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Analysis of the sigma filter using robust estimation

In this paper, we analyze a computationally efficient nonlinear edge-preserving smoothing filter, the sigma filter, in the framework of robust estimation. The sigma filter is nearly W-estimator of robust estimation using the metric trimming influence function with a subtle difference. Based on the analysis, we further develop another form of the sigma filter as M-estimator of robust estimation using the same metric trimming influence function. The new form of the sigma filter is more suitable for hardware implementation. We also compare the sigma filter with other nonlinear edge-preserving filters in the framework of robust estimation. Finally, experimental results are reported and discussed.