Gradient Based Image Motion Estimation Without Computing Gradients

Abstract

Computing an optical flow field using the classical image motion constraint equation $I_x u + Iy\upsilon + I_t = 0,$ is difficult owing to the aperture problem and the need to compute the image intensity derivatives via numerical differentiation—an extremely unstable operation. We integrate the above constraint equation over a significant spatio-temporal support and use Gauss's Divergence theorem to replace the volume integrals by surface integrals, thereby eliminating the intensity derivatives and numerical differentiation. We tackle the aperture problem by fitting an affine flow field model to a small space-time window. Using this affine model our new integral motion constraint approach leads to a robust and accurate algorithm to compute the optical flow field. Extensive experimentation confirms that the algorithm is indeed robust and accurate.