An adaptive finite element method for large scale image processing

Nonlinear diffusion methods have proved to be powerful methods in the proce ssing of 2D and 3D images. They allow a denoising and smoothing of image in tensities while retaining and enhancing edges. As time evolves in the corre sponding process, a scale of successively coarser image details is generate d. Certain features, however, remain highly resolved and sharp. On the othe r hand, compression is an important topic in image processing as well. Here a method is presented which combines the two aspects in an efficient way. It is based on a semi-implicit finite element implementation of nonlinear d iffusion. Error indicators guide a successive coarsening process. This lead s to locally coarse grids in areas of resulting smooth image intensity, whi le enhanced edges are still resolved on fine grid levels. Special emphasis has been put on algorithmical aspects such as storage requirements and effi ciency. Furthermore, a new nonlinear anisotropic diffusion method for vecto r field visualization is presented. (C) 2000 Academic Press.