Optical Flow Estimation: An Error Analysis of Gradient-Based Methods with Local Optimization

Multiple views of a scene can provide important information about the structure and dynamic behavior of three-dimensional objects. Many of the methods that recover this information require the determination of optical flow—the velocity, on the image, of visible points on object surfaces. An important class of techniques forestimating optical flow depend on the relationship between the gradients of image brightness. While gradient-based methods have been widely studied, little attention has been paid to accuracy and reliability of the approach. Gradient-based methods are sensitive to conditions commonly en-countered in real imagery. Highly textured surfaces, large areas of constant brightness, motion boundaries, and depth discontinuities can all be troublesome for gradient-based methods. Fortunately, these problematic areas are usually localized can be identified in the image. In this paper we examine the sources of errors for gradient-based techniques that locally solve for optical flow. These methods assume that optical flow is constant in a small neighborhood. The consequence of violating in this assumption is examined. The causes of measurement errors and the determinants of the conditioning of the solution system are also considered. By understanding how errors arise, we are able to define the inherent limitations of the technique, obtain estimates of the accuracy of computed values, enhance the performance of the technique, and demonstrate the informative value of some types of error.