<title>Determining Optical Flow</title>

TLDR

Optical flow requires an additional constraint because a single image point provides only one measurement while the flow has two components. The study proposes a method to compute optical flow by assuming that the apparent brightness velocity varies smoothly almost everywhere in the image. The method estimates flow by enforcing smoothness of the brightness velocity across the image to resolve the underdetermined problem. An iterative implementation successfully computes optical flow on synthetic sequences, remaining robust to coarse spatial/temporal quantization, brightness quantization, additive noise, and even when smoothness assumptions are violated at singularities.

Abstract

Optical flow cannot be computed locally, since only one independent measurement is available from the image sequence at a point, while the flow velocity has two components. A second constraint is needed. A method for finding the optical flow pattern is presented which assumes that the apparent velocity of the brightness pattern varies smoothly almost everywhere in the image. An iterative implementation is shown which successfully computes the optical flow for a number of synthetic image sequences. The algorithm is robust in that it can handle image sequences that are quantized rather coarsely in space and time. It is also insensitive to quantization of brightness levels and additive noise. Examples are included where the assumption of smoothness is violated at singular points or along lines in the image.