Frenet Frame-Based Generalized Space Curve Representation for Pose-Invariant Classification and Recognition of 3-D Face

The state-of-the-art methods in classifying 3-D representation of the face involve challenges in extracting representative features directly from the large volume of facial data. These methods mostly ignore the effect of pose distortions on 3-D facial data and entail heavy computations as well as manual processing steps. This work proposes a novel Frenet frame-based generalized space curve representation method for 3-D pose-invariant face and facial expression recognition and classification. Three-dimensional facial curves are extracted from either frontal or synthetically posed 3-D facial data to derive the proposed Frenet frame-based features. A mathematical framework shows the proof of pose invariance property for the features. The effectiveness of the proposed method is evaluated in two recognition tasks: 3-D face recognition (3D-FR) and 3-D facial expression recognition (3D-FER) using benchmarked 3-D datasets. The proposed framework yields 96% rank-I recognition rate for 3D-FR and 91.4% area under ROC curves for six basic 3D-FER. The performance evaluation also shows that the proposed mathematical framework yields pose-invariant 3D-FR and 3D-FER for a wide range of pose angles. This pose invariance property of the Frenet frame-based features alleviates the need for an expensive 3-D face registration in the preprocessing step, which, in turn, enables a faster processing time. The evaluation results further suggest that the proposed method is not only computationally efficient and versatile, but also offers competitive performance when compared with the existing state-of-the-art methods reported for either 3D-FR or 3D-FER.