## 1 Introduction  
In our previous work [1; 2; 3], we have justified that though the visual macro differences between patterns are significantly distinct, they nevertheless share a common feature: they have layers. A majority of arbitrary patterns could be described as being comprised of a very short layer system. Even when these short layers are detectable by the naked eye, they are not a visually dominant feature of an image and thus are not used as building blocks to assess that image's morphology.  
Studying the growth rates of fish scales [4; 5] and lamellar bones [1; 6; 7] brought to our attention the fact that short layers could serve as a structural building block of arbitrary patterns. This resulted in the development of 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 EM is comprised of an N-partite graph G(N), a Boolean function (BF), and table T\({}_{\text{M,N}}\), where G(N) and BF describe the structure of an arbitrary binary image and T\({}_{\text{M,N}}\) describes the image size along transects R\({}_{1}\),..., R\({}_{j}\),..., R\({}_{N}\); EM = {G(N), BF, T\({}_{\text{M,N}}\)}. A property of EM is that isotropic and anisotropic edges/vertices (i.e., isotropic/anisotropic connections) of G(N) serve as building blocks for the calculation of DStr. This means that forms of lines play no role as a morphological factor for very narrow areas of an image. Instead, types of line connectivity, i.e., isotropic/anisotropic connections are responsible for the description of an image's structure.  
This statement is the basic concept of our approach to the morphological analysis of arbitrary patterns. In addition, DStr, DSize, and PCom are dependent on an image's orientation. Thus, DStr, DSize, and PCom represent the morphological characteristics of an image as a function of its rotation.  
The focus of our previous work [1; 2; 3; 5; 6; 7] was binary patterns and their analysis based on the EM. The goal of the present work is to justify the possibility of making the EM applicable to 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.  
Any grayscale image formed in nature and beyond, irrespective of its size and structure, is called a grayscale arbitrary image (GAI). Both images that exhibit high and low edge gradients are used for this experimental study. The robustness of the morphological characteristics of DStr and DSize against GAI binarization is described in both absolute (deviation from the average) and relative (Pearson's coefficient [8] linear correlation) terms. The image global threshold is used to convert a GAI with a high edge gradient into binary mode and a watershed algorithm [9; 10] is applied for the binarization of a GAI with a low edge gradient. The output of the watershed algorithm is a binary contour map. Various grid sizes of contour maps and the Gaussian blur radius are used to generate sets of contour maps in order to estimate the robustness of DStr and DSize against GAI binarization.  
The paper is organized as follows. The proposed method is detailed in Section 2. Experimental results are provided in Section 3. A discussion is provided in Section 4. Concluding remarks are presented in Section 5.