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Finding the Optical Flow

The above smoothness constraint is not necessarily entirely consistent with the optical flow constraint. We can express how much a solution for u and v deviates from the condition required by the optical flow constraint equation by evaluating

To meaningfully combine these two constraints, we use the technique of Lagrangian multipliers:

Minimising the resulting integral can be done by using standard techniques from the calculus of variations, which show that the functions u and v which are required satisfy the coupled pair of differential equations:


The derivatives of I for each pixel are obtained from the original image, and tex2html_wrap_inline3740 is chosen as above. An iterative method can then be used to solve these equations for u and v at each pixel.

tex2html_wrap_inline2984 David Marshall 1994-1997