Solution of nonlinear diffusion appearing in image smoothing and edge detection Original Research Article

A numerical approximation of the nonlinear diffusion problem appearing in image processing is discussed. The mathematical model is proposed by Catté, Lions, Morel and Coll and represents an improvement of the original model of Perona and Malik. The scheme is linear, based on Rotheʹs approximation in time and on the finite element approach in space. The approximating solutions converge strongly in C(I, L2)∩L2(I, V) space to the variational solution.