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.