Towards a Generalized Map Algebra: Principles and Data Types

Map Algebra is a collection of functions for handling continuous spatial data, which allows modeling of different problems and getting new information from the existing data. There is an established set of map algebra functions in the GIS literature, originally proposed by Dana Tomlin. However, the question whether his proposal is complete is still an open problem in GIScience. This paper describes the design of a map algebra that generalizes Tomlin’s map algebra by incorporating topological and directional spatial predicates. Our proposal enables operations that are not directly expressible by Tomlin’s proposal. One of the important results of our paper is to show that Tomlin’s Map Algebra can be defined as an application of topological predicates to coverages. This paper points to a convergence between these two approaches and shows that it is possible to develop a foundational theory for GIScience where topological predicates are the heart of both object-based algebras and field-based algebras.