Refraction wiggles for measuring fluid depth and velocity from video

We present principled algorithms for measuring the velocity and 3D location of refractive fluids, such as hot air or gas, from natural videos with textured backgrounds. Our main observation is that intensity variations related to movements of refractive fluid elements, as observed by one or more video cameras, are consistent over small space-time volumes. We call these intensity variations "refraction wiggles", and use them as features for tracking and stereo fusion to recover the fluid motion and depth from video sequences. We give algorithms for 1) measuring the (2D, projected) motion of refractive fluids in monocular videos, and 2) recovering the 3D position of points on the fluid from stereo cameras. Unlike pixel intensities, wiggles can be extremely subtle and cannot be known with the same level of confidence for all pixels, depending on factors such as background texture and physical properties of the fluid. We thus carefully model uncertainty in our algorithms for robust estimation of fluid motion and depth. We show results on controlled sequences, synthetic simulations, and natural videos. Different from previous approaches for measuring refractive flow, our methods operate directly on videos captured with ordinary cameras, do not require auxiliary sensors, light sources or designed backgrounds, and can correctly detect the motion and location of refractive fluids even when they are invisible to the naked eye.