A.V. Bogoslovsky1, S.V. Vasilyev2, I.V. Zhigulina3

1-3 MESC AF “N.E. Zhukovsky and Y.A. Gagarin Air Force Academy” (Voronezh, Russia)

1 p-digim@mail.ru; 2 stanislav-vas1986@mail.ru; 3 ira_zhigulina@mail.ru

In the tasks of determining the location of objects and identifying movement, it is important to use the phase information contained in the phase-frequency spatial spectrum. In these problems, the phase-energy spectrum can be applied, which combines the advantages of the energy and phase spectra. A frame of a video sequence can be associated with a discrete vector field of the phase-energy spectrum; its components are located throughout the image. No less informative, but much simpler for analysis, is the discrete vector field of phase-energy characteristics. Its components are formed by the amplitudes of the harmonics of the phase-energy spectrum of a two-dimensional frame. To use the vector field of phase-energy characteristics in algorithms for identifying dynamic objects, information about interframe changes in its components is important.

In this paper, the features of the change in the components of the vector field for the cases of horizontal and vertical movement of a rectangular object of constant brightness against a homogeneous background are investigated. Graphical representations of scalar fields of phase-energy functions are given. Characteristic regions are identified and their projections onto the coordinate plane are made. It is shown that two characteristic areas are the near and far hills, by analyzing which it is possible to determine the spatial coordinates of the object before the start of movement and the value of the object's inter-frame shift. The special areas of scalar fields of phase-energy functions are determined for the case of object motion in an arbitrary direction.

It has been established that the presence of extended extrema in the graphs of phase-energy functions indicates a strictly vertical or horizontal movement of the object, and the presence of point extrema indicates the movement of the object “at an angle”, and the boundaries of the moving object and the magnitude of its displacement horizontally and vertically are completely determined by the coordinates of the point extrema. A number of options for finding the parameters of objects by extremums and/or by the boundaries of characteristic regions of phase-energy functions are proposed. The "boundary" and "extreme" approaches can be applied in vision systems as both an additional and a main tool for motion identification.

Bogoslovsky A.V., Vasilyev S.V., Zhigulina I.V. Two-dimensional vector field of the phase energy spectrum application for motion identification. Radiotekhnika. 2023. V. 87. № 10. P. 96−106. DOI: https://doi.org/10.18127/j00338486-2023010-11 (In Russian)

1. Koul A., Gandzhu S., Kazam M. Iskusstvennyj intellekt i komp'juternoe zrenie. Real'nye proekty na Python, Keras i Tensor Flow. SPb: Piter. 2023. 624 s. (in Russian).
2. Klette R. Komp'juternoe zrenie. Teorija i algoritmy. Per. s angl. V.V. Slinkin. M.: DMK Press. 2019. 506 s. (in Russian).
3. Markus G., Djevis Je. Iskusstvennyj intellekt: Perezagruzka. Kak sozdat' mashinnyj razum, kotoromu dejstvitel'no mozhno doverjat'. M.: Intellektual'naja Literatura, 2021. 304 s. (in Russian).
4. Gonsales R., Vuds R. Cifrovaja obrabotka izobrazhenij. Izd. 3-e, ispr. i dop. M.: Tehnosfera, 2019. 1104 s. (in Russian).
5. Korennoj A.V., Kozhevnikov A.A., Jashhenko E.A. Kompleksnaja obrabotka izobrazhenij vidimogo i infrakrasnogo diapazonov. Radiotehnika. 2021. T. 85. № 4. S. 77-88. DOI: 10.18127/j00338486-202104-09 (in Russian).
6. Babajan P.V., Kozhina E.S. Avtomaticheskoe vydelenie i obnaruzhenie dvizhushhihsja ob’ektov s ispol'zovaniem videokamery s izmenjajushhimsja polem zrenija. Vestnik Rjazanskogo gosudarstvennogo radiotehnicheskogo universiteta, 2023. № 83. S. 84-94 (in Russian).
7. Udot S.A., Astashev N.L. Algoritmy raspoznavanija napravlenija dvizhenija ob’ekta avtomatizirovannoj sistemoj tehnicheskogo kontrolja, vkljuchajushhej v svoj sostav optiko-jelektronnye sredstva obnaruzhenija. Radiotehnika, 2017. № 1. S. 34-36 (in Russian).
8. Obrabotka mnogomernyh signalov. V 2-h knigah. Kn. 1. Linejnaja mnogomernaja diskretnaja obrabotka signalov. Metody analiza i sinteza. Pod red. A.V. Bogoslovskogo. M.: Radiotehnika. 2013. 168 s. (in Russian).
9. Bogoslovskij A.V., Suharev V.A., Zhigulina I.V., Pantjuhin M.A. Vektornye polja, porozhdaemye preobrazovaniem Fur'e videosignalov izobrazhenij. Radiotehnika. 2021. № 7. S. 127-139. DOI: 10.18127/j00338486-202107-17 (in Russian).
10. Zhigulina I.V. Jenergeticheskie harakteristiki izobrazhenij i videoposledovatel'nostej. Materialy 13-j Mezhdunarod. konf. «Televidenie: peredacha i obrabotka izobrazhenij». SPb.: GJeU «LJeTI» im. V.I. Ul'janova (Lenina). 2016. S. 128-131 (in Russian).
11. Bogoslovskij A.V., Zhigulina I.V., Suharev V.A. Vektornoe pole fazojenergeticheskogo spektra izobrazhenija i videoposledovatel'nosti. Radiotehnika. 2018. № 11. S. 11-16. DOI: 10.18127/j00338486-201811-02 (in Russian).
12. Bogoslovskij A.V., Vasil'ev S.V., Zhigulina I.V. Dvumernye fazojenergeticheskie harakteristiki. Sb. dokladov XXV Mezhdunarod. nauch. konf. «Cifrovaja obrabotka signalov i ee primenenie (DSPA-2023)». M.: RNTORJeS im. A.S. Popova. 2023. S. 256-259 (in Russian).