## 2 The Proposed Network
### 3D Face Preprocessing  
It should be noted that 3D scanning devices are subject to their own or environmental interference when capturing facial information, and the obtained 3D faces are susceptible to noise [40]. Noise removal improves the localization accuracy of a landmark on the face and reduces the possibility of some of the noise being used as distinguishing features of the face during the training of the convolutional network. We use a statistical filter to remove sparse outlier points. The basic principle is to calculate the average distance \(d(x,y,z)\) from each point \((x,y,z)\) to the \(K\) nearest points in the original point cloud \(P_{O}\). We remove the outliers by judging the relationship between each point and the mean \(\mu\) and standard deviation \(\sigma\) of the average distance to all points. The equation for obtaining new 3D points by eliminating noise through the statistical filter is as follows:  
\[\{(x,y,z)\in P_{O}|d(x,y,z)-\mu-\alpha\times\sigma<0,\sigma\in[1,5]\} \tag{1}\]  
The ideal frontal face model is usually obtained directly from the unconstrained environment. To reduce the impact of pose variations on recognition performance, we need to uniformly correct the faces of all poses to the frontal face. The coordinate space of this frontal face is identified as the reference coordinate space. Positioning facial landmarks for detection is the first step of pose correction. Many researchers have proposed using 3D facial landmarks detection methods [28; 41; 42] and alignment methods [6; 43] when the face pose or expression changes or when self-occlusion is present. Figure 2a shows the locations of the detected facial feature points (yellow dots) when the pose changes (left) and when self-occlusion is present (right). The computational resources of the alignment step can be reduced by calculating the transformation matrix between the corresponding  
Figure 1: Architecture of our proposed 3D occlusion facial recognition network.  
points and then applying this transformation matrix to the whole uncorrected face. After obtaining \(N\) pairs of feature-corresponding point pairs, we use the least squares fitting method proposed by [PERSON] (2016) to solve the rotation translation relationship between the original point set \(P_{O}\) and the target point set \(P_{T}\):  
\[\begin{split}[U,S,V]&=SVD\left(\sum_{i=1}^{N}\left(P _{O}^{i}-\overline{P_{O}}\right)\left(P_{T}^{i}-\overline{P_{T}}\right)\right) \\ R^{\prime}&=VU^{T},t^{\prime}=\overline{P_{T}}-R^{ \overline{P_{O}}}\end{split} \tag{2}\]  
where \(\overline{P_{O}}\) and \(\overline{P_{T}}\) are the centers of mass of \(P_{O}\) and \(P_{T}\), respectively, and \(N\) is the number of 3D points. Then, we coarse align the point set using the rotation matrix \(R^{\prime}\) and the translation matrix \(t^{\prime}\). To make the system robust to small alignment errors, this system does not use the ICP algorithm for fine alignment. In the left column of Figure 2b,c are the spatial relative relations before alignment between the frontal face model (blue) and the model to be aligned (red). Figure 2b shows the face alignment of the pose variation, and Figure 2c shows the face alignment of self-occlusion.  
The resulting 3D model includes facial information and also redundant object information such as the neck, ears, and hair. Usually, we take the detected nose-tip point as the center of the circle and take the 3D points in the fixed radius length sphere space as reliable facial information. The facial points after the above alignment and cropping operations are shown in the right columns of Figure 2b,c.  
Figure 2: (**a**) Probe faces in different states (pose variation and self-occlusion) marked with 3D facial landmarks. The left columns of (**b,c**) are before alignment, and the right columns are after alignment; (**b**) facial alignment of pose variation; (**c**) face alignment of self-occlusion.