Qualitative change to 3-valued regions

Abstract

Regions which evolve over time are a significant aspect of many phenomena in the natural sciences and especially in geographic information science. Examples include areas in which a measured value (e.g. temperature, salinity, height, etc.) exceeds some threshold, as well as moving crowds of people or animals. There is already a well-developed theory of change to regions with crisp boundaries. In this paper we develop a formal model of change for more general 3-valued regions. We extend earlier work which used trees to represent the topological configuration of a system of crisp regions, by introducing trees with an additional node clustering operation. One significant application for the work is to the decentralized monitoring of changes to uncertain regions by wireless sensor networks. Decentralized operations required for monitoring qualitative changes to 3-valued regions are determined and the complexity of the resulting algorithms is discussed. © 2010 Springer-Verlag.