Distance-Based 3D Face Reconstruction Using Regularization

Abstract

This study addresses the problem of reconstructing 3D face shapes from a small set of 2D facial points. By using Maximum Posterior Probability estimation, prior information modeled by PCA is connected to Tikhonov regularization method in order to solve the ill-posed problem of 3D face reconstruction. The prior information is learned from 3D faces of a standard 3D database. However, the optimal value of the regularization parameter λ is usually not available in advance. To overcome this problem, we restrict the distance between the reconstructed 3D face and the average 3D face close to the average of the distances between sample 3D faces and the average 3D face. This is due to the fact that the sample data are mostly located at the boundary of the data space for high dimensional and low sample size problems, which is the case for 3D faces. The optimal regularization parameter is then obtained to reconstruct the 3D face shape of a given 2D near frontal image using limited number of feature. The solution is plausible while not over-smoothing. By warping the 2D texture to the reconstructed face shape, 3D face reconstruction is achieved. Our experimental results justify the robustness of the proposed approach with respect to the reconstruction of realistic 3D face shapes from a small set of 2D facial coordinates.