Least-squares congealing for large numbers of images

In this paper we pursue the task of aligning an ensemble of images in an unsupervised manner. This task has been commonly referred to as “congealing” in literature. A form of congealing, using a least-squares criteria, has been recently demonstrated to have desirable properties over conventional congealing. Least-squares congealing can be viewed as an extension of the Lucas & Kanade (LK) image alignment algorithm. It is well understood that the alignment performance for the LK algorithm, when aligning a single image with another, is theoretically and empirically equivalent for additive and compositional warps. In this paper we: (i) demonstrate that this equivalence does not hold for the extended case of congealing, (ii) characterize the inherent drawbacks associated with least-squares congealing when dealing with large numbers of images, and (iii) propose a novel method for circumventing these limitations through the application of an inverse-compositional strategy that maintains the attractive properties of the original method while being able to handle very large numbers of images.