Connecting perception and action by associating symmetries in vision and language

Symmetries are of fundamental importance in information processing. It is well understood how important visual symmetries are in the understanding of scenes. This paper explores the symmetries of languages of actions, and relates them to visual symmetries. Linguistic symmetry is explored in the context of problem solving. Algebraic techniques permit the representation and manipulation of linguistic symmetry, and the exploration of its connection to perceptual symmetry. It is shown that the invariants of the decomposition of a language of actions form a complete and independent set of perceptual features that naturally describe the search space.