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In the present study a novel method is introduced to detect meaningful regions of a gray-level noisy images of binary structures. The method consists in generating surrogate data for an analyzed image. A surrogate image has the same (or almost the same) power spectrum and histogram of gray-level values as the original one but is random otherwise. ; Then minmax paths are generated in the original image, each characterized by its length, minmax intensity and the intensity of the starting point. If the probability of the existence of a path with the same characteristics but within surrogate images is lower than some user-specified threshold, it is concluded that the path in the original image passes through a meaningful object. The performance of the method is tested on images corrupted by noise with varying intensity.