• M. M. Filyak Cand. Sci. (Eng.), Associate Professor of the Department of Industrial Electronics and Informing and Measuring Techniques, Orenburg State University; tel.: +7(3532) 372874, e-mail:
  • A. G. Chetverikova Cand. Sci. (Phys.-Math.), Associate Professor, Dean of the Physics Department, Orenburg State University; tel.: +7(961) 9378459, e-mail:
  • O. N. Kanygina Dr. Sci. (Phys.-Math.), Full Professor, Professor of the Department of General Physics, Orenburg State University, tel.: +7 (3532) 372439, e-mail:
Keywords: surface of condensed matter, structural element, size, image, model, wavelet spectrum


The main tasks when it comes to the image processing of condensed matter surfaces are dispersion and morphological analyses. Determining the size and shape of the structural elements that form condensed matter is of paramount importance. Getting the most out of the image is a key issue. Recently, similar studies have been conducted using a continuous wavelet transform.

The method of determining the structural element sizes on the surface of condensed media by means of the wavelet transform of the generated models of optical images is proposed. The choice of method is due to the possibility of transition to a frequency-spatial representation of the object without preliminary image processing. A large statistical sampling and adaptation to an almost unlimited number of surface morphological features provides additional advantages.

During the simulation, the real particles of irregular shape are replaced by equivalent particles of regular geometric shapes, for example, rectangles or tetrahedra. To restore the size of real particles, the concept of an equivalent diameter is used.

Correct tetrahedrons are chosen as reference structural objects for the modelling. This choice is mainly due to the isometric or fragmented form of natural clay particles on which the method is tested.

The result of wavelet processing of optical images is the wavelet spectrum W (m, n). The particle size is related to the scale m, on which the apexes of “arches” are found by a simple relation.

The method was tested on the generated model with particle sizes (μm) of 120, 240, and 600 and a natural clay powder containing fragments of fragment form (600£d£630 μm).

The proposed method makes it possible to estimate the equivalent particle diameters values of irregular shapes in real monomorphic systems and to reveal structural inhomogeneities. This is a highly informative method and complements the method list for studying the surface structures of real materials.



The reported study was supported by the Russian Foundation for Basic Research and the Government of the Orenburg Region as a part of research project №17-42-560069 r_a “New optical and mathematical methods for the analysis of structural variations of disperse and nanostructured systems.”


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How to Cite
Filyak, M. M., Chetverikova, A. G., & Kanygina, O. N. (2018). DETERMINATION OF THE DIMENTIONS OF STRUCTURAL ELEMENTS ON THE CONDENSED MATTER SURFACE BY WAVELET-TRANSFORMATION OF GENERATED OPTICAL IMAGES. Kondensirovannye Sredy I Mezhfaznye Granitsy = Condensed Matter and Interphases, 20(1), 156-164.