Figure 4.

(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 $\left[{\mathcal{Z}}_3,{\hat{\mathcal{Z}}}_4\right]$ 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$\left({\mathbf{\epsilon }}_0=\left[{\mathcal{Z}}_3,{\hat{\mathcal{Z}}}_4\right]\right)$ with the registered images of Z₁ and Z₂$\mathbf{\epsilon }=\left[{\mathcal{Z}}_1,{\tilde{\mathcal{Z}}}_2\right]$. At each registration step (line 13), a transformation T is determined by ${\text{argmax}}_{\mathbf{T}}\left[I_2^{*}\left(\mathbf{\epsilon },\mathbf{T}\left({\mathbf{\epsilon }}_0\right)\right)\right]$ and ε is then expanded by $\mathbf{\epsilon }\leftarrow {\tilde{\mathbf{\epsilon }}}_0=\mathbf{T}\left({\mathbf{\epsilon }}_0\right)$ (lines 14 and 15 of MACMIreg). The output of (a), containing all of the coregistered images in Z, is $\mathbf{\epsilon }=\left[{\mathcal{Z}}_1,{\tilde{\mathcal{Z}}}_2,{\tilde{\mathcal{Z}}}_3,{\tilde{\mathcal{Z}}}_4\right]$.