Automatic construction of robust spherical harmonic subspaces

In this paper we propose a method to automatically recover a class specific low dimensional spherical harmonic basis from a set of in-the-wild facial images. We combine existing techniques for uncalibrated photometric stereo and low rank matrix decompositions in order to robustly recover a combined model of shape and identity. We build this basis without aid from a 3D model and show how it can be combined with recent efficient sparse facial feature localisation techniques to recover dense 3D facial shape. Unlike previous works in the area, our method is very efficient and is an order of magnitude faster to train, taking only a few minutes to build a model with over 2000 images. Furthermore, it can be used for real-time recovery of facial shape

Automatic construction of robust spherical harmonic subspaces

In this paper we propose a method to automatically recover a class specific low dimensional spherical harmonic basis from a set of in-the-wild facial images. We combine existing techniques for uncalibrated photometric stereo and low rank matrix decompositions in order to robustly recover a combined model of shape and identity. We build this basis without aid from a 3D model and show how it can be combined with recent efficient sparse facial feature localisation techniques to recover dense 3D facial shape. Unlike previous works in the area, our method is very efficient and is an order of magnitude faster to train, taking only a few minutes to build a model with over 2000 images. Furthermore, it can be used for real-time recovery of facial shape

Symmetry adapted ro-vibrational basis functions for variational nuclear motion calculations: TROVE approach

We present a general, numerically motivated approach to the construction of symmetry adapted basis functions for solving ro-vibrational Schr\"{o}dinger equations. The approach is based on the property of the Hamiltonian operator to commute with the complete set of symmetry operators and hence to reflect the symmetry of the system. The symmetry adapted ro-vibrational basis set is constructed numerically by solving a set of reduced vibrational eigenvalue problems. In order to assign the irreducible representations associated with these eigenfunctions, their symmetry properties are probed on a grid of molecular geometries with the corresponding symmetry operations. The transformation matrices are re-constructed by solving over-determined systems of linear equations related to the transformation properties of the corresponding wavefunctions on the grid. Our method is implemented in the variational approach TROVE and has been successfully applied to a number of problems covering the most important molecular symmetry groups. Several examples are used to illustrate the procedure, which can be easily applied to different types of coordinates, basis sets, and molecular systems

Variational Uncalibrated Photometric Stereo under General Lighting

Photometric stereo (PS) techniques nowadays remain constrained to an ideal laboratory setup where modeling and calibration of lighting is amenable. To eliminate such restrictions, we propose an efficient principled variational approach to uncalibrated PS under general illumination. To this end, the Lambertian reflectance model is approximated through a spherical harmonic expansion, which preserves the spatial invariance of the lighting. The joint recovery of shape, reflectance and illumination is then formulated as a single variational problem. There the shape estimation is carried out directly in terms of the underlying perspective depth map, thus implicitly ensuring integrability and bypassing the need for a subsequent normal integration. To tackle the resulting nonconvex problem numerically, we undertake a two-phase procedure to initialize a balloon-like perspective depth map, followed by a "lagged" block coordinate descent scheme. The experiments validate efficiency and robustness of this approach. Across a variety of evaluations, we are able to reduce the mean angular error consistently by a factor of 2-3 compared to the state-of-the-art.Comment: Haefner and Ye contributed equall