LAMBDA-TAU-SPACE REPRESENTATION OF IMAGES AND GENERALIZED EDGE DETECTOR

An image and surface representation based on regularization theory is introduced in this paper. This representation is based on a hybrid mod el derived from the physical membrane and plate models. The representa tion, called the lambda tau-representation, has two dimensions; one di mension represents smoothness or scale while the other represents the continuity of the image or surface. It contains images/surfaces sample d both in scale space and the weighted Sobolev space of continuous fun ctions. Thus, this new representation can be viewed as an extension of the well-known scale space representation. We have experimentally sho wn that the proposed hybrid model results in improved results compared to the two extreme constituent models, i.e., the membrane and the pla te models. Based on this hybrid model, a generalized edge detector (GE D) which encompasses most of the well-known edge detectors under a com mon framework is developed. The existing edge detectors can be obtaine d from the generalized edge detector by simply specifying the values o f two parameters, one of which controls the shape of the filter (tau) and the other controls the scale of the filter (lambda). By sweeping t he values of these two parameters continuously, one can generate an ed ge representation in the lambda tau space, which is very useful for de veloping a goal-directed edge detection scheme for a specific task. Th e proposed representation and the edge detector have been evaluated qu alitatively and quantitatively on several different types of image dat a such as intensity, range, and stereo images.