|Temporal Lucas Kanade|
The temporally filtered Lucas-Kanade algorithm is another approach to extract optic flow over the temporal domain. While the combination of the Lucas-Kanade algorithm with a Kalman Filter included temporal filtering as a post-processing step the following approach includes the temporal filter directly in the estimation step.
In the Lucas-Kanade algorithm the optic flow constraintis solved by weighted least-squares estimation over the spatial domain. Here we extend the estimation to the temporal domain leading to the following minimization problem:
The solution to this minimization problem is given by equation 2. By choosing an exponential temporal weighting function (equation 3) we avoid to fully recompute G and B in every step. Instead we can compute G and B iteratively (equations 4 and 5).
The properties of the temporal filtering are controlled by parameter α which must lie between 0 and 1 where larger values mean less filtering over the temporal domain.
Fleet, D., & Langley, K. (1995). Recursive filters for optical flow. IEEE Transactions on Pattern Analysis and Machine Intelligence, 17(1), 61-67
This method is available as an implementation for microcontroller as well as a generic C algorithm in the Library in