Optical Flow with Harmonic Constraint and Oriented Smoothness

Computation of the optical flow from a sequence of images remains open in the community of computer vision. Two classical models for this problem are the global smoothness algorithm proposed by Horn-Schunck and the oriented smoothness algorithm by Nagel and Enkelmann. In order to increase the accuracy of motion discontinuity, we propose a new optical flow model which incorporates the harmonic smoothness constraint borrowed from the harmonic gradient vector flow (HGVF) model into the oriented smoothness constraint. In particular, we combine the curl term of the harmonic constraint with the oriented smoothness to control the direction of the displacement vectors together and introduce two spatially varying weighting functions to control the above-mentioned two terms. The benefit of the suggested strategies is illustrated qualitatively on the synthetical image and quantitatively on the Middlebury optical flow benchmark. Compared with the classical Horn-Schunck and Nagel-Enkelmann methods, this method can provide more accurate estimation of optical flow around motion discontinuities.