  A robust estimator, namely M-smoother, for piecewise-constant smoothing is
revisited in this paper. Starting from its generalized formulation, we propose
a numerical scheme/framework for solving it via a series of weighted-average
filtering (e.g., box filtering, Gaussian filtering, bilateral filtering, and
guided filtering). Because of the equivalence between M-smoother and
local-histogram-based filters (such as median filter and mode filter), the
proposed framework enables fast approximation of histogram filters via a number
of box filtering or Gaussian filtering. In addition, high-quality
piecewise-constant smoothing can be achieved via a number of bilateral
filtering or guided filtering integrated in the proposed framework. Experiments
on depth map denoising show the effectiveness of our framework.

Computer Vision and Pattern Recognition