Approximate answering of queries involving polyline-polyline topological relationships

In geographic information systems, pictorial query languages are visual languages which make easier the user to express queries by free-hand drawing. In this perspective, this article proposes an approach to provide approximate answers to pictorial queries that do not match with the content of the database, that is, the results are null. It addresses the polyline-polyline topological relationships and is based on an algorithm, called Approximate Answer Computation algorithm, which exploits the notions of Operator Conceptual Neighborhood graph and 16-intersection matrix. The operator conceptual neighborhood graph represents the conceptual topological neighborhood between Symbolic Graphical Objects and is used for relaxing constraints of queries. The nodes of the operator conceptual neighborhood graph are labeled with geo-operators whose semantics has been formalized. The 16-intersection matrix provides enriched query details with respect to the well-known Dimensionally Extended 9-Intersection Model proposed in the literature. A set of minimal 16-intersection matrices associated with each node of the operator conceptual neighborhood graph, upon the external space connectivity condition, is defined and the proof of its minimality is provided. The main idea behind each introduced notion is illustrated using a running example throughout this article.