Related papers: Some enumerations of binary digital images
Figures visually represent an essential piece of information and provide an effective means to communicate scientific facts. Recently there have been many efforts toward extracting data directly from figures, specifically from tables,…
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…
We show that discrete and classical homotopy theories are equivalent after localizing at n-equivalences for any non-negative integer n. By constructing an explicit homotopy inverse to the graph nerve functor associating an n-fibrant cubical…
The constitutive characterization of the uniformity and homogeneity of binary elastic composites is presented in terms of a combination of the material groupoids of the individual constituents. The incorporation of these two groupoids…
Given based cellular spaces X and Y, X compact, we define a sequence of increasingly fine equivalences on the based-homotopy set [X,Y].
Discrete tomography deals with the reconstruction of images from projections collected along a few given directions. Different approaches can be considered, according to different models. In this paper we adopt the grid model, where pixels…
We prove the existence of lattice isomorphic line arrangements having $\pi_1$-equivalent or homotopy-equivalent complements and non homeomorphic embeddings in the complex projective plane. We also provide two explicit examples, one is…
Homotopy is an important feature of associative and Jordan algebraic structures: such structures always come in families whose members need not be isomorphic among other, but still share many important properties. One may regard homotopy as…
A formal theory based on a binary operator of directional associative relation is constructed in the article and an understanding of an associative normal form of image constructions is introduced. A model of a commutative semigroup, which…
In dealing with asymptotic approximation of possibly divergent nets of probability distributions, we are led to study uniform structures on the set of distributions. This paper identifies a class of such uniform structures that may be…
Many real-world complex networks contain a significant amount of structural redundancy, in which multiple vertices play identical topological roles. Such redundancy arises naturally from the simple growth processes which form and shape many…
We present an intrinsic and concrete development of the subdivision of small categories, give some simple examples and derive its fundamental properties. As an application, we deduce an alternative way to compare the homotopy categories of…
We study the topological structure and the topological dynamics of groups of homeomorphisms of scattered spaces. For a large class of them (including the homeomorphism group of any ordinal space or of any locally compact scattered space),…
Scientists, engineers, biologists, and technology specialists universally leverage image segmentation to extract shape ensembles containing many thousands of curves representing patterns in observations and measurements. These large curve…
We classify the finite connected-homogeneous digraphs, as well as the infinite such digraphs with precisely one end. This completes the classification of all the locally finite connected-homogeneous digraphs.
Multimodal classification research has been gaining popularity in many domains that collect more data from multiple sources including satellite imagery, biometrics, and medicine. However, the lack of consistent terminology and architectural…
Digital images enable quantitative analysis of material properties at micro and macro length scales, but choosing an appropriate resolution when acquiring the image is challenging. A high resolution means longer image acquisition and larger…
We carefully evaluate a number of algorithms for learning in a federated environment, and test their utility for a variety of image classification tasks. We consider many issues that have not been adequately considered before: whether…
Consider complex semisimple Lie algebras of a given dimension specified by their structure constants. We describe a finite collection of rational functions in the structure constants that form a complete set of invariants: two sets of…
In the current study, we explore digital homology and cohomology modules, and investigate their fundamental properties on pointed digital images. We also examine pointed digital Hopf spaces and base point preserving digital Hopf functions…