Multi-granularity and metric spatial reasoning

• Multi-granularity composition reasoning which is very useful in many applications is systematically studied for the first time.
• Metric spatial reasoning which is a special case of multi-granularity composition reasoning is firstly discussed.
• The general frameworks and basic theories for multi-granularity and metric spatial reasoning are put forward.
• Multi-granularity and metric spatial relations models for distance, topology and direction are presented.
• Multi-granularity and metric spatial reasoning can be potentially applied in robot navigation and other applications.

Composition reasoning is a basic reasoning task in qualitative spatial reasoning (QSR). It is an important qualitative method for robot navigation, node localization in wireless sensor networks and other fields. The previous composition reasoning works dedicated in single granularity framework. Multi-granularity spatial relation is not rare in real world, and some qualitative spatial relation models are multi-granularity models, such as RCC, STARm, CDCm and OPRAm. Although multi-granularity composition reasoning is very useful in many applications, it has not been systematically studied before. A special case of multi-granularity composition reasoning, referred to as metric spatial reasoning, is also discussed here. The general frameworks and basic theories for multi-granularity and metric spatial reasoning are put forward here. Furthermore, we redefine the spatial relation models for distance, topology and direction under the proposed multi-granularity and metric frameworks. We add metric representation for the OPRAm. The multi-granularity and metric reasoning tasks are studied for these four models for the first time. Finally we perform some experiments on OPRAm with encouraging results to verify our theories. Multi-granularity and metric spatial reasoning tasks are new problems in QSR and quite different from the previous works. Our works can be potentially applied in robot navigation, wireless sensor networks and other applications.