Generalized Procrustes analysis

The Procrustes distance provides a metric to minimize in order to align a pair of shape instances annotated by Landmark points. The Generalized Procrustes Analysis (GPA) is a procedure applying the aforementioned Procrustes analysis method to align a population of shapes instead of only two shape instances.

GPA This is one of the methods achieving this goal, namely useful to build a Point Distribution Model or to undertake any shape study on the training set. The algorithm outline is the following:

• 1: choose a reference shape among the training set instances
• 2: align all other instances on current reference
• 3: compute the mean shape of the current training set
• 4: if the proscrustes distance between the mean shape and the reference is above a threshold, set reference to mean an continue to step 2.

Some reference articles

[1]: @book{drydenmardiabook, editor = "Ian L. Dryden and Kanti V. Mardia", publisher = "John Wiley and Sons", title = "Statistical Shape Analysis", isbn = "0-471-95816-6", year = 1998 }