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

Robust Piecewise-Constant Smoothing: M-Smoother Revisited