A generative theory of shape (Q5952662)

This book is intended for a general scientifically interested audience and not so much for the specialized mathematical reader. The author develops a generative theory of shape along two principles fundamental to intelligence -- maximization of transfer and maximization of recoverability. He proceeds by using an algebraically flavoured approach characterizing features as symmetry groups while the addition of features corresponds to group extension. The process results in a transfer structure described by an iterated wreath product. Starting from an alignement kernel the control group acts on the fibers by misalignment, producing, an unfolding effect. The group theoretic description reflects the transfer structure in the starting state and the minimal history as the fiber level and the control level, respectively. The generative theory is used in several application areas like visual perception, robotics and computer-aided geometric design.