Local subspace smoothness alignment for constrained local model fitting

Constrained local model (CLM) is a classic method for facial landmarks estimation. While the CLM enhances the well-known active shape model with discriminative local appearance models, its shape model is based on the point distribution model, which is essentially principal component analysis over the training facial shape vectors and hence the nonlinear manifold of facial shapes is not well embedded. In this paper, we propose a novel manifold learning method, i.e., local subspace smoothness alignment (LSSA), to address this issue. The LSSA approach smoothes the nonlinear structure directly in the original feature space, with a newly defined geometric measure for the curvature of the local structures. We then proceed to apply this method for face alignment, with an ensemble of correlated local subspaces derived from LSSA. The proposed method is demonstrated on both toy data and real-world datasets that it yields reasonable manifold embedding and leads to encouraging performance for face alignment even under difficult conditions.