Table of Contents
ISRN Discrete Mathematics
Volume 2014, Article ID 436419, 6 pages
http://dx.doi.org/10.1155/2014/436419
Research Article

Mathematical Morphology on Hypergraphs Using Vertex-Hyperedge Correspondence

1Department of Computer Applications, Cochin University of Science and Technology, Cochin 682022, India
2Naval Physical and Oceanographic Laboratory, Cochin 682021, India
3Department of Mathematics, Rajagiri School of Engineering and Technology, Cochin 682039, India

Received 18 December 2013; Accepted 27 January 2014; Published 13 March 2014

Academic Editors: A. V. Kelarev, W. F. Klostermeyer, and X. Meng

Copyright © 2014 Bino Sebastian et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The focus of this paper is to develop computationally efficient mathematical morphology operators on hypergraphs. To this aim we consider lattice structures on hypergraphs on which we build morphological operators. We develop a pair of dual adjunctions between the vertex set and the hyperedge set of a hypergraph , by defining a vertex-hyperedge correspondence. This allows us to recover the classical notion of a dilation/erosion of a subset of vertices and to extend it to subhypergraphs of . This paper also studies the concept of morphological adjunction on hypergraphs for which both the input and the output are hypergraphs.