Lucas-Kanade 20 Years On: A Unifying Framework: Part 3

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, tracking, and layered motion, to mosaic construction, medical image registration, and face coding. Numerous algorithms have been proposed and a variety of extensions have been made to the original formulation. We present an overview of image alignment, describing most of the algorithms 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 the Lucas-Kanade algorithm can be used with the inverse compositional algorithm without any significant loss of efficiency, and which cannot. In this paper, Part 3 in a series of papers, we cover the extension of image alignment to allow linear appearance variation. We first consider linear appearance variation when the error function is the Euclidean L2 norm. We describe three different algorithms, the simultaneous, project out, and normalization inverse compositional algorithms, and empirically compare them. Afterwards we consider the combination of linear appearance variation with the robust error functions described in Part 2 of this series. We first derive robust versions of the simultaneous and normalization algorithms. Since both of these algorithms are very inefficient, as in Part 2 we derive efficient approximations based on spatial coherence. We end with an empirical evaluation of the robust algorithms.