Learning filter systems

A study is made of properties of so-called basic units. The authors investigate an eigenvalue problem that turns up in the study of the stable states of such units. Basic units using Hebb-type learning rules converge to stable states which are eigenfunctions of an integral equation whose kernel is given by the covariance function of the input process. The authors investigate one basic unit and assume that the set of input patterns of this basic unit is regular in the sense that all patterns can be derived from a single prototype pattern by a group-theoretically defined transformation. They show that the stable states of the unit are uniquely determined by the symmetry of the input set. It is demonstrated that the system stabilizes in a state in which the different basic units are characterized by the group-theoretically derived filter functions. The authors train the system with an input set consisting of rotated edge and line patterns and show that the stable states of the system are characterized by pure line and pure edge detectors. How the system can be used in texture segmentation is described