Sparse Optical Flow Computation Using Wave Equation-Based Energy

Abstract

Identification of motion in videos is a fundamental task for several computer vision problems. One of the main tools for motion identification is 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: a data term based on brightness constancy and a regularization term based on energy of the wave. Flow is determined by solving a system of linear equations. The decoupling of the pixels in the solution allows solving the system by a direct or iterative approach and makes the method suitable for parallelization. We present the convergence conditions for our method since it does not converge for all the image points. For comparison purposes, we create a global video descriptor based on histograms of optical flow for the problem of action recognition. Despite its sparsity, results show that our method improves the average motion estimation, compared with classical methods. We also evaluate optical flow error measures in image sequences of a classical dataset for method comparison.