1. Introduction
The bilateral filter of Tomasi and Maduchi [1] is a particular instance of an edge-preserving smoothing filter. The origins of the filter can be traced back to the work of Lee [2] and Yaroslavsky [3]. The SUSAN framework of Smith and Brady [4] is also based on a similar idea. The relation between the bilateral and other closely related filters is surveyed in [5]. The bilateral filter has turned out to be a versatile tool that has found widespread applications in image processing, computer graphics, computer vision, and computational photography. A detailed survey of some of these applications can be found in [6]. More recently, the bilateral filter has received renewed attention in the context of image denoising [7], [8]. The original bilateral filter [1] has a straightforward extension to signals of arbitrary dimension and, in particular, to video and volume data [6]. Thus, while we will limit our discussion to images in this paper, the ideas that we present next can also be extended to higher-dimensional signals.