Local configuration measures for categorical spatial data: binary regular lattices

This paper examines the utility of a number of pattern measures for local exploratory analysis of binary spatial data. Based on a review of existing pattern measures in cartography, geography, image analysis, and landscape ecology, two fundamental classes of such measures, termed compositional and configurational, are identified. The paper focuses on configurational measures and it is suggested that as many as five such measures (join counts, patch numbers, patch sizes, patch proximity, and distribution of the classes relative to the focal cell of the window) are required to differentiate between all possible local categorical maps. This suggestion is explored by examining aspects of the statistical behaviour (probability distributions and correlations between extreme values of pairs of measures) of a set of 12 configurational measures. Their use is also demonstrated by means of an empirical example.