Multilevel nonlinear filters for edge detection and noise suppression

Two new classes of multilevel nonlinear filters are introduced for simultaneous edge detection and noise suppression, which the authors call a nested median filter/median averaging filter (NMF/MAF) pair and a delayed decision filter/embedded median trimmed filter (DDF/EMTF) pair. Median filters and median-related filter cause an edge shift in the presence of an impulse near the edge. The proposed filters reduce such edge shifting while suppressing impulsive as well as nonimpulsive noise. It is shown that at the noisy edge point the NMF and the DDF are substantially superior both theoretically and experimentally to the median filter, the α-TM filter, and the STM filter in two respects: (1) the output bias error and (2) the output mean square error. It is also shown that in the noisy homogeneous region (nonedge point), the bias errors of the MAF are zero and the output mean square errors of the MAF are substantially close to those of the optimized single-level filters: the averager, the median filter, and the min-max filter under Gaussian, Laplacian, and uniform noise, respectively. Test results confirm that the NMF/MAF pair and the DDF/EMTF structure are each robust in preserving sharp edges, inhibiting edge shifting, and suppressing a wide variety of noise