**Article details**

**Title: **Best Mean Rank Vector Filter for Impulsive and Uniform Noise Reduction in Color Images

**Author(s): ***Valeriu Vrabie* *Constantin Vertan* *Mihai Ciuc* *Michel Herbin*

**Abstract: **Rank order based filters are generally implemented by using reduced ordering since there is no natural way to order vector data such as the pixel values of color images. According to the reduced ordering, several vector filters have been defined. The classical and adaptive vector median filters, basic vector directional filter, adaptive hybrid directional filter and directional-distance filter represent some examples of the most used vector filters in color image processing. However, in the presence of high percentage of impulsive or uniform noise, all those filters showed theirs limits. This paper proposes to aggregate partial ordering ranks in order to obtain a mean rank of multivariate data. This statistic is used for the reduced ordering of vector data; the median statistic is characterized by the best mean rank vector (BMRV). The results of the BMRV-based filter on different images heavily corrupted by impulsive or uniform noises are qualitatively and quantitatively compared with those obtained by using classical vector filters.

**Keywords: **image processing, nonlinear filters, vector median filter, partial ordering ranks, mean rank of multivariate data, best mean rank vector.

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