Perceptual organization as nested control.

It is argued here that perceptual organization is the structuring of environmental stimuli into nested structures of control. This view is derived from our proposal that the perceptual system forces any stimulus set to have the algebraic structure G of a machine, and that G is given a specific factorization sequence, G = G1 X G2 X ... X Gn, induced by dynamical systems criteria which the organism imposes on the environment. An investigation into these factorization sequences reveals that any such sequence is split into two subsequences, one structuring the way in which the stimulus set can change under external action, and the other describing the way in which the set is perceived as internally generated. An examination of the nested control structure of the latter yields a theory of grouping. The external and internal sequences are shown to be strongly related to each other in that the symmetry axes of the internal sequence are eigenspaces of the most stable subgroup factors of the external sequence. It is claimed that cartesian reference frames are subsequences of the full sequences. Using these principles, a unified theory is offered of several apparently quite separate perceptual areas; e.g. Marr-Nishihara shape perception, gestalt grouping, the orientation-and-form problem, and motion perception. The final claim is that planning hierarchies have the same dynamically-structured algebraic sequences and therefore that the study of perceptual organization should, in a very deep sense, be formally equivalent to the study of planning.