Tikhonov Regularization versus Scale Space: A New Result (MA-P2)

Author(s) : Luc Florack (Eindhoven University of Technology, The Netherlands) Remco Duits (Eindhoven University of Technology, The Netherlands) Joris Bierkens (Eindhoven University of Technology, The Netherlands)

Abstract : It is well-known that scale space theory and Tikhonov regularization are close-knit. In previous studies qualitative analogies and formal relations had 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.

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