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

Detection and tracking are essential to technical space monitoring systems, which must process substantial data volumes under stringent real-time constraints. For image-based systems, computational costs drop significantly when processing is confined to the frame region containing the object – the tracking window. This reduces tracking to determining how this window should shift in accordance with the object's motion. Solving the tracking problem requires detecting when a moving object enters the frame and establishing its coordinates and velocity. This calls for high-speed peripheral processing using computationally inexpensive yet sufficiently accurate features for characterizing dynamic objects. The image's phase-energy spectrum – a vector function combining energy and phase-frequency properties – offers a promising solution. For moving objects, the spectrum's most informative characteristic is its circulation.

This study investigates whether phase-energy spectrum vector field circulation can support algorithms tracking objects that shift between frames. We derive an analytical expression for circulation along an arbitrary rectangular contour. The integration contours chosen are the boundaries of the phase plane's first and second quadrants, traversed positively. Specific expressions for circulation around these quadrants are provided.

Results show zero circulation at two-dimensional period boundaries but non-zero values along quadrant boundaries. Absolute circulation values prove equal for both even and odd quadrants, justifying our focus on adjacent quadrant boundaries alone.

Analysis reveals a relationship between circulation values over the selected contours and the object's frame position. Absolute circulation decreases as the object approaches the corresponding frame diagonal. This finding underpins an iterative algorithm for centering the tracking window – the frame subregion containing the object – between consecutive frames. We establish relations for the angle determining window displacement direction and demonstrate algorithm performance on real video footage. Computational cost estimates suggest the algorithm can run on specialized graphics hardware under demanding real-time operational requirements.

These findings on vector field circulation generated by the image phase-energy spectrum can inform algorithm development for various observation systems: intelligent autonomous search, detection and tracking platforms, transportation analytics, industrial process control, and related applications.

Bogoslovsky A.V., Vasilyev S.V., Zhigulina I.V. Using the phase-energy spectrum vector field circulation to track moving objects. Radiotekhnika. 2026. V. 90. № 5. P. 131−140. DOI: https://doi.org/10.18127/j00338486-202605-16 (In Russian)

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