From Regions to Transitions, From Transitions to Objects

Paulo Santos and Murray Shanahan

This paper describes the construction of a qualitative spatial reasoning system based on the sensor data of a mobile robot. The spatial knowledge of the robot is formalised in three sets of axioms. First of all, axioms for relations between pairs of spatial regions are presented. Assuming the distance between regions as a primitive function in the language, the main purpose of this initial axiom set is the classification of relations between images of objects (from the robot’s vision system) according to their degree of displacement. Changes in the sensor data, due to the movement either of objects in the robot’s environment or of the robot itself, are represented by transitions between the displacement relations. These transitions are formalised by the second set of axioms. The predicates defining the transitions between image relations are connected to possible interpretations for the sensor data in terms of object-observer relations, this issue is handled by the third set of axioms. These three axiom sets constitute three layers of logic-based image interpretation via abduction on transitions in the sensor data.

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