PCA-based Reconstruction of 3D Face shapes using Tikhonov Regularization

Reconstructing a 3D face shape from a limited number of 2D facial feature points is considered as an ill-posed problem which can be solved using regularization. Tikhonov regularization is a popular method that incorporates prior information towards providing the existence of closed-form solutions which we obtain as a result of applying PCA, in order to solve the ill-posed problem. The common factors that generally affect Tikhonov regularization are the regularization matrix, the number of feature points, regularization parameters and noise. In this study we report our findings on how various factors influence the reconstruction accuracy based on a case study performed on the USF Human ID 3D database. Further, a statistical comparison between two Tikhonov regularization matrices viz., the identity matrix and the diagonal matrix comprising of the eigenvalues (eigenvalue matrix), has been performed. We found that, the reconstruction error can be reduced significantly by using the later one. Finally our study aids to determine the most feasible interval in conjunction with optimal regularization parameters which would lead towards achieving accurate and plausible solutions.