Tikhonov regularization versus scale space: a new result [image processing applications]

It is well-known that scale space theory and Tikhonov regularization are close-knit. In previous studies, qualitative analogies and formal relations have already been found, but none of these established both an exact as well as operational connection. We establish such a connection for the case of a Gaussian scale space representation and a first order Tikhonov scheme. The free parameter of the latter turns out to be related to a particular attenuation of scales in a procedure whereby one "collapses" the scale space image along the scale axis via the Laplace transform. The result provides a physical interpretation of first order Tikhonov regularization and its associated control parameter.