Three-Dimensional Face Recognition Using Solid Harmonic Wavelet Scattering and Homotopy Dictionary Learning

Data representation has been one of the core topics in 3D graphics and pattern recognition in high-dimensional data. Although the high-resolution geometrical information of a physical object can be well preserved in the form of metrical data, e.g., point clouds/triangular meshes, from a regular data (e.g., image/audio) processing perspective, they also bring excessive noise in the course of feature abstraction and regression. For 3D face recognition, preceding attempts focus on treating the scan samples as signals laying on an underlying discrete surface (mesh) or morphable (statistic) models and by embedding auxiliary information, e.g., texture onto the regularized local planar structure to obtain a superior expressive performance to registration-based methods, but environmental variations such as posture/illumination will dissatisfy the integrity or uniform sampling condition, which holistic models generally rely on. In this paper, a geometric deep learning framework for face recognition is proposed, which merely requires the consumption of raw spatial coordinates. The non-uniformity and non-grid geometric transformations in the course of point cloud face scanning are mitigated by modeling each identity as a stochastic process. Individual face scans are considered realizations, yielding underlying inherent distributions under the appropriate assumption of ergodicity. To accomplish 3D facial recognition, we propose a windowed solid harmonic scattering transform on point cloud face scans to extract the invariant coefficients so that unrelated variations can be encoded into certain components of the scattering domain. With these constructions, a sparse learning network as the semi-supervised classification backbone network can work on reducing intraclass variability. Our framework obtained superior performance to current competing methods; without excluding any fragmentary or severely deformed samples, the rank-1 recognition rate (RR1) achieved was 99.84% on the Face Recognition Grand Challenge (FRGC) v2.0 dataset and 99.90% on the Bosphorus dataset.