Material for : Adaptive Cascaded Regression

Given a set of N such shape samples {s, . . . , s}, a parametric statistical subspace of the object’s shape variance can be retrieved by first applying Generalised Procrustes Analysis on the shapes to normalise them with respect to the global similarity transform (i.e., scale, in-plane rotation and translation) and then using Principal Component Analysis (PCA). The returned shape subspace is further augmented with four eigenvectors that control the global similarity transform of the object’s shape. Please refer to [1] for further details about orthonormalising the similarity eigenvectors with the PCA basis. The resulting shape model {Us, s̄} consists of the orthonormal basis Us ∈ R2n×ns with ns eigenvectors (including the four similarity components concatenated before the eigenvectors) and the mean shape vector s̄ ∈ R. This parametric model can be used to generate new shape instances as