Three-Dimensional Face Recognition Using Solid Harmonic Wavelet Scattering and Homotopy Dictionary Learning
- Inspired by the high-resolution texture discrimination, this paper proposes a novel process–model approach to obtain the discriminative and stable facial features from pure point coordination representation for automatic face recognition; here, the facial shape clues are enhanced in a regularized domain.
- We modify the original holistic solid harmonic wavelet scattering transform approach into a windowed integral function to provide a higher-resolution representation.
- We learned a 3D facial texton dictionary, which is specifically based on the co-occurrences of filter responses across different extrinsic perturbances, e.g., head pose/illumination variation/occlusion, and succeed in achieving competitive recognition accuracy compared with alternative currently available methods.
2. Related Works
2.1. Point Cloud Deep Learning
2.2. Dictionary Learning on Scattering Coefficients
2.3. 3D Face Recognition
3. Materials and Methods
3.1. The Stochastic Process Model on Point Cloud Faces
|Algorithm 1 The Local Lattice Operation:|
|Algorithm 2 Windowed Solid Harmonic Wavelet Scattering|
3.2. Piece-Wise Smoothed Solid Harmonic Scattering Coefficient Representation
3.3. Constructing a Local Dictionary with Semi-Supervised Sparse Coding on Scattering Coefficients
|Algorithm 3 Dictionary learning on local facial coefficients|
4.1. The Evaluation Protocol and Metrics
- The 3D solid scattering coefficient representation: As introduced in Section 2, we transformed the raw point cloud into representative zero-, first-, and second-order cascades of the solid harmonic scattering coefficients (shown in Figure 5); the implementation was based on an open-source framework .
- The sparse dictionary learning structure is demonstrated in Figure 6. It remained a very wide feature vector when we directly input a batch of scattering coefficients into the ISTC layer; therefore, we applied a convolution operation with batch normalization to reduce it to . Furthermore, it included learned parameters. The N was set to 3 since it was experimentally sufficient to allow the sparsity to reach the extremum.
4.3. Hyperparameter Tuning Process
- Parameters in Solid Harmonic Scattering: Figure 10 demonstrates the rank-1 recognition rate on the Bosphorus dataset by training the network with J = 3, 4, 5, 6, 7, 8, 9 values under C = 128. It can be seen that the dimension of each sub-dictionary had to be subsequent to satisfy overcompleteness; it can be seen from the blue/green lines that when and , the recognition rate barely grows.
- Parameters in Sparse Dictionary Coding: We fixed ; here, we found that a variation in J in (5, 7, 9) reached its best spot on . Figure 11 depicts the varying performance; we applied [J = 7, = 150, C = 128, = 512] as the principle experimental configuration of this framework.
4.4. Comparison with Other Methods
- Results on the FRGCv2 dataset: The FRGC v2.0 dataset  contained 4007 scans of 466 subjects in total; we followed its protocol to train on the Spring2003 partition and used the remaining data for testing. The results of running our proposed method and the state-of-the-art methods on the FRGC v2.0 dataset are shown in Table 2. The methods that used corresponding 2D photos are denoted as (2D+3D) and the ones that used a fine-tuning strategy are marked with (FT). Note that our approach required no information other than the positions of the point clouds; this property allowed for a much simpler sampling process in actual scenarios, whereas the illumination/rotation variants have been “compressed” in our representations. The recognition accuracy of our approach was also competitive with a rank-1 recognition rate of .
- Results on the Bosphorus dataset: The Bosphorus dataset  has 4666 scans collected from 105 subjects, with very rich variants in expression, systematic variations in poses, and different types of occlusions.
|Mian et al.  (2008)|
|Al-Osaimi.  (2016)|
|Ouamane et al.  (2017)||−|
|Ouamane et al.  (2017) [2D+3D]||−|
|Gilani and Miancite  (2018)||−|
|Gilani and Mian  (2018) (FT)||−|
|Cai et al.  (2019) (FT)|
|Yu et al. (2022)|
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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He, Y.; Cheng, P.; Yang, S.; Zhang, J. Three-Dimensional Face Recognition Using Solid Harmonic Wavelet Scattering and Homotopy Dictionary Learning. Entropy 2022, 24, 1646. https://doi.org/10.3390/e24111646
He Y, Cheng P, Yang S, Zhang J. Three-Dimensional Face Recognition Using Solid Harmonic Wavelet Scattering and Homotopy Dictionary Learning. Entropy. 2022; 24(11):1646. https://doi.org/10.3390/e24111646Chicago/Turabian Style
He, Yi, Peng Cheng, Shanmin Yang, and Jianwei Zhang. 2022. "Three-Dimensional Face Recognition Using Solid Harmonic Wavelet Scattering and Homotopy Dictionary Learning" Entropy 24, no. 11: 1646. https://doi.org/10.3390/e24111646