Fast n-dimensional non linear filter
Résumé
In this communication, we propose an original approach for the diffusion paradigm in image processing. Our starting point is the iterative resolution of partial differential equations (PDE) according to the explicit resolution scheme. We simply consider that this iterative process is nothing but a fixed point search. So, we obtain a convergence condition which applies to a large set of image processings PDE. That allows us to introduce a new smoothing process with strong abilities to preserve any structure of interest in the images. As an example, we here choose a linear isotropic diffusion for the denoising performances. Thus while resolving the equation of isotropic diffusion and by using an adaptive resolution parameter, we obtain a filtering process which can preserve arbitrary dimension object edges as one-dimensional signals, gray level images, color images, volumes, films, etc. We show the edge localization preserving property of the process and the computational effort is linear in size and the dimension of the object. We compare the complexity of the process with the Perona and Malik explicit scheme, and the Weickert AOS scheme. We establish that the computational effort of our scheme is lower than this of the two others. For illustration, we apply this new process to denoising of different kinds of medical images like MRI, angiograms, etc.