A General Motion Model and Spatio-Temporal Filters forComputing Optical Flow

  • Authors:

  • Hongche Liu;Tsai-Hong Hong;Martin Herman;Rama Chellappa

  • Affiliations:

  • Intelligent Systems Division, National Institute of Standards and Technology (NIST), Blg. 220, Rm B124, Gaithersburg, MD 20899;Intelligent Systems Division, National Institute of Standards and Technology (NIST), Blg. 220, Rm B124, Gaithersburg, MD 20899;Intelligent Systems Division, National Institute of Standards and Technology (NIST), Blg. 220, Rm B124, Gaithersburg, MD 20899;Center for Automation Research/Department of Electrical Engineering, University of Maryland, College Park 20742

  • Venue:
  • International Journal of Computer Vision
  • Year:
  • 1997

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Abstract

Traditional optical flow algorithms assume local image translationalmotion and apply simple image filtering techniques. Recent studies have taken two separateapproaches toward improving the accuracy of computed flow: the application ofspatio-temporal filtering schemes and the use of advanced motion models such as the affinemodel. Each has achieved some improvement over traditional algorithms in specializedsituations but the computation of accurate optical flow for general motion has been elusive. In thispaper, we exploit the interdependency between these two approaches and propose a unifiedapproach. The general motion model we adopt characterizes arbitrary 3-D steady motion.Under perspective projection, we derive an image motion equation that describes thespatio-temporal relation of gray-scale intensity in an image sequence, thus making theutilization of 3-D filtering possible. However, to accommodate this motion model, we need toextend the filter design to derive additional motion constraint equations. Using Hermitepolynomials, we design differentiation filters, whose orthogonality and Gaussian derivativeproperties insure numerical stability; a recursive relation facilitates application ofthe general nonlinear motion model while separability promotes efficiency. The resultingalgorithm produces accurate optical flow and other useful motion parameters. It isevaluated quantitatively using the scheme established by Barron et al. (1994) andqualitatively with real images.