Related papers: The Depth of a Hypersubstitution
General structure of the multivariate plain and q-hypergeometric terms and univariate elliptic hypergeometric terms is described. Some explicit examples of the totally elliptic hypergeometric terms leading to multidimensional integrals on…
We consider the following problem: Given a nested sum expression, find a sum representation such that the nested depth is minimal. We obtain a symbolic summation framework that solves this problem for sums defined, e.g., over…
Neural networks have shown great abilities in estimating depth from a single image. However, the inferred depth maps are well below one-megapixel resolution and often lack fine-grained details, which limits their practicality. Our method…
We give a formula and an estimation for the number of irreducible polynomials in two (or more) variables over a finite field.
We define and inverstigate a generalization of the pfaffian for multiple array which interpolate between the hyperdeterminant and the hyperp-faffian.
In this paper an explicit formula for a lower bound on the volume of a hyperbolic orbifold, dependent on dimension and the maximal order of torsion in the orbifolds' fundamental group, is constructed.
Depth information plays a crucial role in autonomous systems for environmental perception and robot state estimation. With the rapid development of deep neural network technology, depth estimation has been extensively studied and shown…
We prove several inequalities estimating the distance between volumes of two bodies in terms of the maximal or minimal difference between areas of sections or projections of these bodies. We also provide extensions in which volume is…
Single-view depth estimation refers to the ability to derive three-dimensional information per pixel from a single two-dimensional image. Single-view depth estimation is an ill-posed problem because there are multiple depth solutions that…
We consider possible reconstructions of a binary image of which the row and column sums are given. For any reconstruction we can define the length of the boundary of the image. In this paper we prove a new lower bound on the length of this…
Hyperdimensional (HD) computing is a set of neurally inspired methods for obtaining high-dimensional, low-precision, distributed representations of data. These representations can be combined with simple, neurally plausible algorithms to…
Blur is an image degradation that is difficult to remove. Invariants with respect to blur offer an alternative way of a~description and recognition of blurred images without any deblurring. In this paper, we present an original unified…
We give explicit formulas for the Hodge filtration on mixed Hodge modules associated with certain hypersurfaces.
The perception of transparent objects is one of the well-known challenges in computer vision. Conventional depth sensors have difficulty in sensing the depth of transparent objects due to refraction and reflection of light. Previous…
We discuss a generalisation of the Herbert formula for double points, when the normal bundle of an immersion admits an additional structure, and an application.
We showed that a 2D depth map representing an incoherent 3D opaque scene is directly encoded in the response function of an imaging optics. As a result, the optics creates an image that depends nonlinearly on the depth map. Furthermore,…
We propose a simple derivation of an upper bound for the perimeter of an ellipse. The procedure, which relies on the use of elliptic integrals, consists in introducing, via inequalities and convexity properties, specific integrals which can…
Existing depth estimation methods are fundamentally limited to predicting depth on discrete image grids. Such representations restrict their scalability to arbitrary output resolutions and hinder the geometric detail recovery. This paper…
Conditions, related to the so-called bending problem are considered for hypersurfaces of a pseudo-Euclidean space. Corresponding theorems are proved.
Any permutation-invariant function of data points $\vec{r}_i$ can be written in the form $\rho(\sum_i\phi(\vec{r}_i))$ for suitable functions $\rho$ and $\phi$. This form - known in the machine-learning literature as Deep Sets - also…