Nonlinear diffusion of scalar images using well-posed differential operators

In recent years several nonlinear diffusion schemes have been introduced. We discuss the numerical implementation of a number of current nonlinear evolution schemes, using the notion of well-posed differentiation by Gaussian kernels. The infinitesimal change of an image when increasing scale depends on the local differential invariants evaluated at the scale of the image considered, i.e. on terms of the local jet (the set of all spatial partial derivatives at that point). All these differential terms can be obtained in a well-posed fashion by a convolution of the original image with the family of the Gaussian and its derivatives. The nonlinear partial differential evaluation can thus be numerically approximated by an iterative calculation of the appropriate terms in the local jet. Examples are given for medical images