Comparing the Hyperplane Approximation and Gradient-based Optical Flow Methodologies applied to Global Image Motion

The hyperplane approximation technique is a recent popular approach to motion estimation applied to a range of computer vision techniques such as active appearance models and template matching. Simply, the method learns a linear relationship between artificially applied parametric motion perturbations and the consequent induced pixel greylevel differences. Once trained, solving for any new motion is equivalent to solving a set of linear equations in a multi-dimensional space, and, unlike the gradient-based approach, the hyperplane approximation avoids the need for extracting the grey-level gradients. Common to both the gradient-based and the hyperplane approximation technique, the motion field can be modeled parametrically. As the hyperplane approximation approach is both an approximation and potentially computationally expensive to train, this article will comparatively evaluate the approach against the traditional gradient-based optical flow methodology.