Improved Edge Awareness in Discontinuity Preserving Smoothing
  Discontinuity preserving smoothing is a fundamentally important procedure that is useful in a wide variety of image processing contexts. It is directly useful for noise reduction, and frequently used as an intermediate step in higher level algorithms. For example, it can be particularly useful in edge detection and segmentation. Three well known algorithms for discontinuity preserving smoothing are nonlinear anisotropic diffusion, bilateral filtering, and mean shift filtering. Although slight differences make them each better suited to different tasks, all are designed to preserve discontinuities while smoothing. However, none of them satisfy this goal perfectly: they each have exception cases in which smoothing may occur across hard edges. The principal contribution of this paper is the identification of a property we call edge awareness that should be satisfied by any discontinuity preserving smoothing algorithm. This constraint can be incorporated into existing algorithms to improve quality, and usually has negligible changes in runtime performance and/or complexity. We present modifications necessary to augment diffusion and mean shift, as well as a new formulation of the bilateral filter that unifies the spatial and range spaces to achieve edge awareness. 
Stuart B. Heinrich and Wesley E. Snyder
cs.CV