Tangent flow estimation based on 3-D gradient constraint

Due to the limitation of the gradient constraint, only the normal flow, which is one of the optical flow components that is in the direction of the image gradient, can be computed directly. Consequently, an additional smoothness assumption has to be imposed in order to compute the optical flow. However, such assumption could yield a mismatch, especially on the boundaries of moving objects, besides the computational complexity issue. To address these concerns, in this paper, a three-dimensional (3-D) gradient constraint is developed and imposed for computing the optical flow without exploiting any smoothness assumption on the motion field. Based on this 3-D gradient constraint, the tangent flow, which is another optical flow component that is perpendicular to the normal flow, could be obtained through our derived closed-form solution at each pixel position. This also means that the standard aperture problem could be efficiently solved. The experimental results show that the proposed approach yields a fairly precise optical flow field with a very low computational load.