相关论文: Reflection in a Translation Invariant Surface

Shape from shading is a classical inverse problem in computer vision. This shape reconstruction problem is inherently ill-defined; it depends on the assumed light source direction. We introduce a novel mathematical formulation for…

A theoretical study of the resonance optical response of assemblies of oriented short (as compared to an optical wavelength) linear Frenkel chains is carried out using a two-level model. We show that both transmittivity and reflectivity of…

We provide a deterministic channel model for a scenario where wireless connectivity is established through a reflection from a planar smooth surface of an infinite extent. The developed model is rigorously built upon the physics of wave…

In this dissertation, we explore the structure of inversion graphs of permutations--a class of graphs that naturally arises by representing each permutation as a graph, where vertices correspond to entries and edges encode inversions.…

Understanding reflection remains a long-standing challenge in 3D reconstruction due to the entanglement of appearance and geometry under view-dependent reflections. In this work, we present the Pygmalion Effect in Vision, a novel framework…

Reflection equation for the scattering of lines moving in half-plane is obtained. The corresponding geometric picture is related with configurations of half-planes touching the boundary plane in 2+1 dimensions. This equation can be obtained…

Recent neural rendering methods have demonstrated accurate view interpolation by predicting volumetric density and color with a neural network. Although such volumetric representations can be supervised on static and dynamic scenes,…

Symmetry is one of the significant visual properties inside an image plane, to identify the geometrically balanced structures through real-world objects. Existing symmetry detection methods rely on descriptors of the local image features…

We describe a method that uses total internal reflection at the water-air interface inside a large, transparent tank, to measure the interface's deflections. Using this configuration, we obtain an optical set-up where the liquid surface…

Obtaining complete information about the shape of an object by looking at it from a single direction is impossible in general. In this paper, we theoretically study obtaining differential geometric information of an object from orthogonal…

Diffraction tomography aims to recover an object's scattering potential from measured wave fields. In the classical setting, the object is illuminated by plane waves from many directions, and the Fourier diffraction theorem provides a…

Eliminating reflections caused by incident light interacting with reflective medium remains an ill-posed problem in the image restoration area. The primary challenge arises from the overlapping of reflection and transmission components in…

We introduce the notion centre of a convex set and study the space of continuous affine functions on a compact convex set with a centre. We show that these spaces are precisely the dual of a base normed space in which the underlying base…

The notion of a "root base" together with its geometry plays a crucial role in the theory of finite and affine Lie theory. However, it is known that such a notion does not exist for the recent generalizations of finite and affine root…

The purpose of this paper is to study the reflections of a convex body. In particular, we are interested in orthogonal reflections of its sections that can be extended to reflections of the whole body. For this reason, we need to study the…

Symmetry is an important factor in human perception in general, as well as in the visualization of graphs in particular. There are three main types of symmetry: reflective, translational, and rotational. We report the results of a human…

This paper considers some open questions related to the inverse problem of pure point diffraction, in particular, what types of objects may diffract, and which of these may exhibit the same diffraction. Some diverse objects with the same…

In many computer vision and shape analysis tasks, practitioners are interested in learning from the shape of the object in an image, while disregarding the object's orientation. To this end, it is valuable to define a rotation-invariant…

According to Huygens' principle, all points on a wave front act as secondary sources emitting spherical waves, and the envelope of these spherical waves forms a new wave front. In the mathematical formulation of Huygens' principle, the…

Given a genus two curve $X: y^2 = x^5 + a x^3 + b x^2 + c x + d$, we give an explicit parametrization of all other such curves $Y$ with a specified symplectic isomorphism on three-torsion of Jacobians $\mbox{Jac}(X)[3] \cong…