The bilateral filter (BF) is a nonlinear and low-pass filter which can smooth an image while preserving detail structures. However, the filer is time consuming for real-time processing. In this paper, we bring forward a fresh idea that bilateral filtering can be accelerated by a multigrid (MG) scheme. Our method is based on the following two facts. a) The filtering result by a BF with a large kernel size on the original resolution can be approximated by applying a small kernel sized (3x3) version on the lower resolution many times on the premise of visual acceptance. Early work has shown that a BF can be viewed as nonlinear diffusion. The desired filtering result is actually an intermediate status of the diffusion process. b) Iterative linear equation techniques are sufficiently mature to cope with the nonlinear diffusion equation, which can be accelerated by the MG scheme. Experimental results with both simulated data sets and real sets are provided, and the new method is demonstrated to achieve almost twice the speed of the state-of-the-art. Compared with previous efforts for finding a generalized representation to link bilateral filtering and nonlinear diffusion by adaptive filtering, a novel relationship between nonlinear diffusion and bilateral filtering is explored in this study by focusing attention on numerical calculus.
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