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On a Constraint Equation for the Estimation of Displacement Rates in Image Sequences
January 1989 (vol. 11 no. 1)
pp. 13-30

The commonly used constraint equation Delta g/sup T/u+g/sub t/=0 for the estimation of optical flow can only be justified by assumptions that are, in general, far too restrictive for image sequences of real world scenes. B.G. Schunck (1985, 86) recently argued that a constraint equation for the estimation of what he called image flow has to include a term containing the divergence of this image flow without presenting, however, a stringent derivation based on perspective projection from 3-D scene space. The present author derives a constraint equation based on a combination of perspective projection and notions from differential geometry. In addition, he demonstrates the quantitive effects of taking into account radiometric considerations based on the use of Lambertian reflection properties and isotropic illumination in scene space.

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Index Terms:
picture processing; image sequences; constraint equation; optical flow; real world scenes; image flow; perspective projection; differential geometry; Lambertian reflection; isotropic illumination; optical information processing; picture processing; radiometry
H H. Nagel, "On a Constraint Equation for the Estimation of Displacement Rates in Image Sequences," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 11, no. 1, pp. 13-30, Jan. 1989, doi:10.1109/34.23110
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