Lucas-Kanade 20 Years On: A Unifying Framework Part 1: The Quantity Approximated, the Warp Update Rule, and the Gradient Descent Approximation

Since the Lucas-Kanade algorithm was proposed in 1981 image alignment has become one of the most widely used techniques in computer vision. Applications range from optical flow and tracking to layered motion, mosaic construction, and face coding. Numerous algorithms have been proposed and a wide variety of extensions have been made to the original formulation. We present an overview of image alignment, describing most of the algorithms and their extensions in a consistent framework. We concentrate on the inverse compositional algorithm, an efficient algorithm that we recently proposed. We examine which of the extensions to Lucas-Kanade can be used with the inverse compositional algorithm without any significant loss of efficiency, and which cannot. In this paper, Part 1 in a series of papers, we cover the quantity approximated, the warp update rule, and the gradient descent approximation. In future papers we will cover the choice of the norm, how to allow linear appearance variation, how to impose priors on the parameters, and various techniques to avoid local minima.