Adaptive symmetric mean filter: A new noise-reduction approach based on the slope facet model

Two new noise-reduction algorithms, namely, the adaptive symmetric mean filter (SMF) and the hybrid filter, are presented in this paper. The idea of the ASMF is to find the largest symmetric region on a slope facet by incorporation of the gradient similarity criterion and the symmetry constraint into region growing. The gradient similarity criterion allows more pixels to be included for a statistically better estimation, whereas the symmetry constraint promises an unbiased estimate if the noise is completely removed. The hybrid filter combines the advantages of the ASMF, the double-window modified-trimmed mean filter, and the adaptive mean filter to optimize noise reduction on the step and the ramp edges. The experimental results have shown the ASMF and the hybrid filter are superior to three conventional filters for the synthetic and the natural images in terms of the root-mean-squared error, the root-meansquared difference of gradient, and the visual presentation.