## 4 Discussion
### Areas of Application  
Experiments in the Results section justify the possibility of using the EM to quantify the morphological characteristics of various arbitrary patterns. The parameters DStr, DSize, and PCom are used for tracking changes in the size and structure of patterns, revealing anomalies in their shapes and structure that can be used for quality control of products of various categories.  
The EM can be used for digitizing large collections of specimens stored in national and international repositories and natural history museums. For instance, marine organizations around the word have for decades collected samples of fish scales [70; 71] and otoliths [72] as a source of information about marine life. Only a very small part of these fish scale and otolith images are available in a digital format for analysis. Our proposed technology could be used to convert each fish scale and otolith pattern into the EM and then calculate the DStr, DSize, and PCom in order to develop a searchable morphological database of growth patterns [73]. Such a morphological database, together with the World Ocean Database [74] and regional oceanographic databases [75], will allow us to better understand the life cycle and predict the space-time distribution of fish schools, which can have both scientific and commercial applications.  
Different categories of contour maps in different space-time domains have been collected for decades across various countries. International and national environmental agencies have made these data sets publicly available for the international community viathe Internet. The EM could be potentially used to develop a searchable morphological database of these contour maps. The DStr, DSize, and PCom can serve as tools for retrieving maps according to their dynamics in the space-time domain, describing changes in the contours' morphology, revealing anomalies in contour structure and size, and tracing the evolution of those anomalies.  
Being able to describe binary patterns in terms of a Boolean function and G(N) allows us to formulate new problems and propose formal procedures to solve those problems. For instance, binary patterns in the raster format cannot be absolutely precise, which resulted in the notion of graph stability [76]. It is possible to interpret the stability of G(N) as the robustness of the DStr, DSize, and PCom to minor changes in structure and size of arbitrary patterns. This problem can be formulated and solved in terms of G(N) and a Boolean function, which is important for medical applications, since patterns of living systems such as tumors have fuzzy borders resulting from uncertainty in the description of the system's morphological characteristics. Thus, the EM could be used to quantify the robustness of the morphological description of medical patterns.  
Macro-, micro-, and nanostructures play a vital role in understanding pattern formation and relationships between processes and structures [77]. A central problem in studying the structure of arbitrary patterns--particularly in materials science [78] and biomimetic research [79; 80]--is how to quantitatively describe the relationship between a pattern's structure and its properties. For instance, geometrical features are used to quantify the shapes of nanoparticles, since magnetic properties of materials are substantially dependent on the shape characteristics [54]. The parameters DStr, DSize, and PCom could be also used for the formalization of nanoparticles to describe in quantitative terms the correspondence morphology vs. properties.