Modeling Spatial Relationships between 3D Objects

In this paper, we propose an original modeling technique which enables quantitative non-symbolic representation and comparison of the mutual spatial positioning of extended entities in a 3D space. The representation accounts for the overall distribution of relationships among the individual points of two objects. Properties of the model are expounded to develop an efficient computation technique and to motivate and assess a metric of similarity for quantitative comparison of spatial relationships between object pairs. Experiments compare the proposed approach against two different solutions