Algorithm for detecting brightness differences in noisy images based on the Wilcoxon criterion

To detect brightness differences in grayscale images, in previous works it was proposed to use the nonparametric Wilcoxon criterion. At the same time, the obtained research results showed a sufficient effectiveness of the application of the criterion for highlighting the brightness differences in images with noise without preliminary filtering. The application of the criterion involves the transformation of the image into such an attribute as the value of the rank function for each pixel of the analyzed image area. Calculation of the extremum of the rank function makes it possible to establish the location and type of brightness differences in the image. However, as studies have shown, the value of the extremum value depends on the signal-to-noise ratio in the image and, along with the true extrema, local extrema are also distinguished, which complicates the solution of the problem of further image segmentation. This paper presents the results of statistical studies on the use of the Wilcoxon test for detecting brightness differences in images with different signal-to-noise ratios and sample sizes. The minimum signal-to-noise ratio at which the extremum of the rank function tends to its maximum or minimum value has been established. Also, based on the statistical analysis of the behavior of the rank function to exclude the allocation of local extrema, it is proposed to use the difference of the rank functions for the analyzed rows and columns of the processed image