Related papers: Image transformations on locally compact spaces

For two not necessarily commutative topological groups G and T, let H(G,T) denote the space of all continuous homomorphisms from G to T with the compact-open topology. We prove that if G is metrizable and T is compact then H(G,T) is a…

For digital images, there is an established homotopy equivalence relation which parallels that of classical topology. Many classical homotopy equivalence invariants, such as the Euler characteristic and the homology groups, do not remain…

Local scaling of a set means that in a neighborhood of a point the structure of the set can be mapped into a finer scale structure of the set. These scaling transformations are compact sets of locally affine (that is: with uniformly…

Metamorphism is a recently introduced integral transform, which is useful in solving partial differential equations. Basic properties of metamorphism can be verified by direct calculations. In this paper we present metamorphism as a sort of…

This paper combines image metamorphosis with deep features. To this end, images are considered as maps into a high-dimensional feature space and a structure-sensitive, anisotropic flow regularization is incorporated in the metamorphosis…

We show that for any smooth Hausdorff manifolds M and N, which are not necessarily second countable, paracompact or connected, any isomorphism from the algebra of smooth (real or complex) functions on N to the algebra of smooth functions on…

We investigate dynamical systems consisting of a locally compact Hausdorff space equipped with a partially defined local homeomorphism. Important examples of such systems include self-covering maps, one-sided shifts of finite type and, more…

In this article we observe that a locally compact group $G$ is completely determined by the algebraic properties of its Feichtinger's Segal algebra $S_0(G).$ Let $G$ and $H$ be locally compact groups. Then any linear (not necessarily…

We argue that computation is an abstract algebraic concept, and a computer is a result of a morphism (a structure preserving map) from a finite universal semigroup.

We give a definition of a functor compactifying the functor of bundles on a surfaces. Earlier different authors have defined similar spaces as either images under a morphism or a quotient by an equivalence relation. We use the technique of…

Simply by rearranging the regions of an image, we can create a new image of any subject matter. The definition of regions is user definable, ranging from regularly and irregularly-shaped blocks, concentric rings, or even individual pixels.…

We show that with few exceptions every local isometric automorphism of the group algebra $L^p(G)$ of a compact group $G$ is an isometric automorphism.

\emph{Scalable spaces} are simply connected compact manifolds or finite complexes whose real cohomology algebra embeds in their algebra of (flat) differential forms. This is a rational homotopy invariant property and all scalable spaces are…

In a category with enough limits and colimits, one can form the universal automorphism on an endomorphism in two dual senses. Sometimes these dual constructions coincide, as in the categories of finite sets, finite-dimensional vector…

The local histogram transform of an image is a data cube that consists of the histograms of the pixel values that lie within a fixed neighborhood of any given pixel location. Such transforms are useful in image processing applications such…

The Hausdorff-Alexandroff Theorem states that any compact metric space is the continuous image of Cantor's ternary set $C$. It is well known that there are compact Hausdorff spaces of cardinality equal to that of $C$ that are not continuous…

A local homeomorphism between open subsets of a locally compact Hausdorff space induces dynamical systems with a wide range of applications, including in C*-algebras. In this paper, we introduce the concepts of nonwandering and wandering…

The topology of digital images has been studied much in recent years, but no attempt has been made to exhaustively catalog the structure of binary images of small numbers of points. We produce enumerations of several classes of digital…

A concept of defining images based on its own approximate ones is proposed here, which is called 'Self-ception'. In this regard, an algorithm is proposed to implement the self-ception for images, which we call it 'Image Self-ception' since…

Let $G$ be a locally compact group and also let $H$ be a compact subgroup of $G$. It is shown that, if $\mu$ is a relatively invariant measure on $G/H$ then there is a well-defined convolution on $L^1(G/H,\mu)$ such that the Banach space…