Project-Out Cascaded Regression with an application to face alignment

Cascaded regression approaches have been recently shown to achieve state-of-the-art performance for many computer vision tasks. Beyond its connection to boosting, cascaded regression has been interpreted as a learning-based approach to iterative optimization methods like the Newton's method. However, in prior work, the connection to optimization theory is limited only in learning a mapping from image features to problem parameters. In this paper, we consider the problem of facial deformable model fitting using cascaded regression and make the following contributions: (a) We propose regression to learn a sequence of averaged Jacobian and Hessian matrices from data, and from them descent directions in a fashion inspired by Gauss-Newton optimization. (b) We show that the optimization problem in hand has structure and devise a learning strategy for a cascaded regression approach that takes the problem structure into account. By doing so, the proposed method learns and employs a sequence of averaged Jacobians and descent directions in a subspace orthogonal to the facial appearance variation; hence, we call it Project-Out Cascaded Regression (PO-CR). (c) Based on the principles of PO-CR, we built a face alignment system that produces remarkably accurate results on the challenging iBUG data set outperforming previously proposed systems by a large margin. Code for our system is available from http://www.cs.nott.ac.uk/~yzt/.