(a) Graphical representation of the organization of four images (Z1,…,Z4) within a family of image sets (Z={{Z1},{Z2},{{Z3},{Z4}}}) and the application of the MACMIreg algorithm for alignment of all four images. Since only Z3 contains subsets (i.e., |Z3|=2), line 3 of MACMIreg in (a) begins a new instance of the algorithm in (b) with Z={{Z3},{Z4}} as the input. The instance in (b) brings Z3 and Z4 into alignment and returns the ensemble to the instance in (a). The instance in (a) first brings Z1 and Z2 into alignment and then align the ensemble of registered images from Z3 with the registered images of Z1 and Z2. At each registration step (line 13), a transformation T is determined by and ε is then expanded by (lines 14 and 15 of MACMIreg). The output of (a), containing all of the coregistered images in Z, is .