, by illuminating it with electromagnetic waves. It employs all the spatial degrees of freedom of N entangled…
In this paper, we introduce a mathematical structure called Euclidean Universe. This structure provides a basic framework for Non-Archimedean Mathematics and in particular for Nonstandard Analysis.
Random search methods are widely used for global optimization due to their theoretical generality and implementation simplicity. This paper proposes a depth-first directional search (DFDS) algorithm for globally solving nonconvex…
Inverse rendering of outdoor scenes from unconstrained image collections is a challenging task, particularly illumination/albedo ambiguities and occlusion of the illumination environment (shadowing) caused by geometry. However, there are…
A study of the generalized Weierstrass system which can be used to induce mean curvature surfaces in three-dimensional Euclidean space is presented.
We propose a modification of the three-manifold invariant based on the use of Euclidean metric values ascribed to the elements of manifold triangulation. We thus obtain a nontrivial invariant that can, in particular, distinguish…
We consider the challenging problem of outdoor lighting estimation for the goal of photorealistic virtual object insertion into photographs. Existing works on outdoor lighting estimation typically simplify the scene lighting into an…
This paper tackles a new photometric stereo task, named universal photometric stereo. Unlike existing tasks that assumed specific physical lighting models; hence, drastically limited their usability, a solution algorithm of this task is…
Differentiable rendering methods promise the ability to optimize various parameters of 3d scenes to achieve a desired result. However, lighting design has so far received little attention in this field. In this paper, we introduce a method…
I describe the manifestation of the non-Euclidean geometry in the behavior of collective observables of some complex physical systems. Specifically, I consider the formation of equilibrium shapes of plants and statistics of sparse random…
In this paper the use of Random Sprays Retinex (RSR) algorithm for global illumination estimation is proposed and its feasibility tested. Like other algorithms based on the Retinex model, RSR also provides local illumination estimation and…
Motivated by the problem of counting finite BPS webs, we count certain immersed metric graphs, tripods, on the flat torus. Classical Euclidean geometry turns this into a lattice point counting problem in $\mathbb C^2$, and we give an…
Here we present a new non-parametric approach to density estimation and classification derived from theory in Radon transforms and image reconstruction. We start by constructing a "forward problem" in which the unknown density is mapped to…
We present a method to compute the magnification of a finite source star lensed by a triple lens system based on the image boundary (contour integration) method. We describe a new procedure to obtain continuous image boundaries from…
In this paper, we seek to construct nontrivial global solutions to some quasilinear wave equations in three space dimensions. We first present a conditional result on the construction of nontrivial global solutions to a general system of…
A result due to Burago and Zalgaller (1960, 1995) states that every orientable polyhedral surface, one that is obtained by gluing Euclidean polygons, has an isometric piecewise linear (PL) embedding into Euclidean space $\mathbb{E}^3$. A…
In this article we propose an original classification method for unobscured imaging systems unfolded in two dimensions. This classification is based on a study of off-axis properties, and relies on topology and algorithm of real algebraic…
In the present paper which a sequel to dg-ga/9511005 and dg-ga//9610013 a global Weierstrass representation of an arbitrary closed oriented surface of genus $\geq 1$ in the the three-space is constructed. The Weierstrass spectrum of a torus…
We construct the first non-trivial examples of compact non-isometric Alexandrov spaces which are isospectral with respect to the Laplacian and not isometric to Riemannian orbifolds. This construction generalizes independent earlier results…
We present a novel algorithm for light source estimation in scenes reconstructed with a RGB-D camera based on an analytically-derived formulation of path-tracing. Our algorithm traces the reconstructed scene with a custom path-tracer and…