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

The effective use of phase-energy spectra in methods for processing and analyzing video information is impossible without a thorough investigation of the characteristics of two-dimensional discrete fields generated by these spectra. The phase-energy spectrum is clearly not a purely potential vector field; therefore, vorticity is one of its most important differential characteristics. The aim of this work is to investigate the properties of the phase-energy spectrum’s vector field and the possibilities of applying these properties in image analysis.

This work demonstrates that the components of the phase-energy spectrum are more sensitive to the phase content of the image than the autocorrelation fiction. This is related to the fact that the autocorrelation function can only determine the position of objects on finite images, whereas the components of the phase-energy spectrum contain phase information in explicit form.

The amplitudes of the spatial harmonics of the rotor of the flat vector field of the phase-energy spectrum are considered as an independent new rotor characteristic since they contain an important informational component about the image. Since even in the simplest case, determining the location of an object on the image directly from the rotor characteristic graph and its projection onto the phase plane is challenging, a modified rotor characteristic is introduced. This characteristic is defined as the difference between the functions of auto-convolution and autocorrelation of the image.

The properties of the modified rotor characteristic are investigated. Analytical expressions for the one-dimensional rotor characteristics of test images are obtained. Their graphical representations are provided and projections onto the phase plane are constructed. Particular areas of interest are highlighted for analyzing rotor characteristics. It is established that the analysis process can be simplified by finding modified rotor characteristics for images without a constant component. In this case, the absolute values of the extrema increase, making them more pronounced in the graphs, while the amplitudes of extended impulses significantly decrease. It is shown that the modified rotor characteristic has advantages over the phase-energetic characteristic, as it has clearly defined extrema indicating the geometric centers of objects.

The study investigates a two-dimensional rotor characteristic, represented as a scalar field. Examples of rotor characteristics for a set of test images are provided, demonstrating that the configuration of images can be determined from the level lines. The main properties of the modified rotor characteristic of the phase-energy spectrum are formulated. It is establishes that, unlike other characteristics used in the energetic analysis of images, the rotor characteristic contains information about the shape of objects.

The results of determining the location and shape of objects in images through the analysis of rotor characteristics of phase-energy spectra can be utilized in algorithms for detection, recognition, and identification. The use of vector fields generated by phase-energy spectra can serve as an additional tool for automating the processing of video information in technical vision systems.

Bogoslovsky A.V., Vasilyev S.V., Zhigulina I.V. Vortex characteristics of image phase-energy spectrum. Radiotekhnika. 2025. V. 89.
№ 1. P. 37−49. DOI: https://doi.org/10.18127/j00338486-202501-03 (In Russian)

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