Conservative image transformations with restoration and scale-space properties

Many image processing applications require to solve problems such as denoising with edge enhancement, preprocessing for segmentation, or the completion of interrupted lines. This may be accomplished by applying a suitable nonlinear anisotropic diffusion process to the image. Its diffusion tensor is adapted to the differential structure of the underlying image. Although being image enhancement tools, filters of this class are well-posed. The temporal evolution of the diffusion process creates a scale-space whose causality properties can be understood in a deterministic, stochastic, information theory based and Fourier based way. The well-posedness and scale-space results carry over to the discrete setting, which gives rise to reliable algorithms preserving all properties of the continuous framework.