Analysis of Optical Flow

Abstract

Abstract If the motion of objects (or the camera) is very small, the corresponding image motion defines an optical flow. Since the displacement of each image point is small (theoretically infinitesimal), it appears that computations based on optical flow are unstable and sensitively affected by image noise. However, the use of optical flow has the advantage that the flow is detected densely (usually at each pixel) over the entire frame by straightforward operations, whereas matching feature points over multiple frames for a finite motion is a very difficult task. Hence, it is expected that a reliable 3-D interpretation can be obtained from optical flow by optimization over the entire frame. As in the case of finite motion, we begin with planar surface motion and derive an analytical solution. Planar surface optical flow is easily determined by two methods—the flow-based approach and the contour-based approach. We then go on to general optical flow and present a robust analytical procedure. This procedure is almost identical to that for finite motion-all we need to solve is the epipolar equation written in terms of the essential parameters and the twisted optical flow. In order to ensure robustness in the presence of noise, the problem is also formulated in the form of optimization in two different ways. Finally, the critical surface that yields ambiguous 3-D interpretations is discussed.