相关论文: Reflection in a Translation Invariant Surface

Invariant representations are core to representation learning, yet a central challenge remains: uncovering invariants that are stable and transferable without suppressing task-relevant signals. This raises fundamental questions, requiring…

We review the complex differential geometry of the space of oriented affine lines in ${\Bbb{R}}^3$ and give a description of Hamilton's characteristic functions for reflection in an oriented C$^1$ surface in terms of this geometry.

In this work, we propose an inverse rendering model that estimates 3D shape, spatially-varying reflectance, homogeneous subsurface scattering parameters, and an environment illumination jointly from only a pair of captured images of a…

In this work, we present a detailed procedure of computer implementation of the laws of refraction and reflection on an arbitrary surface with rotational symmetry with respect to the propagation axis. The goal is to facilitate the…

We study relations between reflections in (positive or negative) points in the complex hyperbolic plane. It is easy to see that the reflections in the points q_1,q_2 obtained from p_1,p_2 by moving p_1,p_2 along the geodesic generated by…

On the basis of general theoretical results developed previously in [JETP 112, 246 (2011)], we analyze the reflection of quasiresonant light from a plane surface of dense and disordered ensemble of motionless point scatters. Angle…

The problem of the reflectance of a photon by a metallic mirror whose position is treated quantum mechanically is considered. The interaction between the metallic surface and the light is treated classically. It is shown that the…

We study the problem of constructing an optical surface separating two homogeneous, isotropic media, one of which has a negative refractive index. In doing so, we develop a vector form of Snell's law, which is used to study surfaces…

We introduce a technique for recovering a sufficiently smooth function from its ray transform over a wide class of curves in a general region of Euclidean space. The method is based on a complexification of the underlying vector fields…

We are interested in the study of caustics by reflection of irreducible algebraic planar curves (in the complex projective plane). We prove the birationality of the caustic map (for a generic light position). We also give simple formulas…

Score-based diffusion models learn to reverse a stochastic differential equation that maps data to noise. However, for complex tasks, numerical error can compound and result in highly unnatural samples. Previous work mitigates this drift…

Light rays incident on a transparent object of uniform refractive index undergo deflections, which uniquely characterize the surface geometry of the object. Associated with each point on the surface is a deflection map (or spectrum) which…

Plane mirror can make one object into two for observers on the object's side. Yet, there seems no way to achieve the same effect for observers from all directions. In this letter, we will design a new class of gradient index lenses from…

Let $X$ be a smooth polarized algebraic surface over the compex number field. We discuss the invariants obtained from the moduli stacks of semistable sheaves of arbitrary ranks on $X$. For that purpose, we construct the virtual fundamental…

Reflected diffusions in convex polyhedral domains arise in a variety of applications, including interacting particle systems, queueing networks, biochemical reaction networks and mathematical finance. Under suitable conditions on the data,…

A light ray in space is characterized by two vectors: (i) a transverse spatial-vector associated with the point where the ray intersects a given spherical cap; (ii) an angular-frequency vector which defines the ray direction of propagation.…

We consider the inverse scattering problem associated with any number of interacting modes in one-dimensional structures. The coupling between the modes is contradirectional in addition to codirectional, and may be distributed continuously…

We formally deduce closed-form expressions for the transmitted effective wavenumber of a material comprising multiple types of inclusions or particles (multi-species), dispersed in a uniform background medium. The expressions, derived here…

Precise calibration is a must for high reliance 3D computer vision algorithms. A challenging case is when the camera is behind a protective glass or transparent object: due to refraction, the image is heavily distorted; the pinhole camera…

In this paper we will show how to constructed an Skew-Field with trace-preserving endomorphisms of the affine plane. Earlier in my paper, we doing a detailed description of endomorphisms algebra and trace-preserving endomorphisms algebra in…