Lucas-Kanade 20 Years On: Part 5

Abstract

Image alignment is 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 model fitting. The original image alignment algorithm was the Lucas-Kanade algorithm. Since then, numerous extensions have been made to it. In particular, Baker and Matthews recently proposed the inverse compositional algorithm, an efficient algorithm applicable to most 2D image alignment problems. In this report, we investigate whether the 2D inverse compositional algorithm can be generalized to 2.5D and 3D. By 3D we mean volumetric data consisting of a dense 3D array of voxels. By 2.5D we mean a surface in 3D represented by a collection of 3D surface points. We show that the inverse compositional algorithm is easily generalized to 3D. On the other hand, while algebraically it appears as though the 2.5D case may be treated similarly, doing so violates one of the assumptions in the proof of equivalence of the two algorithms.