A new hardware structure for implementation of soft morphological filters is presented in this paper. This is based on the modification of the majority gate technique. A pipelined systolic array architecture suitable to perform real-time soft morphological filtering is presented as an illustrative example. The processing times of the proposed hardware structure do not depend on the data window ...

In digital topology, the use of a pair of connectivities is required to avoid topological paradoxes. In mathematical morphology, selfdual operators and methods also rely on such a pair of connectivities. There are several major issues: self-duality is impure, the image graph structure depends on the image values, it impacts the way small objects and texture are processed, and so on. A sub-class...

X iv :1 61 2. 07 70 8v 1 [ cs .E T ] 1 5 D ec 2 01 6 Experimental prototype of a spin-wave majority gate T. Fischer, 2, a) M. Kewenig, D. A. Bozhko, 2 A. A. Serga, I. I. Syvorotka, F. Ciubotaru, 5 C. Adelmann, B. Hillebrands, and A. V. Chumak Fachbereich Physik and Landesforschungszentrum OPTIMAS, Technische Universität Kaiserslautern, 67663 Kaiserslautern, Germany Graduate School Materials Sci...

An antimedian of a profile π = (x1, x2, . . . , xk) of vertices of a graph G is a vertex maximizing the sum of the distances to the elements of the profile. The antimedian function is defined on the set of all profiles on G and has as output the set of antimedians of a profile. It is a typical location function for finding a location for an obnoxious facility. The ‘converse’ of the antimedian f...

we only show one further result that emphasizes our point that understanding LMP is fundamental to understanding any generalization of this process. A simple generalization of the local majority process would allow vertex v to have some resistivity towards color switch. Formally, for a nonnegative integer kv, we de ne a kv-local majority rule for vertex v: ct+1 v = ( ctv if jfw 2 Nv : ctw = ctv...

Suppose we are given a set of n balls {b1, . . . , bn} each colored either red or blue in some way unknown to us. To find out some information about the colors, we can query any triple of balls {bi1 , bi2 , bi3}. As an answer to such a query we obtain (the index of) a majority ball, that is, a ball whose color is the same as the color of another ball from the triple. Our goal is to find a non-m...

Abstract The general problem in location theory deals with functions that find sites on a graph (discrete case) or network (continuous case) in such a way as to minimize some cost (or maximize some benefit) to a given set of clients represented by vertices on the graph or points on the network. The axiomatic approach seeks to uniquely distinguish, by using a list of intuitively pleasing axioms,...

In this paper we introduce a median operator between two sets of interpretations (worlds) in a finite propositional language. Our definition is based on morphological operations and Hausdorff distance. It provides a result which lies “halfway” between both sets and accounts for the “extension” or “shape” of the sets. We prove several interesting properties of this operator and compare it with f...