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11 May 1987 A Closed-Form Solution For The Estimation Of Optical Flow
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A closed-form solution for the determination of optical flow is presented. In addition to being closed-form, this approach does not require the optical flow field to be spatially smooth. By assuming that the m-th order time-derivative of the optical flow is zero, (m can be chosen as large as required depending on the desired accuracy), the relationships between optical flow and its derivatives in a sequence of frames to those at a particular frame of the sequence are obtained. These relations in conjunction with the brightness constraint equation are used to form a system of linear equations in which the unknowns are the components of optical flow which can be recovered by the inversion of a 2m x 2m matrix. The entries of this matrix contain only the first order spatial and temporal brightness derivatives. An alternative solution to the problem is considered in which each component of the optical flow is modelled as a polynomial (in time) of degree m-l.
© (1987) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Shankar Moni "A Closed-Form Solution For The Estimation Of Optical Flow", Proc. SPIE 0786, Applications of Artificial Intelligence V, (11 May 1987);

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