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A vector field of the phase-power spectrum of an image and a video sequence

DOI 10.18127/j00338486-201811-02

Keywords:

A.V. Bogoslovsky – Honored Scientist of RF, Dr.Sc.(Eng.), Professor, Department of Mathematics, MESC «Zhukovsky–Gagarin Air Force Academy» (Voronezh)
E-mail: p-digim@mail.ru
I.V. Zhigulina – Ph.D.(Eng.), Associate Professor, Professor, Department of Mathematics, MESC «Zhukovsky–Gagarin Air Force Academy» (Voronezh)
E-mail: ira_zhigulina@mail.ru
V.A. Sukharev – Ph.D.(Eng.), Senior Lecturer, MESC «Zhukovsky–Gagarin Air Force Academy» (Voronezh)
E-mail: vladimir-a-sukharev@yandex.ru


A vector field of the phase-power spectrum is proposed here as a new method for image and video sequence analysis. Power-phase spectrum is a new integral characteristic, which contained both, amplitude and phase information about the image and video sequence. For the 2D case, the components of the phase-power spectrum were found and the spectrum was analysed in a random direction within the spatial frequencies. The rations between 2D phase-power spectrum to 1D phase-power spectra of columns and rows of an image were found. This involves, the mathematics of the field theory. The curl of the vector field of the phase-power spectrum and the circulation around a closed curve in the spatial frequencies. It is shown that the circulation around a closed curve across all spatial frequencies identically zero. The proposed method was generalized to video sequences. To do this, the 3D vector field with depended components from the two spatial and one time frequencies was analysed.

References:
  1. Bogoslovskij A.V. Ispol’zovanie fazochastotny’x prostranstvenny’x xarakteristik dlya oczenki dvizheniya // Uspexi sovremennoj radioe’lektroniki. 2009. № 11. S. 61−63.
  2. Bogoslovskij A.V., Zhigulina I.V., Kopy’lov O.E., Yakovlev V.A. Opredelenie parametrov dvizheniya ob’‘ekta po izobrazheniyu na osnove mezhkadrovy’x raznostej chastotny’x xarakteristik // Radiotexnika. 2010. № 5. S. 55−59.
  3. Bogoslovskij A.V., Ponomarev A.V., Kopy’lov O.E., By’kov Yu.A. Modeli e’nergeticheskix xarakteristik videosignala izobrazheniya modeli e’nergeticheskix xarakteristik videosignala izobrazheniya // Radiotexnika. 2016. № 10. S. 110−115.
  4. Bogoslovskij A.V., Zhigulina I.V., Suxarev V.A., Ponomarev A.V. Korrelyaczionny’j analiz finitny’x po prostranstvu odnomerny’x signalov // Radiotexnika. 2017. № 12. S. 4−7.
  5. Zhigulina I.V. E’nergeticheskie xarakteristiki izobrazhenij i videoposledovatel’nostej // Materialy’ 13 j Mezhdunar. konf. «Televidenie: peredacha i obrabotka izobrazhenij». S.-Peterburg: SGE’U «LE’TI» im. V.I. Ul’yanova (Lenina). 2016. S. 128−131.
May 29, 2020

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