Precise differentiation can significantly improve the accuracy of optical flow measurements

Optical flow algorithms for estimating image local motion in video sequences are based on the first term Taylor series expansion approximation of image variations caused by motion, which requires computing image spatial derivatives. In this paper we report an analytical assessment of lower bounds of optical flow estimation errors defined by the accuracy of the Taylor series expansion approximation of image variations and results of experimental comparison of performance of known optical flow methods, in which image differentiation was implemented through different commonly used numerical differentiation methods and through DFT/DCT based algorithms for precise differentiation of sampled data. The comparison tests were carried out using simulated sequences as well as real-life image sequences commonly used for comparison of optical flow methods. The simulated sequences were generated using, as test images, pseudo-random images with uniform spectrum within a certain fraction of the image base band specified by the image sampling rate, the fraction being a parameter specifying frequency contents of test images. The experiments have shown that performance of the optical flow methods can be significantly improved compared to the commonly used numerical differentiation methods by using the DFT/ DCT- based differentiation algorithms especially for images with substantial high-frequency content