# Multi-Layer Progressive Face Alignment by Integrating Global Match and Local Refinement
## 4 Experimental Results and Analysis
### Comparison Experiment  
To quantitatively evaluate the performance of our algorithm, the following four popular algorithms are chosen for comparison. 1. Explicit Shape Regression (ESR) performs cascade shape regression for face alignment by minimizing regression error [26]. 2. Supervised descent method (SDM) minimizes the Non-linear least squares objective using the learned a sequence of descent directions [23]. 3. Cascade gaussian regression (CGR) builds gaussian process trees for landmark position regression based on cascade stage-wise manner [21]. 4. Deep neural network (DNN) extracts local features for optimization and the resulting deep regressor gradually and evenly approaches the true landmarks stage by stage [42]. These methods have been widely used in recent years and have achieved the best performance on larger databases. They are excellent in accuracy and computing speed, especially for alignment under real environments. Our algorithm and the contrastive ones are respectively trained and test experiments are performed on several databases. The qualitative analysis and quantitative comparison based on the corresponding experimental results are shown. Figure 18 shows the cumulated error curves of different algorithms on different databases, where the x-coordinate indicates mean alignment error and the y-coordinate indicates test image proportion. All faces from the IMM database are front. Some faces from BioID database have a slight pose and all landmarks are visible. On these two databases, our algorithm respectively has 81.5% and 78.1% samples with the average error of less than 4, which is higher than the contrasted ones. Most faces from the LFPW database are close to the front, while many images with higher resolution from HELEN database are non-front and have relatively low accuracy. On these two databases, our algorithm respectively has 83.9% and 81.1% samples with average error of less than 8 respectively. Although the performance is still relatively better, the improvement of our method is limited for faces over a certain angle. In contrastive methods, our method has the best performance and ESR has the worst. The variation tendency on the four databases keeps accordance. Compared with deep learning methods, traditional methods based on the local features and global regression, including ESR, SDM and CGR, have lower accuracies because the simple local features and rough linear regression cannot handle the non-linear alignment problem. Our method introduces prior knowledge into the CNN networks and integrates global and local alignment, which can achieve better performance compared to a single CNN. The above comparitive results indicate that the single global or local method is insufficient to describe complicated face texture variations and is very sensitive to tremendous variations of occlusion and illumination, both of which lead to worse performance. The multi-mode features are more descriptive than single scale features, and the combination of the two alignments has huge advantages, which helps to handle the nonlinear variation caused by illumination and occlusion. The hardware configuration in this paper is as follows: A 3.33 GHz i7 CPU, 16 GB RAM, a GeForce GTX 1070 graphics card. All algorithms in this paper are partially optimized. Table 1 compares the corresponding computation efficiency on different databases by the mean time of one image. It can be seen that more complex methods take longer, and the tendency on different databases keeps accordance. Compared with the former two databases, LFPW and HELEN databases have more non-front faces under more difficult conditions, which partially increases the computational complexity. The maximum demands of our method are due to the multi-mode feature extraction and encoding. Moreover, the two alignments are performed and integrated. Naturally, the calculation consumption is greater than the other algorithms. But the features and methods we proposed are more descriptive and more effective, which can achieve better performance.