# Tightly-Coupled Data Compression for Efficient Face Alignment
## 1 Introduction  
Face alignment is an important part of facial image analysis. It automatically localizes facial feature points such as eyes, nose, eyebrows, mouth, etc. from a face image. It plays an important role in popular applications such as face recognition [1; 2], attribute computing [3; 4], and expression recognition [5]. Face alignment technology is usually applied to get some anchor points for affine warping so that the face recognition procedure is robust against pose variations. In [3], facial landmarks were used to outline a fetus's face. In [4], facial landmarks helped to localize and represent salient regions of the face. Figure 1 shows an example of a face alignment algorithm with the supervised descent method (SDM) [6]. According to a recent survey [7], face alignment methods can be divided into two categories: generative methods and discriminative methods. Generative methods explicitly construct generative models for the shape and/or appearance of the face. Feature locations are derived according to the best fit of the model to the test image. [PERSON] et al. proposed a famous algorithm that is called active shape models (ASM) to calculate an appearancemodel for every facial part separately [8]. In [9], the authors proposed the Gauss-Newton Deformable Part Model (GN-DPM) that can construct generative models for each facial part simultaneously. The classical active appearance models (AAM) [10], which contain the shape model, appearance model, and motion model, also belong to this category. The AAM's defect is that this method is not robust against occlusions. Different from generative methods, discriminative methods aim to estimate the mapping between the facial appearances and the features' locations directly. Constrained local models (CLM) are able to learn independent local detector for each feature point [13]. Then, a shape model is used to regularize these local models. Different from CLM, cascaded regression methods learn a vectorial regression function directly to calculate the face shape stage-by-stage. Explicit shape regression (ESR) [14] was one of the first algorithms in this category. It is a two-stage boosted regression framework. [PERSON] et al. introduced occlusion information into the regression process [15] in order to improve robustness. [PERSON] and [PERSON] proposed to use regression trees instead of random ferns and achieved super-fast speed [16]. Besides the above mentioned two-level boosted regression framework, [PERSON] and [PERSON] presented a cascaded linear regression method with hand-crafted features [6]. The contribution of [6] is a provable supervised descent method (SDM). It also extends SDM to Global SDM in order to cope with the problem of conflicting gradient directions [17]. SDM is a popular face alignment method especially for resource restricted applications since it can achieve state-of-the-art results in real 2D scenarios and still achieve real-time performance. With the advent of the deep learning era, deep neural networks have been successfully applied in many computer vision tasks in recent years. [PERSON] et al. were the first to use the deep convolutional network cascade for face alignment [18]. Reference [19] proposed a recurrent neural networks approach. Recently, there were works to achieve 3D face alignment by fitting a 3D Morphable Model (3 DMM) through convolutional neural networks (CNN) [20; 21]. Reference [22] proposed a 3D face alignment network (3D-FAN) by stacking four hourglass networks. Reference [23] proposed a two-stage method with the help of a deep residual network [24]. In this method, heat-maps of 2D landmarks are first calculated using convolutional-part heat-map regression. Then, these heat-maps along with the original RGB image are used to regress the depth information with a very deep residual network. Although deep learning methods, especially 3D ones, perform better on images with large head poses than do traditional methods, they are not easily applied in mobile platforms.