  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.
