Let the Shape Speak - Discriminative Face Alignment using Conjugate Priors
Pedro Martins, Rui Caseiro, João Henriques, Jorge P. Batista · 2012
This work presents a novel Bayesian formulation for aligning faces in unseen images. Our approach is closely related to Constrained Local Models (CLM) [2] and Active Shape Models (ASM) [6], where an ensemble of local feature detectors are constrained to lie within the subspace spanned by a Point Distribution Model (PDM). Fitting a model to an image typically involves two steps: a local search using a detector, obtaining response maps for each landmark (likelihood term) and a global optimization that finds the PDM parameters that jointly maximize all the detections. The global optimization can be seen as a Bayesian inference problem, where the posterior distribution of the PDM parameters (and pose) can be inferred in a maximum a posteriori (MAP) sense. We present a novel Bayesian global optimization strategy, where the prior is used to encode the dynamic transitions of the PDM parameters. Using recursive Bayesian estimation we model the prior distribution of the data as being Gaussian. The mean and covariance were assumed to be unknown and treated as random variables. The Shape Model: The shape of a PDM is represented by the 2D locations of a mesh s = (x1,y1, . . . ,xv,yv) (v landmarks). Applying PCA on training examples, results in the parametric model s = s0 + Φb + Ψq, where s0 is the mean shape, Φ is the shape subspace matrix (n eigenvectors), b is a vector of shape parameters, q the pose parameters vector and Ψ holds four special eigenvectors that linearly model the 2D pose [4]. Goal: Given a 2v vector of observed positions y, the goal is to find the optimal set of parameters b that maximizes the posterior probability of being aligned. Using an Bayesian approach, the shape parameters are