Scalar fields features of video sequences energy characteristics
Authors: Vasilyev S.V. , Bogoslovsky A.V. , Zhigulina I.V. 
Published: April 2024

To improve the methods of spatio-temporal filtering, an approach based on the analysis of finitary images energy spectra can be used. The purpose of this work is to study the possibility of using energy spectra for motion identification in video sequence frames. Each frame of a video sequence is a spatially finite image, the energy spectrum of which contains information about the phase components. This information is of particular importance for determining the location of dynamic objects. The most important information is also contained in the harmonic amplitude increments of the frame energy spectra, i.e. the energy spectrum generates a scalar discrete field. The energy functions describe inter-frame changes in the amplitudes of harmonics of the energy spectrum. To apply energy spectra in motion identification algorithms, it is necessary to analyze the properties of these scalar fields. Scalar fields generated by energy spectra of frames of test video sequences are studied. Test video sequences with an object moving in an arbitrary direction are used. Scalar fields of energy functions are presented graphically. Characteristic regions of scalar fields are identified and their projections are built using isolines. The boundaries of the characteristic areas and the coordinates of extrema of energy functions are determined. From them, all coordinates of the dynamic object and its horizontal/vertical displacements can be found. The dependence of phase-energy function extrema on the position of the object before the motion and on the direction of motion is studied. When moving in an arbitrary direction, different types of extrema are observed: point and extended. At vertical or horizontal movements, the energy functions graphs have only two-dimensional pulses. Additional criteria for eliminating ambiguities are proposed. The ambiguities are due to the fact that the number and nature of extrema may coincide for different directions of motion and location of objects in different quadrants of the coordinate plane. The extrema of energy functions for object movements in all possible directions and locations in any quadrant of a video sequence frame are determined. The obtained results showed that energy functions for object motion in arbitrary direction have a large number of characteristic regions containing point and extended extrema. The configuration of extrema depends both on the direction of motion and on the quadrant of the image in which the object is located. Therefore, it is most advisable to begin to determine the spatial coordinates of an object and the magnitude of its horizontal/vertical movement by finding the maximum and minimum boundaries of energy functions, and then refine it using the coordinates of the extrema. Consideration of characteristic regions and extrema of scalar fields of energy functions can be used in the development of algorithms effective in terms of "accuracy/speed" ratio, and can increase the performance of image and video processing systems. Algorithms for determining the object position, velocity and direction of its movement by analyzing scalar fields of energy spectra components can be used as an additional or main tool for motion identification in technical vision systems.