Robust Optical Flow Integration

We analyze the problem of how to correctly construct dense point trajectories from optical flow fields. First, we show that simple Euler integration is unavoidably inaccurate, no matter how good is the optical flow estimator. Then, an inverse integration scheme is analyzed which is more robust to bias and input noise and shows better stability properties. Our contribution is threefold: 1) a theoretical analysis that demonstrates why and in what sense inverse integration is more accurate; 2) a rich experimental validation both on synthetic and real (image) data; and 3) an algorithm for approximate online inverse integration. This new technique is precious whether one is trying to propagate information densely available on a reference frame to the other frames in the sequence or, conversely, to assign information densely over each frame by pulling it from the reference.