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In our previous work, we introduced an empirical model (EM) of arbitrary binary images and three morphological characteristics: disorder of layer structure (DStr), disorder of layer size (DSize), and pattern complexity (PCom). The basic concept of the EM is that forms of lines play no role as a morphological factor in any narrow area of an arbitrary binary image; instead, the basic factor is the type of line connectivity, i.e., isotropic/anisotropic connections. The goal of the present work is to justify the possibility of making the EM applicable for the processing of grayscale arbitrary images. One of the possible ways to reach this goal is to assess the influence of image binarization on the robustness of DStr and DSize. Images that exhibit high and low edge gradient are used for this experimental study. The robustness of DStr and DSize against the binarization procedure is described in absolute (deviation from average) and relative (Pearson’s coefficient correlation) terms. Images with low edge gradient are converted into binary contour maps by applying the watershed algorithm, and DStr and DSize are then calculated for these maps. The robustness of DStr and DSize were assessed against the image threshold for images with high edge gradient and against the grid size of contour maps and Gaussian blur smoothing for images with low edge gradient. Experiments with grayscale arbitrary patterns, such as the surface of Earth and Mars, tidal sand ripples, turbulent flow, a melanoma, and cloud images, are presented to illustrate the spectrum of problems that may be possible to solve by applying the EM. The majority of our experiments show a high level of robustness for DStr and DSize.

Assessing Robustness of Morphological Characteristics of Arbitrary Grayscale Images