Related papers: The Depth of a Hypersubstitution
It is shown how the dimension of any arbitrary over-determined system of differential equations can be reduced, which makes the system suitable for numerical solution modeling. Specifically, over-determined equations of hydrodynamics are…
We present a method for inferring dense depth maps from images and sparse depth measurements by leveraging synthetic data to learn the association of sparse point clouds with dense natural shapes, and using the image as evidence to validate…
The goal of our work is to complete the depth channel of an RGB-D image. Commodity-grade depth cameras often fail to sense depth for shiny, bright, transparent, and distant surfaces. To address this problem, we train a deep network that…
We present a new method for 3D shape reconstruction from a single image, in which a deep neural network directly maps an image to a vector of network weights. The network \textcolor{black}{parametrized by} these weights represents a 3D…
We survey some aspects of the perfect matching problem in hypergraphs, with particular emphasis on structural characterisation of the existence problem in dense hypergraphs and the existence of designs.
Depth image super-resolution is an extremely challenging task due to the information loss in sub-sampling. Deep convolutional neural network have been widely applied to color image super-resolution. Quite surprisingly, this success has not…
This paper will be replaced later by a revised version.
We consider the characteristic problem for the ultrahyperbolic equation in the Euclidean space. The value of a solution is prescribed on the characteristic hyperplane. A well-posed set-up of the problem is discussed. We obtain a certain…
We survey recent studies and results on the following problem: which numerical functions can be the depth function of powers and symbolic powers of homogeneous ideals.
We extend the definition of algebraic entropy to semi-discrete (difference-differential) equations. Calculating the entropy for a number of integrable and non integrable systems, we show that its vanishing is a characteristic feature of…
Depth in the real world is rarely singular. Transmissive materials create layered ambiguities that confound conventional perception systems. Existing models remain passive; conventional approaches typically estimate static depth maps…
Integral transformations are used to estimate high order derivatives of various special functions. Applications are given to numerical integration, where estimates of high order derivatives of the integrand are needed to achieve bounds on…
We present a novel approach designed to address the complexities posed by challenging, out-of-distribution data in the single-image depth estimation task. Starting with images that facilitate depth prediction due to the absence of…
In this article, we define the notion of a filtration and then give the basic theorems on initial and progressive enlargements of filtrations.
Two approximations of the integral of a class of sinusoidal composite functions, for which an explicit form does not exist, are derived. Numerical experiments show that the proposed approximations yield an error that does not depend on the…
We consider shift spaces in which elements of the alphabet may overlap nontransitively. We define a notion of entropy for such spaces, give several techniques for computing lower bounds for it, and show that it is equal to a limit of…
A method for computing the multigraded Hilbert depth of a module was presented in [16]. In this paper we improve the method and we introduce an effective algorithm for performing the computations. In a particular case, the algorithm may…
The Whittaker function and its diverse extensions have been actively investigated. Here we introduce an extension of the Whittaker function by using the known extended confluent hypergeometric function $\Phi_{p,v}$ and investigate some of…
Hilbert algebras are the implicative subreducts of Heyting algebras. It is shown that having depth at most n is an equational condition in Hilbert algebras. This generalizes an analogous well-known result in the setting of Heyting algebras.
We derive continuity equation and exact expression for flow probability density in a space with arbitrary deformed algebra leading to minimal length. In coordinate representation the flow probability density is presented as infinite series…