Procrustes Distances
•Full Procrustes Distance.  DF
–min(s, q) ||U – sXR(q).||  That is, we find a scaling and rotation of X that minimizes the euclidean distance to U.  (R(q) means rotate by q).
•Partial Procrustes Distance.  DP
–min(q) ||U – XR(q)||.  That is, rotate X to minimize the euclidean distance to U.
•Procrustes Distance.  r
–Rotate X to minimize the geodesic distance on the sphere from X to U.