A new Least Squares based congealing technique

Groupwise Image Alignment via Self Quotient Images

“…However, this total cost function is difficult optimize directly [26] and the minimization of the individual cost function (p n ) for each geometrically distorted image i w (p m ), that was proposed, demands the solution of O(N 2 ) pairwise alignment problems. Instead of the CSME defined in Equation 4, in [25] the following total mean misalignment function:…”

“…Note however, that since the "mean" imageī is unknown, the optimal values of the perturbations in (11) can not be computed. For avoiding this obstacle a strategy based on the use of a particle system and imposing its center of mass to be motionless during the optimization process was proposed in [25]. In the next paragraph, we propose the solution of the above-mentioned problem formulating a different optimization problem.…”

“…In groupwise alignment techniques computational complexity is a critical aspect, since they handle large sets of images. Considering the alignment process of a set of N images, of size N x × N y each, aiming to estimate a deformation vector with N p parameters, the computational complexity of LKE [24], LS centroid [25] and the proposed are presented in Table 1 Table 1. Computational complexity of groupwise alignment techniques.…”