P systems and computational algebraic topology

Abstract

Membrane Computing is a paradigm inspired from biological cellular communication. Membrane computing devices are called P systems. In this paper we calculate some algebraic-topological information of 2D and 3D images in a general and parallel manner using P systems. First, we present a new way to obtain the homology groups of 2D digital images in time logarithmic with respect to the input data involving an improvement with respect to the algorithms development by S. Peltier et al. Second, we obtain an edge-segmentation of 2D and 3D digital images in constant time with respect to the input data.