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In this paper a novel method of impulsive noise removal in color images is presented. The proposed filtering design is based on a new measure of pixel similarity, which takes into account the structure of the local neighborhood of the pixels being compared. Thus, the new distance measure can be regarded as an extension of the reachability distance used in the construction of the local outlier factor, widely used in the big data analysis. Using the new similarity measure, an extension of the classic Vector Median Filter (VMF) has been developed. The new filter is extremely robust to outliers introduced by the impulsive noise, retains details and has the unique ability to sharpen image edges. Using the structure of the developed filter, a new impulse detector has been constructed. The cumulated sum of smallest reachability distances in the filtering window serves as a robust measure of pixel outlyingness. In this way, a pixel will be treated as corrupted if a predefined threshold is exceeded and will be replaced by the average of pixels which were found to belong to the original, pristine image; otherwise the processed pixel will be retained. This structure is similar to the Fast Averaging Peer Group Filter, however the incorporation of the reachability measure makes this technique more robust. The new filtering design can be applied in real time scenario, as its computational efficiency is comparable with the standard VMF, which is fast enough to be used for the enhancement of video sequences. The new filter operates in a 3×3 filtering window, however the information acquired from a larger window is processed. The source of additional information is the local neighborhood of pixels, which is used for the determination of the novel reachability measure. The experiments performed on a large database of color images show that the new filter surpasses existing designs especially in the case of highly polluted images. The robust reachability measure assures that the clusters of impulses are being removed, as not only the pixels, but also their neighborhoods are considered. The novel measure of dissimilarity can be also used in other tasks whose main goal is the detection of outliers.
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