## 3 Results
### Morphological Security Code for Art Objects  
It has been demonstrated (Figures 12-14) that the DStr and DSize are sensitive to minor morphological pattern changes. This feature makes it possible to use the DStr and DSize as a pattern morphological security code (MSC), i.e., the unique morphological characteristics of the original artwork, which are difficult to reproduce with the same level of accuracy as an original pattern. One of the areas where an MSC can be applied is in the detection of false art objects. Different technologies have been used to solve this problem [41; 42; 43; 44]. An MSC complements these technologies by creating obstacles to the construction of false art works. Let us consider the example of applying the DStr and DSize to develop an MSC for an art object. Figure 15 shows the artist graphic drawing used for the development of an MSC. The pattern (Figure 15a) is a convenient object for morphological assessment due to several factors: (a) it has a complicated structure, (b) its pattern is comprised of different geometrical objects that have configurations suitable for MSC construction; and (c) its high gradient allows us to use a relatively simple procedure to convert local graphical objects (Figure 15b) into binary patterns A1, A2, A3,..., E6, E7 (Figure 15c). The experiment has the following steps. Step #1: Binary pattern A1 is rotated for angles 0\({}^{\circ}\), 10\({}^{\circ}\),..., 180\({}^{\circ}\). Notation A1(20\({}^{\circ}\)) represents pattern A1, which is rotated by an angle of 20\({}^{\circ}\). Step #2: The DStr is calculated for A1(0\({}^{\circ}\)), A1(10\({}^{\circ}\)),...,A1(180\({}^{\circ}\)). Notation DSize[A2(60\({}^{\circ}\))] represents the DStr for pattern A2, which is rotated by an angle of 60\({}^{\circ}\). Step #3: The DStr parameters are averaged over DStr[A1(0\({}^{\circ}\))], DStr[A1(10\({}^{\circ}\))],..., DStr[A1(180\({}^{\circ}\))], resulting in in DStr\({}_{\text{average}}\)(A1). Step #4: Steps 1 and 3 are repeated for patterns A2, A3,..., E6, E7, resulting in DStr\({}_{\text{average}}\)(A2), DStr\({}_{\text{average}}\)(A3),..., DStr\({}_{\text{average}}\)(E7). Step #5. Steps 1 through 4 are repeated for the DSize, resulting in DSize\({}_{\text{average}}\)(A2), DSise\({}_{\text{average}}\)(A3),..., DSizeAverage(E7). Figure 16a represents the values of DStraverage and DSizeaverage for patterns A1-E7. There are two patterns, A3 and D4, which exhibit extreme values for DStraverage and DSizeaverage. The parameter DStraverage(A3) is extremely high with respect to the rest of the patterns, and the parameter DSizeaverage(A3) is extremely low. Pattern D4 exhibits the opposite morphological characteristics of A3. Another set of morphological characteristics showing differences between A3 and D4 are DStr = f(number of transects) and DSize = f(number of transects). Figure 16b depicts DStr[A3(10\({}^{\circ}\))] = f(number of transects) and DStr[D4(10\({}^{\circ}\))] = f(Number of transects). These two graphs show the robust differences between A3(10\({}^{\circ}\)) and D4(10\({}^{\circ}\)) in terms of the variability of the DStr across different numbers of transects. The same robust differences found between A3 and D4 for the DStr are also seen in DSize[A3(110\({}^{\circ}\))] = f(number of transects) and DSize[D4(110\({}^{\circ}\))] = f(Number of transects) (Figure 16c). Two very small geometrical elements, A3 and D4, seen in Figure 15a,b, could be used for the construction of an MSC. These elements have the following morphological characteristics:  
DStraverage(A3), DStraverage(D4), DSizeaverage(A3), DSizeaverage(D4) and charts  
DStr[A3(10\({}^{\circ}\))] = f(Number of transects), DStr[D4(10\({}^{\circ}\))] = f(Number of transects),  
DSize[A3(110\({}^{\circ}\))] = f(Number of transects), DSize[D4(110\({}^{\circ}\))] = f(Number of transects). Whether to use A3 or D4 to calculate an MSC is based on individual preferences. Any element/elements of a graphical drawing with a relatively complicated structure could be used for the development of an MSC.