A fundamental capacity of the perceptual systems and the brain in general is to deal with the novel and the unexpected. In vision, we can effortlessly recognize a familiar object under novel viewing conditions, or recognize a new object as a member of a familiar class, such as a house, a face, or a car. This ability to generalize and deal efficiently with novel stimuli has long been considered a challenging example of brain-like computation that proved extremely difficult to replicate in artificial systems. In this paper we present an approach to generalization and invariant recognition. We focus our discussion on the problem of invariance to position in the visual field, but also sketch how similar principles could apply to other domains.The approach is based on the use of a large repertoire of partial generalizations that are built upon past experience. In the case of shift invariance, visual patterns are described as the conjunction of multiple overlapping image fragments. The invariance to the more primitive fragments is built into the system by past experience. Shift invariance of complex shapes is obtained from the invariance of their constituent fragments. We study by simulations aspects of this shift invariance method and then consider its extensions to invariant perception and classification by brain-like structures.