Spline Smoothing: A Special Case of Diffusion Smoothing

schemes, it provides a uniform theoretical base for some other smoothing methods. It has shown that the elegant Gaussian smoothing (GS) is equivalent to the initial value problem of DS, and the widely-used Repeated Averaging (RA) is a special case of the explicit DS. This paper further proves that Spline smoothing (SS) is a special case of the explicit DS with a "convex corner cling" boundary condition. This result coincides with Poggio's conclusion However, our proof starts from the diffusion smoothing theory instead of regularisation theory and is given in the mask form, thus is simpler and more straightforward. Moreover, it makes us possible to explicit the scale space behaviour of spline smoothing.