Kalman filtering from a phase based optical flow operator

Abstract

We present an optical flow operator composed of a phase based point disparity measurement combined with a Kalman filter that integrates flow information across the scene to obtain two constraints on the optical flow. The point optical flow value is computed as the time derivative of phase divided by the space derivative.

We maximize the efficiency of the algorithm by using causal filters that respond to a wide range of orientation of features so that we only need to convolve each frame with two filters, with the horizontal and vertical components of optical flow being computed separately.

We obtain simple expressions for computing the uncertainty in the phase of the filter response, and note that the uncertainty in the real and imaginary components are uncorrelated. Thus we are able to compute the uncertainty in the phase of the complex filter response and hence the uncertainty in component optical flow measurement. We note that two causal filters cannot directly provide all of the uncertainty information and so we must settle for the assumption that the information we do have is a single constraint whose orientation we estimate. This allows us to compute an uncertainty covariance matrix.