Figure 4

Clustering of the angular displacement distribution (ADD) for 1000 sentinel patterns given two independently reconstructed volumes \(W_A\) and \(W_B\), in the space of possible unit quaternions. Only the first two components of these quaternions (\(Q_0, Q_1\)) are shown. The disks represent the set of most significant relative quaternions given each sentinel pattern, \(\{{\varvec{Q}}_{BA} \,\vert \,K_\text {S}\}\), as defined by all possible pairs of those in Eq. (12). The opacities of these disks are proportional to the value of the ADD at these quaternions. The blue and red disks represent the ADDs for two specific sentinel patterns respectively. The yellow disk shows the average overall rotation \({\overline{Q}}_{BA}\) as defined in Eq. (16).