In this study, an edge-preserving nonlinear filter is proposed to reduce multiplicative\nnoise by using a filter structure based on mathematical morphology. This method is called the\nminimum index of dispersion (MID) filter. MID is an improved and extended version of MCV\n(minimum coefficient of variation) and MLV (mean least variance) filters. Different from these\nfilters, this paper proposes an extra-layer for the value-and-criterion function in which orientation\ninformation is employed in addition to the intensity information. Furthermore, the selection function\nis re-modeled by performing low-pass filtering (mean filtering) to reduce multiplicative noise. MID\noutputs are benchmarked with the outputs of MCV and MLV filters in terms of structural similarity\nindex (SSIM), peak signal-to-noise ratio (PSNR), mean squared error (MSE), standard deviation,\nand contrast value metrics. Additionally, F Score, which is a hybrid metric that is the combination\nof all five of those metrics, is presented in order to evaluate all the filters. Experimental results\nand extensive benchmarking studies show that the proposed method achieves promising results\nbetter than conventional MCV and MLV filters in terms of robustness in both edge preservation\nand noise removal. Noise filter methods normally cannot give better results in noise removal and\nedge-preserving at the same time. However, this study proves a great contribution that MID filter\nproduces better results in both noise cleaning and edge preservation.
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