You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
Recently, Deep Convolution Networks (DCNNs) have been applied to the task of face alignment and have shown potential for learning improved feature representations. Although deeper layers can capture abstract concepts like pose, it is difficult to capture the geometric relationships among the keypoints in DCNNs. In this paper, we propose a novel convolution-deconvolution network for facial keypoint detection. Our model predicts the 2D locations of the keypoints and their individual visibility along with 3D head pose, while exploiting the spatial relationships among different keypoints. Different from existing approaches of modeling these relationships, we propose learnable transform functions which captures the relationships between keypoints at feature level. However, due to extensive variations in pose, not all of these relationships act at once, and hence we propose, a pose-based routing function which implicitly models the active relationships. Both transform functions and the routing function are implemented through convolutions in a multi-task framework. Our approach presents a single-shot keypoint detection method, making it different from many existing cascade regression-based methods. We also show that learning these relationships significantly improve the accuracy of keypoint detections for in-the-wild face images from challenging datasets such as AFW and AFLW.

Cited Abstract(s):
[1]: Mathematical optimization plays a fundamental role in solving many problems in computer vision (e.g., camera calibration, image alignment, structure from motion). It is generally accepted that second order descent methods are the most robust, fast, and reliable approaches for nonlinear optimization of a general smooth function. However, in the context of computer vision, second order descent methods have two main drawbacks: 1) the function might not be analytically differentiable and numerical approximations are impractical, and 2) the Hessian may be large and not positive definite. Recently, Supervised Descent Method (SDM), a method that learns the “weighted averaged gradients” in a supervised manner has been proposed to solve these issues. However, SDM is a local algorithm and it is likely to average conflicting gradient directions. This paper proposes Global SDM (GSDM), an extension of SDM that divides the search space into regions of similar gradient directions. GSDM provides a better and more efficient strategy to minimize non-linear least squares functions in computer vision problems. We illustrate the effectiveness of GSDM in two problems: non-rigid image alignment and extrinsic camera calibration.

[2]: We present a very efficient, highly accurate, "Explicit Shape Regression" approach for face alignment. Unlike previous regression-based approaches, we directly learn a vectorial regression function to infer the whole facial shape (a set of facial landmarks) from the image and explicitly minimize the alignment errors over the training data. The inherent shape constraint is naturally encoded into the regressor in a cascaded learning framework and applied from coarse to fine during the test, without using a fixed parametric shape model as in most previous methods. To make the regression more effective and efficient, we design a two-level boosted regression, shape indexed features and a correlation-based feature selection method. This combination enables us to learn accurate models from large training data in a short time (20 min for 2,000 training images), and run regression extremely fast in test (15 ms for a 87 landmarks shape). Experiments on challenging data show that our approach significantly outperforms the state-of-the-art in terms of both accuracy and efficiency.

[3]: We present a practical approach to address the problem of unconstrained face alignment for a single image. In our unconstrained problem, we need to deal with large shape and appearance variations under extreme head poses and rich shape deformation. To equip cascaded regressors with the capability to handle global shape variation and irregular appearance-shape relation in the unconstrained scenario, we partition the optimisation space into multiple domains of homogeneous descent, and predict a shape as a composition of estimations from multiple domain-specific regressors. With a specially formulated learning objective and a novel tree splitting function, our approach is capable of estimating a robust and meaningful composition. In addition to achieving state-of-the-art accuracy over existing approaches, our framework is also an efficient solution (350 FPS), thanks to the on-the-fly domain exclusion mechanism and the capability of leveraging the fast pixel feature.

[4]: We present a novel face alignment framework based on coarse-to-fine shape searching. Unlike the conventional cascaded regression approaches that start with an initial shape and refine the shape in a cascaded manner, our approach begins with a coarse search over a shape space that contains diverse shapes, and employs the coarse solution to constrain subsequent finer search of shapes. The unique stage-by-stage progressive and adaptive search i) prevents the final solution from being trapped in local optima due to poor initialisation, a common problem encountered by cascaded regression approaches; and ii) improves the robustness in coping with large pose variations. The framework demonstrates real-time performance and state-of-the-art results on various benchmarks including the challenging 300-W dataset.

[5]: 

[6]: Arguably, Deformable Part Models (DPMs) are one of the most prominent approaches for face alignment with impressive results being recently reported for both controlled lab and unconstrained settings. Fitting in most DPM methods is typically formulated as a two-step process during which discriminatively trained part templates are first correlated with the image to yield a filter response for each landmark and then shape optimization is performed over these filter responses. This process, although computationally efficient, is based on fixed part templates which are assumed to be independent, and has been shown to result in imperfect filter responses and detection ambiguities. To address this limitation, in this paper, we propose to jointly optimize a part-based, trained in-the-wild, flexible appearance model along with a global shape model which results in a joint translational motion model for the model parts via Gauss-Newton (GN) optimization. We show how significant computational reductions can be achieved by building a full model during training but then efficiently optimizing the proposed cost function on a sparse grid using weighted least-squares during fitting. We coin the proposed formulation Gauss-Newton Deformable Part Model (GN-DPM). Finally, we compare its performance against the state-of-the-art and show that the proposed GN-DPM outperforms it, in some cases, by a large margin. Code for our method is available from http: ibug.doc.ic.ac.uk resources

[7]: Cascaded regression has recently become the method of choice for solving non-linear least squares problems such as deformable image alignment. Given a sizeable training set, cascaded regression learns a set of generic rules that are sequentially applied to minimise the least squares problem. Despite the success of cascaded regression for problems such as face alignment and head pose estimation, there are several shortcomings arising in the strategies proposed thus far. Specifically, (a) the regressors are learnt independently, (b) the descent directions may cancel one another out and (c) handcrafted features (e.g., HoGs, SIFT etc.) are mainly used to drive the cascade, which may be sub-optimal for the task at hand. In this paper, we propose a combined and jointly trained convolutional recurrent neural network architecture that allows the training of an end-to-end to system that attempts to alleviate the aforementioned drawbacks. The recurrent module facilitates the joint optimisation of the regressors by assuming the cascades form a nonlinear dynamical system, in effect fully utilising the information between all cascade levels by introducing a memory unit that shares information across all levels. The convolutional module allows the network to extract features that are specialised for the task at hand and are experimentally shown to outperform hand-crafted features. We show that the application of the proposed architecture for the problem of face alignment results in a strong improvement over the current state-of-the-art.

[8]: 

[9]: We propose a new approach for estimation of the positions of facial key points with three-level carefully designed convolutional networks. At each level, the outputs of multiple networks are fused for robust and accurate estimation. Thanks to the deep structures of convolutional networks, global high-level features are extracted over the whole face region at the initialization stage, which help to locate high accuracy key points. There are two folds of advantage for this. First, the texture context information over the entire face is utilized to locate each key point. Second, since the networks are trained to predict all the key points simultaneously, the geometric constraints among key points are implicitly encoded. The method therefore can avoid local minimum caused by ambiguity and data corruption in difficult image samples due to occlusions, large pose variations, and extreme lightings. The networks at the following two levels are trained to locally refine initial predictions and their inputs are limited to small regions around the initial predictions. Several network structures critical for accurate and robust facial point detection are investigated. Extensive experiments show that our approach outperforms state-of-the-art methods in both detection accuracy and reliability.

[10]: The development of facial databases with an abundance of annotated facial data captured under unconstrained 'in-the-wild' conditions have made discriminative facial deformable models the de facto choice for generic facial landmark localization. Even though very good performance for the facial landmark localization has been shown by many recently proposed discriminative techniques, when it comes to the applications that require excellent accuracy, such as facial behaviour analysis and facial motion capture, the semi-automatic person-specific or even tedious manual tracking is still the preferred choice. One way to construct a person-specific model automatically is through incremental updating of the generic model. This paper deals with the problem of updating a discriminative facial deformable model, a problem that has not been thoroughly studied in the literature. In particular, we study for the first time, to the best of our knowledge, the strategies to update a discriminative model that is trained by a cascade of regressors. We propose very efficient strategies to update the model and we show that is possible to automatically construct robust discriminative person and imaging condition specific models 'in-the-wild' that outperform state-of-the-art generic face alignment strategies.
In a framework, image appearances are directly mapped to output space producing keypoint coordinates. Recently, a multitude of cascade regression-based methods [2] , [4] significantly boost the keypoint detection performance, compared to statistical methods described above. However, these methods along with methods from [7] , [10] , [6] and [9] were mostly evaluated on face images where all the facial keypoints are visible. To handle occlusion, [5] proposed an occlusion-robust cascaded regressor. Supervised Descent Method (SDM) [8] learns a cascade of regression models based on SIFT features. To mitigate the conflicting gradient directions in SDM, [1] suggested domain dependent descent maps. Inspired by [1] , Cascade Compositional Learning (CCL) [3] developed a head pose based method by partitioning the optimization domain. Different from all these methods, our approach is a non-iterative single shot method, which along with keypoint locations also provides the estimated 3D head pose and individual visibility of each fiducial point.