Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 598910, 28 pages
Research Article

Computing the Discrete Compactness of Orthogonal Pseudo-Polytopes via Their nD-EVM Representation

Computer Engineering Institute, The Technological University of the Mixteca (UTM), Carretera Huajuapan-Acatlima Km. 2.5, Huajuapan de León, 69000 Oaxaca, Mexico

Received 17 February 2010; Accepted 1 July 2010

Academic Editor: Mohammad Younis

Copyright © 2010 Ricardo Pérez-Aguila. 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.


This work is devoted to present a methodology for the computation of Discrete Compactness in n-dimensional orthogonal pseudo-polytopes. The proposed procedures take in account compactness' definitions originally presented for the 2D and 3D cases and extend them directly for considering the nD case. There are introduced efficient algorithms for computing discrete compactness which are based on an orthogonal polytopes representation scheme known as the Extreme Vertices Model in the n-Dimensional Space (nD-EVM). It will be shown the potential of the application of Discrete Compactness in higher-dimensional contexts by applying it, through EVM-based algorithms, in the classification of video sequences, associated to the monitoring of a volcano's activity, which are expressed as 4D orthogonal polytopes in the space-color-time geometry.