We present a computational theory of cognitive maps which proposes that the cognitive map, a representation for a viewer’s experience of their spatial environment, comprises two loosely coupled modules, the raw cognitive map and the full cognitive map. The raw map is a representation for the spatial arrangement and physical characteristics of surfaces. The various interpretations (or conceptualisations) that are derived from the raw map form the full map. The cognitive map is built from the bottom up, starting with the sensory input. A representation termed an Absolute Space Representation (ASR) is computed for each local space visited and these ASRs connected in the way they are experienced are the raw map. We discuss the current status of our work on computing a cognitive map and in particular present a new algorithm for computing an ASR.