**Ibrahim Furkan Ince 1,\*, Omer Faruk Ince <sup>2</sup> and Faruk Bulut <sup>3</sup>**


Received: 13 July 2019; Accepted: 21 August 2019; Published: 26 August 2019

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

**Keywords:** non-linear filters; MCV and MLV filters; de-noising; noise removal; edge preserving
