A Topological Analysis of the Space of Natural Images
نویسندگان
چکیده
In this paper we study the space of natural images locally. We apply the techniques of computational algebraic topology to the space of 3x3 and 5x5 high-contrast patches and show that in both cases, the subspace of linear and quadratic gradient patches, which forms a dense subset inside the space of all high-contrast patches, possesses an interesting topological filtration and is itself topologically equivalent to the Klein bottle.
منابع مشابه
Menger probabilistic normed space is a category topological vector space
In this paper, we formalize the Menger probabilistic normed space as a category in which its objects are the Menger probabilistic normed spaces and its morphisms are fuzzy continuous operators. Then, we show that the category of probabilistic normed spaces is isomorphicly a subcategory of the category of topological vector spaces. So, we can easily apply the results of topological vector spaces...
متن کاملSome properties of continuous linear operators in topological vector PN-spaces
The notion of a probabilistic metric space corresponds to thesituations when we do not know exactly the distance. Probabilistic Metric space was introduced by Karl Menger. Alsina, Schweizer and Sklar gave a general definition of probabilistic normed space based on the definition of Menger [1]. In this note we study the PN spaces which are topological vector spaces and the open mapping an...
متن کاملمدلسازی روابط توپولوژیک سه بعدی فازی در محیط GIS
Nowadays, geospatial information systems (GIS) are widely used to solve different spatial problems based on various types of fundamental data: spatial, temporal, attribute and topological relations. Topological relations are the most important part of GIS which distinguish it from the other kinds of information technologies. One of the important mechanisms for representing topological relations...
متن کامل$L$-Topological Spaces
By substituting the usual notion of open sets in a topological space $X$ with a suitable collection of maps from $X$ to a frame $L$, we introduce the notion of L-topological spaces. Then, we proceed to study the classical notions and properties of usual topological spaces to the newly defined mathematical notion. Our emphasis would be concentrated on the well understood classical connectedness...
متن کاملTOPOLOGICAL CHARACTERIZATION FOR FUZZY REGULAR LANGUAGES
We present a topological characterization for fuzzy regular languages: we show that there is a bijective correspondence between fuzzy regular languages and the set of all clopen fuzzy subsets with finite image in the induced fuzzy topological space of Stone space (Profinite space), and then we give a representation of closed fuzzy subsets in the induced fuzzy topological space via fuzzy regular...
متن کاملOn the dual of certain locally convex function spaces
In this paper, we first introduce some function spaces, with certain locally convex topologies, closely related to the space of real-valued continuous functions on $X$, where $X$ is a $C$-distinguished topological space. Then, we show that their dual spaces can be identified in a natural way with certain spaces of Radon measures.
متن کامل