Qualitative Spatial Reasoning for Multi-Dimensional Topology and Size Relations

Qualitative spatial reasoning (QSR) studies the spatial relations of objects in the space. Most QSR research work aims at the spatial relations between single dimensional objects (i.e. region-region relation or line-line relation). Spatial relation of multi-dimensional objects is the situation that point, line and region objects appear in one scene at the same time. Spatial relation of multi-dimensional objects is very common in geographical information systems (GIS). Qualitative spatial relation of multi-dimensional objects has very important theoretical meaning and practical value, but very few work in QSR was focused on it before. By improving the previous research on multi-dimensional region connection calculus model, a multi-dimensional topological model (i.e. MRCC5) is given, and the complexity of its constraints satisfaction problem is studied. The multi-dimensional extension of qualitative size relation called MDS model is proposed, its reasoning problem is also investigated. Based on the above work, a model which combines RCC5 and MDS is proposed, so does its reasoning algorithm. This work extends the related work in qualitative spatial reasoning to the multi-dimensional field. The reasoning of multi-dimensional topological relation is improved. It is the first time that multi-dimensional size relation model and relation model integrating topology and size are studied.