A sequential space (X,T) is called minimal sequential if no sequential topology on X is strictly weaker than T . This paper begins the study of minimal sequential Hausdorff spaces. Characterizations ofminimal sequential Hausdorff spaces are obtained using filter bases, sequences, and functions satisfying certain graph conditions. Relationships between this class of spaces and other classes of s...

A Stone-Weierstraß type theorem for semiuniform convergence spaces is proved. It implies the classical Stone-Weierstraß theorem as well as a Stone-Weierstraß type theorem for filter spaces due to Bentley, Hušek and Lowen-Colebunders [1].

In this work we provide polyphase, modulation, and frame theoretical analyses of a filter bank on a discrete abelian group. Thus, multidimensional or cyclic filter banks as well as filter banks for signals in `(Z×Zs) or `(Zr ×Zs) spaces are studied in a unified way. We obtain perfect reconstruction conditions and the corresponding frame bounds.

We propose a new filter called Bi-affinity filter for color images. This filter is similar in structure to the bilateral filter. The proposed filter is based on the color line model, which does not require the explicit conversion of the RGB values to perception based spaces such as CIELAB. The bi-affinity filter measures the affinity of a pixel to a small neighborhood around it and weighs the f...

This paper describes the development of computer simulation models to evaluate the filter algorithms in different color spaces. The objective of this project is to study the extension of filters from a one-dimensional gray-level space to a three-dimensional color space. The principal task of this project was to conduct and evaluate mathematical extensions of filters and determine which combinat...

This technical report summarized facts from the basic theory of filter convergence spaces and gives detailed proofs for them. Many of the results collected here are well known for various types of spaces. We have made no attempt to find the original proofs.