Statistical analysis of median type and morphological filters
J. Neejärvi, Lasse Koskinen, Yrjo A. Neuvo · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1992
In this paper, we analyze statistical properties of 1-D median type and morphological filters. Analytical formulas for the expectation of the dilation and closing in the case of i.i.d. Laplacian noise and explicit formulas for the expectation and variance of the morphological filters in the case of i.i.d. uniformly distributed noise are given. Noise attenuation figures of the filters for Gaussian, Laplacian and uniformly distributed noise are shown. It is shown that noise attenuation of the morphological filters varies considerably depending on the distribution of the noise. We analyze also the five point Morphological-FIR-Median Hybrid (MFMH) filter and its special case, the three point Morphological-Median Hybrid (MMH) filter structure. Responses for rectangular pulses of the MFMH and MMH filters are shown, and the behavior of the filters around noisy edges is studied. The performance of the MFMH filter near noisy edges is better than that of the FMH filter and the properties of the filter are adjustable in larger detail. In addition, an illustrative example of the noise attenuation performance of median type and morphological filters with an image is shown.