On the assessment of generalisation consistency

Theory, algorithms, techniques and tools for producing a generalisation of a map have long been available. In this paper we study the inverse problem, namely, given two maps L and M, whether there exists a generalisation G, such that L=G(M). Answering this problem can help with fundamental issues of consistency in multiresolution databases. We view such a database as a collection of map layers depicting the same geographic area at different levels of detail, related through a generalisation hierarchy. From an engineering perspective, multiple representations, of which multiresolution maps is a special case, imply redundancy, which is a threat to the integrity of a database. For integrity control we need a set of tools that ensure that the metric and topological properties of a map layer are retained or monotonically decreased along the generalisation hierarchy. In this paper we study the former, i.e. we propose a framework for the assessment of metric consistency between two map layers.