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A General Motion Model and Spatio-Temporal Filters for Computing Optical Flow



H Liu, Tsai H. Hong, Martin Herman, Rama Chellappa


Traditional optical flow algorithms assume local image translational motion and apply simple image filtering. Recent studies have taken two separate approaches toward improving the accuracy of computed flow: the application of spatio-temporal filtering schemes and the use of generalized motion models such as the affine model. Each has achieved some improvement over traditional algorithms in specialized situations. In this paper, we analyze the interdependency between them and propose a unified approach. The general motion model we adopt characterizes arbitrary 3-D steady motion. Under perspective projection, we derive an image motion equation that describes the spatio-temporal relation of gray-scale intensity in an image sequence, thus making the utilization of 3-D filtering possible. However, to accommodate this complex motion, we need to extend the filter design to derive additional motion constraint equations. Using Hermite polynomials, we design differentiation filters, whose orthogonality and Gaussian derivative properties insure numerical stability. The resulting algorithm produces accurate optical flow and other useful motion parameters. It is evaluated quantitatively using the scheme established by Barron, et al.[4] and qualitatively with real images.
NIST Interagency/Internal Report (NISTIR) - 5539
Report Number


3-D motion, evaluation, general motion model, gradient-based method


Liu, H. , Hong, T. , Herman, M. and Chellappa, R. (1994), A General Motion Model and Spatio-Temporal Filters for Computing Optical Flow, NIST Interagency/Internal Report (NISTIR), National Institute of Standards and Technology, Gaithersburg, MD, [online], (Accessed April 16, 2024)
Created October 31, 1994, Updated October 12, 2021