Map Algebra Extended with Functors for Temporal Data

Abstract

This paper shows how to extend and generalize Tomlin’s Map Algebra to apply uniformly for spatial, temporal, and spatio-temporal data. A specific data layer can be seen as a function from location to a value (Goodchild’s geographic reality). Map layer but also time series and other similar constructions are functors, mapping local operations to layers, time series, etc. Tomlin’s Focal Operations are mostly convolutions and the zonal operations are summaries for zones. The mathematical framework explained justifies polymorphic overloading of operation names like + are made to work for layers, time series, etc. There is also a uniform method to apply user-defined local functions to them. The result is a consistent extension of Map Algebra with a simplified user interface. The implementation covers raster operations and demonstrates the generality of the concept.