In this paper we describe a new system for the reconstruction of geometric map elements as developed in the Dutch TopSpin-PNEM project 'Knowledge-based conversion of utility maps'. In the knowledge base map conversion process vectorized map elements coming from an image interpretation system must be reconstructed in a geometrically accurate topographic base map. This is done using a map correspondence between the utility map and the base map based on mutual topography and relational information supplied by a map interpretation module. The map interpretation module uses geometrical inference to deduce the relational information, while applying a novel conflict resolution strategy. The map elements are accurately reconstructed, relationally and geometrically, using the map correspondence, the relations and several object-specific functions.