相关论文: Curved Holographic Optical Elements from a Geometr…

Modeling deformations of a real object is an important task in computer vision, biomedical engineering and biomechanics. In this paper, we focus on a situation where a three-dimensional object is rotationally deformed about a fixed axis,…

Nanostructured materials have recently emerged as a promising approach for material appearance design. Research has mainly focused on creating structural colours by wave interference, leaving aside other important aspects that constitute…

In this paper, we investigate the relation between the curvature of the physical space and the deformation function of the deformed oscillator algebra using non-linear coherent states approach. For this purpose, we study two-dimensional…

An unobstructedness theorem is proved for deformations of compact holomorphic Poisson manifolds and applied to a class of examples. These include certain rational surfaces and Hilbert schemes of points on Poisson surfaces. We study in…

We study the evolution of holographic screens, both generally and in explicit examples, including cosmology and gravitational collapse. A screen $H$ consists of a one-parameter sequence of maximal surfaces called leaves. Its causal…

Visual events in computer vision are studied from the perspective of algebraic geometry. Given a sufficiently general curve or surface in 3-space, we consider the image or contour curve that arises by projecting from a viewpoint.…

The mechanism of wavefront reconstruction by a geometric-optical reflection of reconstructing light from surfaces with constant phase differences between the object and reference waves used to record the interference fringe structure in the…

We propose a Lie geometric point of view on flat fronts in hyperbolic space as special omega-surfaces and discuss the Lie geometric deformation of flat fronts.

An effective theory based on wave optics is used to describe indeterminacy of position in holographic spacetime with a UV cutoff at the Planck scale. Wavefunctions describing spacetime positions are modeled as complex disturbances of…

Deformations of spacelike hypersurfaces in space-time play an important role in discussions of general covariance and slicing independence in gravitational theories. In a canonical formulation, they provide the geometrical meaning of gauge…

We describe our recent work on deformations of hyperelliptic curves by means of integrable hierarchy of hydrodynamic type (nlin.SI/0205012). We also discuss a further extension to the case of non-hyperelliptic curves.

We apply the technique of jet differentials to establish a Gauss curvature estimate for an open Riemann surface $M$, equipped with a conformal metric induced from a nonconstant holomorphic map that is highly ramified over a generic…

Object parsing and segmentation from point clouds are challenging tasks because the relevant data is available only as thin structures along object boundaries or other features, and is corrupted by large amounts of noise. To handle this…

Reconstructing dynamic scenes with complex human-object interactions is a fundamental challenge in computer vision and graphics. Existing Gaussian Splatting methods either rely on human pose priors while neglecting dynamic objects, or…

We analyze the nonlinear optics of quasi one-dimensional quantum graphs and manipulate their topology and geometry to generate for the first time nonlinearities in a simple system approaching the fundamental limits of the first and second…

The recently proposed optical elements containing semitransparent wavelike films embedded into the transparent material are investigated. Such optical elements do not distort a wave transmitted through them. Novel optical elements can be…

A nonrelativistic quantum mechanical particle moving freely on a curved surface feels the effect of the nontrivial geometry of the surface through the kinetic part of the Hamiltonian, which is proportional to the Laplace-Beltrami operator,…

We suggest a holographic energy model in which the energy coming from spatial curvature, matter and radiation can be obtained by using the particle horizon for the infrared cut-off. We show the consistency between the holographic…

Holographic screens are codimension-one hypersurfaces that extend the notion of apparent horizons to general (non-black hole) spacetimes and that display interesting thermodynamic properties. We show that if a spacetime contains a…

In this article we propose a new and so-called holomorphic deformation scheme for locally convex algebras and Hopf algebras. Essentially we regard converging power series expansion of a deformed product on a locally convex algebra, thus…