Statistical linear models in Procrustes shape space

The configuration matrix of a set of labeled landmarks is one the most used shape representations. However, it is well-known that the configuration matrix is not invariant under translation, scaling and rotation. This problem is revisited in this work where a local tangent shape space characterization at a reference shape is obtained as the null space of the subspace spanned by the reference shape and the set of translation and rotation generators. This local linear description of the shape space allows us to compute mean and variance of shapes as well as apply classical mutivariate statistical techniques such as Principal Component Analysis. Our proposal is compared with previous approaches, such as the seminal work [1] and more recents works [2] and [3].