Optical flow computation using wave equation based energy

Abstract

Identification of motion in videos is a fundamental task to analyse their semantic informa-tion. One of the main tools for motion identification is the optical flow, which estimates the projection of the 3D velocity of the objects onto the plane of the camera. In this work, we propose a differential optical flow method based on the wave equation. The optical flow is computed by minimizing a functional energy composed by two terms: brightness constancy and energy of the wave. The flow is then determined by solving iteratively a system of linear equations. The decoupling of the pixels in the solution ensures quick convergence and makes the method suitable for parallelization. However, our approach does not converge for all the image points and we present its convergence conditions. We apply our optical flow in the action recognition problem by creating a global video descriptor based on histograms of optical flow (HOF). Despite its sparsity, our method outperforms the classical approaches. We also evaluate optical flow error measures for some known image sequences. The errors found are similar for our method and the classical optical flow approaches.