3-D infinite frequency resolution analysis and spatiotemporal spectrum of a moving object

A movie may be represented as a three-dimensional (3-D) signal and as a spatiotemporal spectrum in a 3-D frequency domain. Most spatiotemporal spectra lie on a theoretical motion plane when an object moves at a uniform velocity in a movie. By calculating the slope of this plane, we can estimate the velocity of the moving object. However, the spatiotemporal spectrum of a frequency analysis method such as a Fast Fourier Transform (FFT), is not always distributed on the theoretical motion plane and depends on the resolution of the frequency analysis method used. Consequently, FFT methods cannot be used for accurate analysis because of the influence of the analysis window. In this study, we develop 3-D infinite frequency resolution analysis (IFRA) by extending IFRA as a high-frequency resolution analysis method. To confirm how close the spectrum exists to the theoretical motion plane, we compare 3-D IFRA with 3-D FFT by calculating the variance. It is found that most of the 3-D IFRA spectra are almost on the theoretical motion plane.