A new Least Squares based congealing technique

The aim of this work is to improve upon the state-of-the-art pixel-level, Least-Squares (LS) based congealing methods. Specifically, we propose a new iterative algorithm, which outperforms in terms of speed, convergence rate and robustness the state-of-the-art inverse compositional LS based iterative scheme. Namely, by associating the geometric distortion of each image of the ensemble with the position of a particle of a multi particle system, we succeed to align the ensemble without having to align all the individual pairs resulting from it. Instead we align each image with the “mean”, but unknown, image. To this end, by imposing the “center of mass” of the particle system to be motionless during each iteration of the minimization process, a sequence of “centroid” images whose limit is the unknown “mean” image is defined, thus solving the congealing problem. The proposed congealing technique is invariant to the size of the image set and depends only on the image size, thus it can be used for the successful solution of the congealing problem on large image sets with low complexity.