Spatial Aggregation: Language and Applications

Spatial aggregation is a framework for organizing computations around image-like, analogue representations of physical processes in data interpretation and control tasks. It conceptualizes common computational structures in a class of implemented problem solvers for difficult scientific and engineering problems. It comprises a mechanism, a language, and a programming style. The spatial aggregation mechanism transforms a numerical input field to successively higher-level descriptions by applying a small, identical set of operators to each layer given a metric, neighborhood relation and equivalence relation. This paper describes the spatial aggregation language and its applications. The spatial aggregation language provides two abstract data types - neighborhood graph and field -- and a set of interface operators for constructing the transformations of the field, together with a library of component implementations from which a user can mix-and-match and specialize for a particular application. The language allows users to isolate and express important computational ideas in different problem domains while hiding low-level details. We illustrate the use of the language with examples ranging from trajectory grouping in dynamics interpretation to region growing in image analysis. Programs for these different task domains can be written in a modular, concise fashion in the spatial aggregation language.