Related papers: A Fundamental Group for Digital Images
Image compression has been applied in the fields of image storage and video broadcasting. However, it's formidably tough to distinguish the subtle quality differences between those distorted images generated by different algorithms. In this…
Every two-sided ideal $\mathfrak a$ in the integral group ring $\mathbb Z[G] $ of a group $G$ determines a normal subgroup $G \cap (1 + \mathfrak a)$ of $G$. In this paper certain problems related to the identification of such subgroups,…
Heisenberg groups over algebras with central involution and their automorphism groups are constructed. The complex quaternion group algebra over a prime field is used as an example. Its subspaces provide finite models for each of the real…
We prove a division algorithm for group rings of high genus surface groups and use it to show that some $2$-complexes with surface fundamental groups are standard. We also give an application of division to cohomological dimension of…
In this paper, for given an algebraic theory $T$ whose category $C$ of models is semi-abelian, we consider the topological models of $T$ called topological $T$-algebras and obtain some results related to the fundamental groups of…
Digital topological methods are often used on computing the topological complexity of digital images. We give new results on the relation between reducibility and digital contractibility in order to determine the topological complexity of a…
We develop a robust foundation for studying the fundamental group(oid) in discrete homotopy theory, including: equivalent definitions and basic properties, the theory of covering graphs, and the discrete version of the Seifert-van Kampen…
In this paper we propose a conceptual framework for higher-order artificial neural networks. The idea of higher-order networks arises naturally when a model is required to learn some group of transformations, every element of which is…
We construct a map from fundamental groups of complements to some plane configurations to the groups $G_{n}^{k}$ for large $k$. We discuss connection between the groups $G_{n}^{k}$ for different $G_{n}^{k}$ and their geometric realization.
In this short paper we first recall the definition and the construction of the fundamental group scheme of a scheme $X$ in the known cases: when it is defined over a field and when it is defined over a Dedekind scheme. It classifies all the…
We study finite-dimensional groups definable in models of the theory of real closed fields with a generic derivation (also known as CODF). We prove that any such group definably embeds in a semialgebraic group. We extend the results to…
A connection between the Galois-theoretic approach to semi-abelian homology and the homological closure operators is established. In particular, a generalised Hopf formula for homology is obtained, allowing the choice of a new kind of…
This review presents various image segmentation methods using complex networks. Image segmentation is one of the important steps in image analysis as it helps analyze and understand complex images. At first, it has been tried to classify…
With the powerful deep network architectures, such as generative adversarial networks, one can easily generate photorealistic images. Although the generated images are not dedicated for fooling human or deceiving biometric authentication…
Detecting manipulated images has become a significant emerging challenge. The advent of image sharing platforms and the easy availability of advanced photo editing software have resulted in a large quantities of manipulated images being…
For any type of fundamental groupoid scheme, we construct an algebraic cohomology theory for varieties with coefficients in the base field. This is a minor variant of \'etale cohomology, involving neither de Rham complexes nor…
Learning a good image prior is a long-term goal for image restoration and manipulation. While existing methods like deep image prior (DIP) capture low-level image statistics, there are still gaps toward an image prior that captures rich…
We introduce a notion of complexity of diagrams (and in particular of objects and morphisms) in an arbitrary category, as well as a notion of complexity of functors between categories equipped with complexity functions. We discuss several…
In a computational topology of digital images, simplexes are replaced by Delta sets in approximating image object shapes. For simplicity, simplexes and Delta sets are restricted to the Euclidean plane. A planar simplex is either a vertex, a…
Image generation remains a fundamental problem in artificial intelligence in general and deep learning in specific. The generative adversarial network (GAN) was successful in generating high quality samples of natural images. We propose a…