On the problem of adjacency relations in the Spatial Aggregation approach

Spatial Aggregation (SA) is a computational approach to the analysis of large spatial data sets. It differs from other tools for data analysis for its hierarchical strategy in aggregating spatial objects at higher and higher levels until the behavioral and structural information about the underlying physical phenomenon, that is required for performing a specific task, is extracted from the data set. This characteristic makes SA an interesting and versatile framework for the development of tools for automated reasoning about physical phenomena spatially represented. The SA approach has been successfully applied to different domains and tasks; but, its soundness strictly depends on the definitions of spatial adjacency relations at different levels of abstraction. The definitions given in cite{Zhao_huang} may reveal to be not fully sound when performing the contouring task. In such a context, the found drawbacks are at least twofold: (1) metric-based adjacency relations are too difficult to be optimally defined, and aggregation may fail to extract isocurves; (2) the soundness of neighborhood relations depends on the density of the isopoint set, and aggregation may fail to extract physical structures as isopoint contiguity may be lost. This paper illustrates the problems above, and presents new definitions and algorithms for their solutions