Scale - Space Properties of

In this paper we show that regularization methods form a scale-space where the regularization parameter serves as scale. In analogy to nonlinear diiusion ltering we establish continuity with respect to scale, causality in terms of a maximum{minimum principle, simpliica-tion properties by means of Lyapunov functionals and convergence to a constant steady-state. We identify nonlinear regularization with a single implicit time step of a diiusion process. This implies that iterated regu-larization with small regularization parameters is a numerical realization of a diiusion lter. We present numerical experiments in two and three space dimensions illustrating the scale-space behaviour of regularization methods.