Incorporating Knowledge via Regularization Theory: Applications in Vision and Image Processing

In computer vision one is faced with the task of discovering the nature of objects that produced the light intensity distribution received by the camera. In order to solve this problem, one usually uses knowledge of the optics, the reflectance properties of surfaces, and of the structure of the objects one is expecting to find in a given scene. In many problems in image processing one is trying to use knowledge of the imaged objects, or of the image formation process, to reconstruct a better image from a degraded image. A proper computational formulation of these problems recognises that they involve inverse processes that are mathematically ill -posed. This allows one to derive systematically, computational schemes based upon regulari zation theory that ensure existence of solution and stability of inversion process. Such approaches often suggest particular types of algorithms for efficient solution to the problems. These, in turn, often are suggestive of implemen tations that are highly parallel, require only local information and simple operations. These implementations have the essential features of neural net work approaches to computation; we present simulations of these.