Blockwise Linear Regression for Face Alignment

In this paper, we present a deeper analysis of linear regression as an efficient method for face alignment. Linear regression for face alignment [2] consists of learning a mapping matrix between image features and shape parameters displacements. Typically, shape parameters are projections of a set of points which follow a Point Distribution Model onto the subspace generated by applying Principal Component Analysis to a set of manually landmarked training images. Often, image features are extracted within patches around each point, and concatenated into a column vector d. We call the features belonging to the i-th patch with di. We can generate examples for each image j by systematically perturbing the ground-truth parameters p j 0 with δp. If we rearrange the training features into the matrix D, and their corresponding perturbations into the matrix P, the mapping matrix is obtained through least squares: