Related papers: The Depth of a Hypersubstitution

In the investigation carried out, the superconducting nanotube paraconductivity calculation algorithm is defined more precisely.

Image super-resolution technology is the process of obtaining high-resolution images from one or more low-resolution images. With the development of deep learning, image super-resolution technology based on deep learning method is emerging.…

We prove a closed formula for the derivative, of any order, of a implicit function, in terms of some binomial building blocks, and explain the combinatorics behind the coefficients appearing in the formula.

In some super-resolution techniques, adjacent points are illuminated at different times. Thereby, their locations and light intensities can be detected even if the images are very blurred due to diffraction. According to conventional…

Let R = K[x1,...,xr] be a polynomial ring over a field K. Let G be a graph with vertex set {1,...,r} and let J be the cover ideal of G. We give a sharp bound for the stability index of symbolic depth function sdstab(J). In the case G is…

In this note we give a closed formula for Faltings' delta-invariant of a hyperelliptic Riemann surface.

We derive a formula connecting the orders of the automorphism groups of a finite group and of its covering groups.

Motivated by the human way of memorizing images we introduce their functional representation, where an image is represented by a neural network. For this purpose, we construct a hypernetwork which takes an image and returns weights to the…

The Simpson's formula is obtained by approximating the integral of a function on some interval by the integral of the quadratic polynomial determined by the function. However, a multidimensional analogue of the formula has not been given as…

We construct an explicit lower bound for the volume of a complex hyperbolic orbifold that depends only on dimension.

Hypersubstitutions are mappings which map operation symbols to terms. Terms can be visualized by trees. Hypersubstitutions can be extended to mappings defined on sets of trees. The nodes of the trees, describing terms, are labelled by…

In this note, a new method for deriving the volume of hypersphere is proposed by using probability theory. The explicit expression of the multiple times convolution of the probability density functions we should use is very complicated. But…

In this paper, we propose a dense depth estimation pipeline for multiview 360{\deg} images. The proposed pipeline leverages a spherical camera model that compensates for radial distortion in 360{\deg} images. The key contribution of this…

Estimating the relative depth of a scene is a significant step towards understanding the general structure of the depicted scenery, the relations of entities in the scene and their interactions. When faced with the task of estimating depth…

Monocular depth estimation is a highly challenging problem that is often addressed with deep neural networks. While these are able to use recognition of image features to predict reasonably looking depth maps the result often has low metric…

The Integral Image algorithm is often applied in tasks that require efficient integration over images, such as object detection. In this paper we discuss theoretical aspects of the algorithm's continuous version. We suggest to define the…

Monocular depth estimation is an interesting and challenging problem as there is no analytic mapping known between an intensity image and its depth map. Recently there has been a lot of data accumulated through depth-sensing cameras, in…

We give a decomposition formula for computing the state polytope of a reducible variety in terms of the state polytopes of its components.

In monocular depth estimation, disturbances in the image context, like moving objects or reflecting materials, can easily lead to erroneous predictions. For that reason, uncertainty estimates for each pixel are necessary, in particular for…

The concept of illumination bodies studied in convex geometry is used to amend the halfspace depth for multivariate data. The proposed notion of illumination enables finer resolution of the sample points, naturally breaks ties in the…