The analysis of textural images on the basis of orthogonal transformations

The aim of the conducted research is development and search of analysis algorithms of textural images. The software products, which allow analyzing successfully textures in details, can be used in different fields of science and the industry. First of all, it is chemistry and materials science. It is possible to analyze materials of organic origin, cuts of metals and minerals, ceramics, etc. Another field of research, where we can effectively apply these methods, is the diagnosis of internal pathologies of human, including malignant, according to the images received by means of the thermal imager. In this study we are talking about application of spectral decomposition on various orthonormalized bases of images, which were received by the translucent electronic microscopy. The program is implemented in the Matlab environment, which allows spectral transformations of six types: 1) cosine, 2) Hadamard of the 2ⁿ order, 3) Hadamard of the order n = p +1, p ≡3(mod4)-prime number, i.e. based on Legendre's symbol, 4) Haar, 5) slant, 6) Dobeshi-4. Various experiments were made. The algorithms, which were studied in this research, have allowed us to allocate effectively on the analyzed images some fields, which can be characterized by different degrees of structure orderliness. To say more precisely, chemists are interested in the “disorder” areas of structure of materials, for example, during studying the ultrastructure of plant cell walls. This research was made for the Institute for Chemistry of Solids and Mechanochemistry of the Siberian Branch of the Russian Academy of Sciences. The main attention was paid to the development of software tools for the analysis of the above microphotographs. It is supposed that received characteristics for different images-textural signs, as well as various spectral coefficients can be further correlated with values, which characterize the physical and chemical properties of the analyzed material: reactivity, porosity, diffusion coefficient, and so on. For correlation, it will be possible to use algorithms for machine learning, for example, based on the neurocomputer approach.