Yi He

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.

As one of the pioneering data representations, the point cloud has shown its straightforward capacity to depict fine geometry in many applications, including computer graphics, molecular structurology, modern sensing signal processing, and more. However, unlike computer graphs obtained with auxiliary regularization techniques or from syntheses, raw sensor/scanner (metric) data often contain natural random noise caused by multiple extrinsic factors, especially in the case of high-speed imaging scenarios. On the other hand, grid-like imaging techniques (e.g., RGB images or video frames) tend to entangle interesting aspects with environmental variations such as pose/illuminations with Euclidean sampling/processing pipelines. As one such typical problem, 3D Facial Expression Recognition (3D FER) has been developed into a new stage, with remaining difficulties involving the implementation of efficient feature abstraction methods for high dimensional observations and of stabilizing methods to obtain adequate robustness in cases of random exterior variations. In this paper, a localized and smoothed overlapping kernel is proposed to extract discriminative inherent geometric features. By association between the induced deformation stability and certain types of exterior perturbations through manifold scattering transform, we provide a novel framework that directly consumes point cloud coordinates for FER while requiring no predefined meshes or other features/signals. As a result, our compact framework achieves $78.33\%$ accuracy on the Bosphorus dataset for expression recognition challenge and $77.55\%$ on 3D-BUFE.