Reasoning about Dynamic Depth Profiles

Reasoning about perception of depth and about spatial relations between moving physical objects is a challenging problem. We investigate the representation of depth and motion by means of depth profiles whereby each object in the world is represented as a single peak. We propose a logical theory, formulated in the situation calculus (SC), that is used for reasoning about object motion (including motion of the observer). The theory proposed here is comprehensive enough to accommodate reasoning about both sensor data and actions in the world. We show that reasoning about depth profiles is sound and complete with respect to actual motion in the world. This shows that in the conceptual neighbourhood diagram (CND) of all possible depth perceptions, the transitions between perceptions are logical consequences of the proposed theory of depth and motion.