# Multi-Layer Progressive Face Alignment by Integrating Global Match and Local Refinement
## 3 The Multi-Layer Progressive Face Alignment Method
### The Global Alignment Based on Shape Parameters Regression
#### 3.2.2 Shape Parameters Regression Based on CNN  
The shape PCA parameters can constrain common variations of whole face shape. Regressing shape parameters within lower dimension parametric space can decrease calculations, and tends to keep global constraint. Instead of the raw face image, according to the former description, the multi-mode LBP images are constructed and applied to regress the face shape parameters. The traditional handcrafted features carefully designed based on expert knowledge only reflect limited aspects of a certain problem. Recently, deep learning algorithms have been widely applied in the face alignment field. However, deep learning requires a large number of training samples, which is not practical in some specific applications. Furthermore, the deep features do not always outperform the handcrafted features in all applications. Prior knowledge can be introduced and the more efficient and richer information can be obtained by combining the above features, which can achieve better alignment performance than single feature. The global feature represented by multi-mode LBP images contains more distinguishable information than the original pixel-level image. So, a simpler network is enough to achieve the same performance as running a deeper network at pixel level. The architecture used here contains 3 convolutional layers, 3 max-pooling layers and 2 fully-connected layers (as shown in Figure 7). The number of neurons of the two FC layers is 4096. The three input multi-mode LBP images are normalized to 224 \(\times\) 224. The model is trained by minimizing loss function with back-propagation. The SGD (stochastic gradient descent) method divides the training set into many mini-batches and updates the network parameters by a mini-batch data every time. Computation over a batch can be much more efficient due to the parallelism afforded by the modern computing platforms. Thus, model training with a large amount of data can successfully and quickly converge. The optimal parameters of the SGD method for training our CNN model are determined by experiments. The parameters are set as follows: Mini-Batch Size = 10, Initial Learning Rate = 0.001, Learning Rate Drop Factor = 0.1, Learning Rate Drop Period = 2 and Momentum = 0.9. Figure 6: The multi-mode LBP feature extraction and encoding. Figure 7: The shape parameters regression based on the LBP images. The distribution of the activations in the intermediate layers constantly changes during training, which slows down the training process in every training step. To reduce the internal covariate shift, the inputs of each layer within the network are normalized to obtain approximately the same distribution. Batch normalization has been the de facto standard in the industry since 2015 [56]. Many different popular deep leaning frameworks also adopt it as a standard setting. In this paper, batch normalization is performed after each convolution layer based on the mean and variance of the values in the current mini-batch (usually zero mean and unit variance). The procedures are as follows: (1) Calculate the mean and variance over a mini-batch. (2) Normalize the input by subtracting the batch mean and dividing by the batch standard deviation. (3) Scale and shift the normalized result to obtain the output. The normalized result is multiplied by a \"standard deviation\" parameter (gamma) and adds a \"mean\" parameter (beta). Batch normalization has the following advantages: (1) it increases the stability of a network and make learning process easier. (2) it speeds up convergence, uses higher learning rates and controls overfitting. (3) it reduces the sensitivity of the network to initial weights. The experiments show that batch normalization obtains 10 times or more improvement in the training speed. Deeper networks can achieve better performance, but are difficult to train and converge. Accordingly, transfer learning based on ImageNet is performed on many tasks. Fine-tuning is necessary for pre-trained deeper networks, followed by own structure.