Algebraic Frames for the Perception-Action Cycle

Most of the processing in vision today uses spatially invariant operations. This gives efficient and compact computing structures, with the conventional convenient separation between data and operations. This also goes well with conventional Cartesian representation of data. Currently, there is a trend towards context dependent processing in various forms. This implies that operations will no longer be spatially invariant, but vary over the image dependent upon the image content. There are many ways in which such a contextual control can be implemented. Mechanisms can be added for the modification of operator behavior within the conventional computing structure. This has been done e.g. for the implementation of adaptive filtering. In order to obtain sufficient flexibility and power in the computing structure, it is necessary to go further than that. To achieve sufficiently good adaptivity, it is necessary to ensure that sufficiently complex control strategies can be represented. It is becoming increasingly apparent that this can not be achieved through prescription or program specification of rules. The reason being that these rules will be dauntingly complex and can not be be dealt with in sufficient detail. At the same time that we require the implementation of a spatially variant processing, this implies the requirement for a spatially variant information representation. Otherwise a sufficiently effective and flexible contextual control can not be implemented. This paper outlines a new structure for effective space variant processing. It utilises a new type of localized information representation, which can be viewed as outputs from band pass filters such as wavelets. A unique and important feature is that convex regions can be built up from a single layer of associating nodes. The specification of operations is made through learning or action controlled association