This paper investigates how far a very deep neural network  is from attaining close to saturating performance on  existing 2D and 3D face alignment datasets. To this end,  we make the following 5 contributions:

• (a) we construct,  for the first time, a very strong baseline by combining a  state-of-the-art architecture for landmark localization with  a state-of-the-art residual block, train it on a very large yet  synthetically expanded 2D facial landmark dataset and finally  evaluate it on all other 2D facial landmark datasets.
•  (b) We create a guided by 2D landmarks network which converts  2D landmark annotations to 3D and unifies all existing  datasets, leading to the creation of LS3D-W, the largest  and most challenging 3D facial landmark dataset to date  (~230,000 images).
• (c) Following that, we train a neural  network for 3D face alignment and evaluate it on the newly  introduced LS3D-W.
• (d) We further look into the effect of all  “traditional” factors affecting face alignment performance  like large pose, initialization and resolution, and introduce  a “new” one, namely the size of the network.
• (e) We show  that both 2D and 3D face alignment networks achieve performance  of remarkable accuracy which is probably close  to saturating the datasets used.

Training and testing code  as well as the dataset can be downloaded from https:  //www.adrianbulat.com/face-alignment/

本文研究了在现有的二维和三维人脸定位数据集上，一个非常深入的神经网络离达到接近饱和的性能还有多远。为此，我们做出了以下5项贡献：

• （a）我们首次通过将最先进的landmark 定位架构与最先进的残差结合，构建了一个非常强大的基线，在一个非常大但经过综合扩展的2D面部landmark 数据集上训练，最后在所有其他2D面部landmark 数据集上对其进行评估。
• （b）我们创建了一个由二维landmark 网络引导的网络，该网络将二维landmark 注释转换为三维，并统一了所有现有数据集，从而创建了迄今为止最大、最具挑战性的三维面部landmark 数据集LS3D-W（约23万张图像）。
• （c） 然后，我们训练了一个用于三维人脸对齐的神经网络，并在新引入的LS3D-W。
• （d）我们进一步研究了影响人脸对齐性能的所有“传统”因素的影响，如大姿态、初始化和分辨率，并引入了一个“新的”因素，即网络的大小。
• （e） 结果表明，二维和三维人脸对齐网络均达到了很高的精度，可能接近于饱和所使用的数据集。

训练和测试代码以及数据集可从/https:  //www.adrianbulat.com/face-alignment/  下载

图1:由4个HGs叠加而成的人脸比对网络(FAN)，其中所有的瓶颈块(以矩形表示)都被替换为[7]的分层、平行和多尺度块。

More recently, fully Convolutional Neural Network architectures  based on heatmap regression have revolutionized  human pose estimation [39, 38, 24, 17, 27, 42, 23, 5]  producing results of remarkable accuracy even for the most  challenging datasets [1]. Thanks to their end-to-end training  and little need for hand engineering, such methods can be  readily applied to the problem of face alignment. Following  this path, our main contribution is to construct and train  such a powerful network for face alignment and investigate  for the first time how far it is from attaining close to saturating  performance on all existing 2D face alignment datasets  and a newly introduced large scale 3D dataset. More specifically,  our contributions are:

• 1. We construct, for the first time, a very strong baseline by combining a state-of-the-art architecture for landmark localization with a state-of-the-art residual block and train it on a very large yet synthetically expanded 2D facial landmark dataset. Then, we evaluate it on all other 2D datasets (~230,000 images), investigating how far are we from solving 2D face alignment
• 2. In order to overcome the scarcity of 3D face alignment datasets, we further propose a guided-by-2D landmarks CNN which converts 2D annotations to 3D 1 and use it to create LS3D-W, the largest and most challenging 3D facial landmark dataset to date (~230,000 images), obtained from unifying almost all existing datasets to date.
• 3. Following that, we train a 3D face alignment network and then evaluate it on the newly introduced large scale 3D facial landmark dataset, investigating how far are we from solving 3D face alignment.
• 4. We further look into the effect of all “traditional” factors affecting face alignment performance like large pose, initialization and resolution, and introduce a “new” one, namely the size of the network.
• 5. We show that both 2D and 3D face alignment networks achieve performance of remarkable accuracy which is probably close to saturating the datasets used.

最近，基于热图回归的全卷积神经网络架构已经彻底改变了人体姿态估计[39,38,24,17,27,42,23,5]，即使对于最具挑战性的数据集[1]也能产生非常精确的结果。由于他们的端到端训练和很少需要手工程，这种方法可以很容易地应用于面部对准的问题。沿着这条道路，我们的主要贡献是构建和训练这样一个强大的人脸比对网络，并首次研究如何在现有的所有2D人脸比对数据集和新引入的大规模3D数据集上实现接近饱和的性能。更具体地说，我们的贡献是:

• 1. 我们首次构建了一个非常强大的基线，将最先进的landmark 定位体系结构与最先进的残块相结合，并将其训练在一个非常大但综合扩展的2D面部地标数据集上。然后，我们在所有其他2D数据集(~230,000张图像)上对其进行评估，研究我们离解决2D人脸对齐问题还有多远
• 2. 为了克服缺乏真实感三维人脸对齐的数据集,我们进一步提出一个guided-by-2D地标CNN把1到3 d和2 d注释使用它来创建LS3D-W,最大的和最具挑战性的3 d面部(~ 230000图像)迄今具有里程碑意义的数据集,从统一获得几乎所有现有的数据集。
• 3.然后，我们训练一个三维人脸比对网络，然后在新引入的大规模三维面部地标数据集上对其进行评估，研究我们离解决三维人脸比对问题还有多远。
• 4. 我们进一步研究了影响人脸对齐性能的所有“传统”因素的影响，如大姿态、初始化和分辨率，并引入了一个“新的”因素，即网络的大小。
• 5. 结果表明，无论是二维还是三维人脸对准网络，其精度都达到了很高的水平，接近所使用数据集的饱和状态。

This Section reviews related work on face alignment and landmark localization. Datasets are described in detail in the next Section. 2D face alignment. Prior to the advent of Deep Learning, methods based on cascaded regression had emerged as the state-of-the-art in 2D face alignment, see for example [8, 43, 50, 41]. Such methods are now considered to have largely “solved” the 2D face alignment problem for faces with controlled pose variation like the ones of LFPW [2], Helen [22] and 300-W [30].

We will keep the main result from these works, namely their performance on the frontal dataset of LFPW [2]. This performance will be used as a measure of comparison of how well the methods described in this paper perform assuming that a method achieving a similar error curve on a different dataset is close to saturating that dataset.

本节回顾了人脸定位和地标定位的相关工作。数据集将在下一节中详细描述。在深度学习出现之前，基于级联回归的方法已经成为二维人脸对准的最新技术，参见[8,43,50,41]。这种方法现在被认为在很大程度上“解决”了具有受控位姿变化的人脸的2D人脸对准问题，比如LFPW[2]、Helen[22]和300-W[30]。

我们将保留这些工作的主要结果，即它们在LFPW[2]的正面数据集上的性能。如果在不同的数据集上实现类似的错误曲线的方法接近于该数据集的饱和状态，那么本文中描述的方法的性能将被用来比较它们的执行情况。

CNNs for face alignment. By no means we are the first to use CNNs for face alignment. The method of [35] uses a CNN cascade to regress the facial landmark locations. The work in [47] proposes multi-task learning for joint facial landmark localization and attribute classification. More recently, the method of [40] extends [43] within recurrent neural networks. All these methods have been mainly shown effective for the near-frontal faces of 300-W [30].

Recent works on large pose and 3D face alignment includes [20, 50] which perform face alignment by fitting a 3D Morphable Model (3DMM) to a 2D facial image. The work in [20] proposes to fit a dense 3DMM using a cascade of CNNs. The approach of [50] fits a 3DMM in an iterative manner through a single CNN which is augmented by additional input channels (besides RGB) representing shape features at each iteration. More recent works that are closer to the methods presented in this paper are [4] and [6]. Nevertheless, [4] is evaluated on [20] which is a relatively small dataset (3900 images for training and 1200 for testing) and [6] on [19] which is of moderate size (16,2000 images for training and 4,900 for testing), includes mainly images collected in the lab and does not cover the full spectrum of facial poses. Hence, the results of [4] and [6] are not conclusive in regards to the main questions posed in our paper.

Landmark localization. A detailed review of state-ofthe-art methods on landmark localization for human pose estimation is beyond the scope of this work, please see [39, 38, 24, 17, 27, 42, 23, 5]. For the needs of this work, we built a powerful CNN for 2D and 3D face alignment based on two components: (a) the state-of-the-art HourGlass (HG) network of [23], and (b) the hierarchical, parallel & multi-scale block recently proposed in [7]. In particular, we replaced the bottleneck block [15] used in [23] with the block proposed in [7].

用于面对齐的CNNs。我们绝不是第一个使用CNNs进行人脸校准的公司。[35]方法利用CNN级联反演面部地标位置。在[47]的工作中，提出了多任务学习联合面部landmark 定位和属性分类。最近，[40]方法在循环神经网络中扩展了[43]。这些方法主要用于300-W[30]的近正面。

最近在大姿态和3D人脸对齐方面的工作包括[20,50]，这些工作通过将3D Morphable Model (3DMM)拟合到2D面部图像来进行人脸对齐。在[20]的工作建议适应一个稠密的3DMM使用级联的CNNs。[50]的方法通过一个单独的CNN以迭代的方式对3DMM进行了拟合，在每次迭代中，CNN被表示形状特征的额外输入通道(除了RGB)所增强。更接近本文方法的是[4]和[6]。然而,评估[4]在[20]这是一个相对较小的数据集(培训3900张图片和1200年测试)和[6][19]这是温和的大小(2000图片4900培训和测试),包括在实验室主要是图像采集和不包括面部造成的全谱。因此，对于本文提出的主要问题，[4]和[6]的结果并不是决定性的。

具有里程碑意义的本地化。对用于人体姿态估计的地标定位方法的详细回顾超出了本工作的范围，请参见[39,38,24,17,27,42,23,5]。为了满足这项工作的需要，我们构建了一个强大的基于两个组件的二维和三维人脸校准CNN: (a)[23]的最先进的沙漏(HG)网络，和(b)最近在[7]中提出的分层、并行和多尺度块。特别是，我们用[7]中提出的块替换了[23]中使用的瓶颈块[15]。

Transferring landmark annotations. There are a few works that have attempted to unify facial alignment datasets by transferring landmark annotations, typically through exploiting common landmarks across datasets [49, 34, 46]. Such methods have been primarily shown to be successful when landmarks are transferred from more challenging to less challenging images, for example in [49] the target dataset is LFW [16] or [34] provides annotations only for the relatively easy images of AFLW [21]. Hence, the community primarily relies on the unification performed manually by the 300-W challenge [29] which contains less than 5,000 near frontal images annotated from a 2D perspective.

Using 300-W-LP [50] as a basis, this paper presents the first attempt to provide 3D annotations for all other datasets, namely AFLW-2000 [50] (2,000 images), 300-W test set [28] (600 images), 300-VW [33] (218,595 frames), and Menpo training set (9,000 images). To this end, we propose a guided-by-2D landmarks CNN which converts 2D annotations to 3D and unifies all aforementioned datasets.

传输具有里程碑意义的注释。有一些研究试图通过传输地标注释来统一面部定位数据集，通常是通过跨数据集利用共同的地标[49,34,46]。这些方法已经被初步证明是成功的，当地标从更具挑战性的图像转移到不太具有挑战性的图像时，例如在[49]中，目标数据集是LFW[16]或[34]仅为AFLW[21]的相对简单的图像提供注释。因此，社区主要依赖于由300-W挑战[29]手动执行的统一，该挑战包含少于5000张从2D角度注释的近正面图像。

本文以300-W- lp[50]为基础，首次尝试为所有其他数据集提供3D标注，即AFLW-2000[50](2000张图像)、300-W测试集[28](600张图像)、300-VW[33](218595帧)和Menpo训练集(9000张图像)。为此，我们提出了一个二维路标CNN，它可以将二维注解转换为三维，并统一所有上述数据集。

在本节中，我们将描述如何使用现有的2D和3D数据集进行实验目的的培训和测试。我们注意到，与2D注释相比，3D注释保留了各个姿势之间的对应关系，一般来说，它们应该是首选。我们强调，3D标注实际上是3D面部地标坐标的2D投影，但为了简单起见，我们将其称为3D。在补充材料中，我们提出了一种将这些注释扩展到完整3D的方法。最后，我们强调我们只执行跨数据库实验。

Table 1: Summary of the most popular face alignment datasets and their main characteristics.

For training and validation, we used 300-W-LP [50], a synthetically expanded version of 300-W [29]. 300-W-LP provides both 2D and 3D landmarks allowing for training models and conducting experiments using both types of annotations. For some 2D experiments, we also used the original 300-W dataset [29] for fine tuning, only. This is because the 2D landmarks of 300-W-LP are not entirely compatible with the 2D landmarks of the test sets used in our experiments (i.e. 300-W test set, [28], 300-VW [33] and Menpo [45]), but the original annotations from 300-W are. 

300-W. 300-W [29] is currently the most widely-used inthe-wild dataset for 2D face alignment. The dataset itself is a concatenation of a series of smaller datasets: LFPW [3], HELEN [22], AFW [51] and iBUG [30], where each image was re-annotated in a consistent manner using the 68 2D landmark configuration of Multi-PIE [13]. The dataset contains in total ~4,000 near frontal facial images. 300W-LP-2D and 300W-LP-3D. 300-W-LP is a synthetically generated dataset obtained by rendering the faces of 300-W into larger poses, ranging from −900 to 900 , using the profiling method of [50]. The dataset contains 61,225 images providing both 2D (300W-LP-2D) and 3D landmark annotations (300W-LP-3D).

为了进行培训和验证，我们使用了300-W- lp[50]，这是300-W[29]的综合扩展版本。300-W-LP提供了2D和3D地标，允许使用这两种类型的注释来训练模型和进行实验。对于一些2D实验，我们也仅使用原始的300-W数据集[29]进行微调。这是因为300w - lp的2D landmark与我们实验中使用的测试集(即300w test set， [28]， 300vw [33]， Menpo[45])的2D landmark并不完全兼容，而300w原始的annotation却兼容。

300 - w。300w[29]是目前野外应用最广泛的二维人脸比对数据集。数据集本身是一系列较小数据集的串联:LFPW[3]、HELEN[22]、AFW[51]和iBUG[30]，其中每个图像都使用68个2D地标式多饼[13]重新进行了一致的注释。该数据库共包含近4000张正面人脸图像。300年w-lp-2d和300 w-lp-3d。300w - lp是一个综合生成的数据集，使用[50]的profiling方法，将300w的面渲染成更大的位姿，范围从−900到900。数据集包含61,225张图像，提供2D (300W-LP-2D)和3D地标注释(300W-LP-3D)。

本节描述用于我们的2D和3D实验的测试集。注意，有大量的2D数据集/注释，但是这些数据集/注释对于中等大小的位姿是有问题的(2D地标丢失对应关系)，并且唯一的野外3D测试集是AFLW2000-3D[50] 2。我们在第6节中解决了3D人脸对准数据集中的这个重要差距。

3.2.1 2D datasets

300-W test set. The 300-W test set consists of the 600 images used for the evaluation purposes of the 300-W Challenge [28]. The images are split in two categories: Indoor and Outdoor. All images were annotated with the same 68 2D landmarks as the ones used in the 300-W data set. 300-VW. 300-VW[33] is a large-scale face tracking dataset, containing 114 videos and in total 218,595 frames. From the total of 114 videos, 64 are used for testing and 50 for training. The test videos are further separated into three categories (A, B, and C) with the last one being the most challenging. It is worth noting that some videos (especially from category C) contain very low resolution/poor quality faces. Due to the semi-automatic annotation approach (see [33] for more details), in some cases, the annotations for these videos are not so accurate (see Fig. 3). Another source of annotation error is caused by facial pose, i.e. large poses are also not accurately annotated (see Fig. 3). Menpo. Menpo is a recently introduced dataset [45] containing landmark annotations for about 9,000 faces from FDDB [18] and ALFW. Frontal faces were annotated in terms of 68 landmarks using the same annotation policy as the one of 300-W but profile faces in terms of 39 different landmarks which are not in correspondence with the landmarks from the 68-point mark-up.

3.2.1 2 d数据集

300-W测试集。300-W测试集包含用于300-W挑战[28]的评估目的的600张图像。这些图片分为两类:室内和室外。所有的图像都被标注上了与300-W数据集中使用的相同的68个2D地标。300-VW[33]是一个大型的人脸跟踪数据集，包含114个视频，总共218,595帧。在114个视频中，有64个用于测试，50个用于培训。测试视频进一步分为三个类别(A、B和C)，最后一个是最具挑战性的。值得注意的是，有些视频(尤其是C类视频)的分辨率很低，质量很差。由于半自动标注方法(详见[33])，在某些情况下，这些视频的标注并不十分准确(见图3)。另一个标注错误的来源是由面部姿态造成的，即大的pose也没有准确的标注(见图3)。Menpo是最近推出的一个数据集[45]，其中包含来自FDDB[18]和ALFW的大约9,000个面孔的地标注释。正面脸被标注了68个地标，使用与300-W相同的标注策略，但侧面脸被标注了39个不同的地标，这些地标与68点标记的地标不一致。

3.2.2 3D datasets

AFLW2000-3D. AFLW2000-3D [50] is a dataset constructed by re-annotating the first 2000 images from AFLW [21] using 68 3D landmarks in a consistent manner with the ones from 300W-LP-3D. The faces of this dataset contain large-pose variations (yaw from −90o to 90o ), with various expressions and illumination conditions. However, some annotations, especially for larger poses or occluded faces are not so accurate (see Fig. 6).

3.2.2 3 d数据集

AFLW2000-3D。AFLW2000-3D[50]是一个数据集，它使用68个3D地标，以与300W-LP-3D一致的方式重新注释来自AFLW[21]的前2000个图像。该数据集的面包含了较大的姿态变化(从−90o到90o的偏航)，具有不同的表达式和光照条件。然而，一些注释，特别是对于较大的姿势或遮挡的面部，并不是很准确(见图6)。

Traditionally, the metric used for face alignment is the point-to-point Euclidean distance normalized by the interocular distance [10, 29, 33]. However, as noted in [51], this error metric is biased for profile faces for which the interocular distance can be very small. Hence, we normalize by the bounding box size. In particular, we used the Normalized Mean Error defined as:

where x denotes the ground truth landmarks for a given face, y the corresponding prediction and d is the squareroot of the ground truth bounding box, computed as d = √ wbbox ∗ hbbox. Although we conducted both 2D and 3D experiments, we opted to use the same bounding box definition for both experiments; in particular we used the bounding box calculated from the 2D landmarks. This way, we can readily compare the accuracy achieved in 2D and 3D.

传统上，用于人脸对齐的度量是点对点欧几里德距离，由眼间距归一化[10,29,33]。然而，正如在[51]中所指出的，这种误差度量对于眼间距可能非常小的侧面是有偏差的。因此，我们通过边界框大小进行规范化。特别地，我们使用归一化平均误差定义为:

其中x为给定人脸的ground truth landmarks, y为相应的预测，d为ground truth绑定框的squareroot，计算为d =√wbbox hbbox。虽然我们同时进行了2D和3D实验，但我们选择对两个实验使用相同的边界框定义;我们特别使用了从2D地标计算出的边界框。这样，我们就可以很容易地比较2D和3D的精度。

本节描述风扇，用于二维和三维人脸对准的网络。它还描述了2D-to-3D FAN，用于构建包含超过230,000个3D地标注释的超大规模3D人脸比对数据集(LS3D-W)的网络。

4.1. 2D and 3D Face Alignment Networks

We coin the network used for our experiments simply Face Alignment Network (FAN). To our knowledge, it is the first time that such a powerful network is trained and evaluated for large scale 2D/3D face alignment experiments.

We construct FAN based on one of the state-of-the-art architectures for human pose estimation, namely the HourGlass (HG) network of [23]. In particularly, we used a stack of four HG networks (see Fig. 1). While [23] uses the bottleneck block of [14] as the main building block for the HG, we go one step further and replace the bottleneck block with the recently introduced hierarchical, parallel and multi-scale block of [7]. As it was shown in [7], this block outperforms the original bottleneck of [14] when the same number of network parameter were used. Finally, we used 300W-LP-2D and 300W-LP-3D to train 2D-FAN and 3DFAN, respectively.

Figure 2: The 2D-to-3D-FAN network used for the creation of the LS3D-W dataset. The network takes as input the RGB image and the 2D landmarks and outputs the corresponding 2D projections of the 3D landmarks.

4.1。二维和三维人脸对准网络

我们创造了用于我们的实验的网络简单地面对对准网络(风扇)。据我们所知，这是第一次为大规模的二维/三维人脸对准实验训练和评估这样一个强大的网络。

我们基于最先进的人体姿态估计架构之一，即[23]的沙漏(HG)网络来构建风扇。特别地，我们使用了4个HG网络的堆栈(见图1)。当[23]使用[14]的瓶颈块作为HG的主要构建块时，我们更进一步，用最近引入的[7]的分级、并行和多尺度块替换瓶颈块。如[7]所示，当使用相同数量的网络参数时，此块的性能优于[14]的原始瓶颈。最后，我们使用300W-LP-2D和300W-LP-3D分别训练2D-FAN和3DFAN。

图2:用于创建LS3D-W数据集的2D-to-3D-FAN网络。网络以RGB图像和二维地标为输入，输出相应的三维地标的二维投影。

4.2. 2D-to-3D Face Alignment Network

Our aim is to create the very first very large scale dataset of 3D facial landmarks for which annotations are scarce. To this end, we followed a guided-based approach in which a FAN for predicting 3D landmarks is guided by 2D landmarks. In particular, we created a 3D-FAN in which the input RGB channels have been augmented with 68 additional channels, one for each 2D landmark, containing a 2D Gaussian with std = 1px centered at each landmark’s location. We call this network 2D-to-3D FAN. Given the 2D facial landmarks for an image, 2D-to-3D FAN converts them to 3D. To train 2D-to-3D FAN, we used 300-W-LP which provides both 2D and 3D annotations for the same image. We emphasize again that the 3D annotations are actually the 2D projections of the 3D coordinates but for simplicity we call them 3D. Please see supplementary material for extending these annotations to full 3D.

4.2。二维到三维人脸对准网络

我们的目标是创建第一个非常大的三维面部地标数据集，其中注释是稀缺的。为此，我们采用了基于指南的方法，其中用于预测3D地标的风扇由2D地标引导。特别地，我们创建了一个3D-FAN，其中输入RGB通道被增加了68个额外通道，每个2D地标一个通道，包含一个2D高斯函数，std = 1px以每个地标的位置为中心。我们称这个网络为2D-to-3D风扇。给定图像的2D面部地标，2D-to-3D FAN将其转换为3D。为了训练2D- To -3D风扇，我们使用了300-W-LP，它为相同的图像提供了2D和3D注释。我们再次强调，3D标注实际上是3D坐标的2D投影，但为了简单起见，我们称它们为3D。请参阅补充材料扩展这些注释到完整的3D。

在我们所有的实验中，我们独立地训练了三个不同的网络:2D-FAN、3D-FAN和2D-to-3DFAN。对于前两个网络，我们将初始学习率设置为10−4，并使用10个小批。在这个过程中，我们在15个时点之后将学习率降低到10 - 5，在15个时点之后将学习率降低到10 - 6，总共训练了40个时点。我们还应用了随机增强:翻转、旋转(从−50o到50o)、颜色抖动、尺度噪声(从0.8到1.2)和随机遮挡。2D-to-3D-FAN模型按照类似的程序进行训练，进一步增加增加量:旋转(从−70o到70o)和缩放(从0.7到1.3)。此外，学习速率最初设置为10−3。所有网络在Torch7[9]中实现，使用rmsprop[37]进行训练。

This Section evaluates 2D-FAN (trained on 300-W-LP2D), on 300-W test set, 300-VW (both training and test sets), and Menpo (frontal subset). Overall, 2D-FAN is evaluated on more than 220,000 images. Prior to reporting our results, the following points need to be emphasized:

• 1. 300-W-LP-2D contains a wide range of poses (yaw angles in [−90◦ , 90◦ ]), yet it is still a synthetically generated dataset as this wide spectrum of poses were produced by warping the nearly frontal images of the 300- W dataset. It is evident that this lack of real data largely increases the difficulty of the experiment.
• 2. The 2D landmarks of 300-W-LP-2D that 2D-FAN was trained on are slightly different from the 2D landmarks of the 300-W test set, 300-VW and Menpo. To alleviate this, the 2D-FAN was further fine-tuned on the original 300-W training set for a few epochs. Although this seems to resolve the issue, this discrepancy obviously increases the difficulty of the experiment.
• 3. We compare the performance of 2D-FAN on all the aforementioned datasets with that of an unconventional baseline: the performance of a recent state-of-the-art method, namely MDM [40] on LFPW test set, initialized with the ground truth bounding boxes. We call this result MDM-on-LFPW. As there is very little performance progress made on the frontal dataset of LFPW over the past years, we assume that a state-of-the-art method like MDM (nearly) saturates it. Hence, we use the produced error curve to compare how well our method does on the much more challenging aforementioned test sets.

Figure 3: Fittings with the highest error from 300-VW (NME 6.8-7%). Red: ground truth. White: our predictions. In most cases, our predictions are more accurate than the ground truth.

本节评估2D-FAN(在300-W- lp2d上进行训练)、300-W测试集、300-VW(包括训练和测试集)和Menpo(正面子集)。总的来说，2D-FAN在超过22万张图片上进行了评估。在报告我们的结果之前，需要强调以下几点:

• 1. 300-W- lv - 2d包含了广泛的姿态(偏航角度在[−90◦，90◦])，但它仍然是一个综合生成的数据集，因为这一广泛的姿态是通过扭曲近正面图像的300-W数据集产生的。很明显，缺乏真实数据在很大程度上增加了实验的难度。
• 2. 2D- fan所训练的300w - lp -2D的2D地标与300w测试集、300vw和Menpo的2D地标略有不同。为了缓解这个问题，2D-FAN在最初的300-W训练集上进行了一些改进。虽然这似乎解决了问题，但这种差异明显增加了实验的难度。
• 3.我们将2D-FAN在上述所有数据集上的性能与非传统基线的性能进行了比较:使用ground truth边界框初始化的最新技术方法，即LFPW测试集上的MDM[40]的性能。我们称这个结果为MDM-on-LFPW。由于LFPW的正面数据集在过去几年中几乎没有取得什么性能进步，所以我们假设MDM(几乎)等最先进的方法使其达到饱和。因此，我们使用产生的误差曲线来比较我们的方法在前面提到的更具挑战性的测试集上的表现。

图3:300-VW的配件误差最大(NME 6.8-7%)。红色:地面真理。白:我们的预测。在大多数情况下，我们的预测比事实更准确。

The cumulative error curves for our 2D experiments on 300-VW, 300-W test set and Menpo are shown in Fig. 8. We additionally report the performance of MDM on all datasets initialized by ground truth bounding boxes, ICCR, the stateof-the-art face tracker of [31], on 300-VW (the only tracking dataset), and our unconventional baseline (called MDMon-LFPW). Comparison with a number of methods in terms of AUC are also provided in Table 2.

With the exception of Category C of 300-VW, it is evident that 2D-FAN achieves literally the same performance on all datasets, outperforming MDM and ICCR, and, notably, matching the performance of MDM-on-LFPW. Out of 7,200 images (from Menpo and 300-W test set), there are in total only 18 failure cases, which represent 0.25% of the images (we consider a failure a fitting with NME > 7%). After removing these cases, the 8 fittings with the highest error for each dataset are shown in Fig. 4.

Figure 4: Fittings with the highest error from 300-W test set (first row) and Menpo (second row) (NME 6.5-7%). Red: ground truth. White: our predictions. In most cases, our predictions are more accurate than the ground truth.

我们在300vw、300w和Menpo上进行的二维实验累积误差曲线如图8所示。此外，我们还报告了MDM在所有数据集上的性能，这些数据集由ground truth包围盒(ICCR，[31]的最先进的面跟踪器)在300-VW(唯一的跟踪数据集)上初始化，以及我们的非常规基线(称为MDMon-LFPW)。表2还提供了在AUC方面与一些方法的比较。

除了300-VW的C类，2D-FAN在所有数据集上的性能都是一样的，优于MDM和ICCR，特别是在性能上与MDM-on- lfpw相当。在7200张图像(来自Menpo和300-W测试集)中，总共只有18张失败案例，占图像的0.25%(我们认为失败是与NME > 7%的拟合)。去除这些情况后，每个数据集误差最大的8个配件如图4所示。

图4:在300-W的测试装置(第一行)和门珀(第二行)(NME 6.5-7%)中，误差最大的配件。红色:地面真理。白:我们的预测。在大多数情况下，我们的预测比事实更准确。

Motivated by the scarcity of 3D face alignment annotations and the remarkable performance of 2D-FAN, we opted to create a large scale 3D face alignment dataset by converting all existing 2D face alignment annotations to 3D. To this end, we trained a 2D-to-3D FAN as described in Subsection 4.2 and guided it using the predictions of 2D-FAN, creating 3D landmarks for: 300-W test set, 300-VW (both training and all 3 testing datasets), Menpo (the whole dataset).

Evaluating 2D-to-3D is difficult: the only available 3D face alignment in-the-wild dataset (not used for training) is AFLW2000-3D [50]. Hence, we applied our pipeline (consisting of applying 2D-FAN for producing the 2D landmarks and then 2D-to-3D FAN for converting them to 3D) on AFLW2000-3D and then calculated the error, shown in Fig. 5 (note that for normalization purposes, 2D bounding box annotations are still used). The results show that there is discrepancy between our 3D landmarks and the ones provided by [50]. After removing a few failure cases (19 in total, which represent 0.9% of the data), Fig. 6 shows 8 images with the highest error between our 3D landmarks and the ones of [50]. It is evident, that this discrepancy is mainly caused from the semi-automatic annotation pipeline of [50] which does not produce accurate landmarks especially for images with difficult poses.

由于3D人脸对齐注释的稀缺性和2D- fan的卓越性能，我们选择通过将所有现有的2D人脸对齐注释转换为3D来创建一个大规模的3D人脸对齐数据集。为此，我们按照4.2小节的描述培训了一个2D-to-3D风扇，并使用2D-FAN的预测指导它，创建了3D地标:300-W测试集、300-VW(包括培训和所有3个测试数据集)、Menpo(整个数据集)。

评估2D-to-3D是困难的:野外唯一可用的3D人脸对准数据集(不用于培训)是AFLW2000-3D[50]。因此，我们在AFLW2000-3D上应用了我们的管道(包括应用2D-FAN生成2D地标，然后应用2D-to-3D FAN将它们转换成3D)，然后计算了误差，如图5所示(注意，出于规范化目的，仍然使用2D包围框注释)。结果表明，我们的三维地标与[50]提供的有差异。在排除了一些失败案例(总共19个，占数据的0.9%)之后，图6显示了8张我们的3D地标和[50]的地标之间的误差最大的图像。很明显，这一差异主要是由于[50]的半自动标注流水线无法生成准确的地标，特别是对于姿态困难的图像。

Table 2: AUC (calculated for a threshold of 7%) on all major 2D face alignment datasets. MDM, CFSS and TCDCN were evaluated using ground truth bounding boxes and the openly available code.

表2:所有主要的2D人脸比对数据集的AUC(阈值为7%)。MDM、CFSS和TCDCN使用ground truth包围盒和公开可用的代码进行评估。

Figure 5: NME on AFLW2000-3D, between the original annotations of [50] and the ones generated by 2D-to-3DFAN. The error is mainly introduced by the automatic annotation process of [50]. See Fig. 6 for visual examples.

Figure 6: Fittings with the highest error from AFLW2000- 3D (NME 7-8%). Red: ground truth from [50]. White: predictions of 2D-to-3D-FAN. In most cases, our predictions are more accurate than the ground truth.

图5:AFLW2000-3D上的NME，在[50]的原始注释和2D-to-3DFAN生成的注释之间。误差主要是由[50]的自动标注过程引起的。图6为可视化示例。

图6:装具误差最高的AFLW2000- 3D (NME 7-8%)。红色:地面真相来自[50]。白色:2d - 3d风扇的预测。在大多数情况下，我们的预测比事实更准确。

真实感三维人脸对齐

本节将评估3D- fan在300-W- lp3d、LS3D-W(在前一节中描述)上的训练，即在300-W测试集、300-VW(包括训练和测试集)、Menpo(整个数据集)和AFLW2000-3D(重新注释)上的3D地标上的训练。总的来说，3D-FAN在大约23万张图像上进行了评估。注意，与第5节报道的2D实验相比，我们的3D实验使用了更多的大位姿图像，包括AFLW2000-3D和Menpo的profile images(总共多了约2000张图像)。我们在300w试验台上、300vw、Menpo和AFLW2000-3D上进行的三维人脸对准实验结果如图9所示。此外，我们还报告了3DDFA(在与3D-FAN相同的数据集上训练)的最新方法在所有数据集上的性能。结论:3D-FAN在所有数据集上产生的准确性基本上都优于3DDFA。与2D-FAN相比，这种精度略有提高，特别是对于误差小于2%的误差曲线部分，这并不奇怪，因为现在训练和测试数据集都使用相同的标记进行注释。

为了进一步研究3D-FAN在复杂条件下的性能，我们首先创建了一个包含来自LS3D-W的7200张图像的数据集，以便在偏航角[0o−30o]、[30o−60o]和[60o−90o]有相同数量的图像。我们称这个数据集为LS3D-W平衡。然后，我们进行了以下实验:

Table 3: AUC (calculated for a threshold of 7%) on the LS3D-W Balanced for different yaw angles.

Table 4: AUC on the LS3D-W Balanced for different levels of initialization noise. The network was trained with a noise level of up to 20%.

Table 5: AUC on the LS3D-W Balanced for various network sizes. Between 12-24M parameters, performance remains almost the same.

Figure 7: AUC on the LS3D-W Balanced for different face resolutions. Up to 30px, performance remains high.

表3:不同偏航角度下LS3D-W平衡时的AUC(阈值为7%)。

表4:在不同初始化噪声水平下，LS3D-W上的AUC平衡。该网络在20%的噪音水平下进行训练。

表5:LS3D-W上的AUC为各种网络大小而平衡。在12-24M参数之间，性能几乎保持不变。

图7:在LS3D-W上的AUC为不同的面分辨率而平衡。高达30px，性能仍然很高。

Performance across pose. We report the performance of 3D-FAN on LS3D-W Balanced for each pose separately in terms of the Area Under the Curve (AUC) (calculated for a threshold of 7%) in Table 3. We observe only a slight degradation of performance for very large poses ([60o − 90o ]). We believe that this is to some extent to be expected as 3D-FAN was largely trained with synthetic data for these poses (300-W-LP-3D). This data was produced by warping frontal images (i.e. the ones of 300-W) to very large poses which causes face distortion especially for the face region close to the ears.

Conclusion: Facial pose is not a major issue for 3D-FAN.

Performance across resolution. We repeated the previous experiment but for different face resolutions (resolution is reduced relative to the face size defined by the tight bounding box) and report the performance of 3D-FAN in terms of AUC in Fig. 7. Note that we did not retrain 3D-FAN to particularly work for such low resolutions. We observe significant performance drop for all poses only when the face size is as low as 30 pixels.

Conclusion: Resolution is not a major issue for 3D-FAN.

Performance across noisy initializations. For all reported results so far, we used 10% of noise added to the ground truth bounding boxes. Note that 3D-FAN was trained with noise level of 20%. Herein, we repeated the previous experiment but for different noise levels and report the performance of 3D-FAN in terms of AUC in Table 4. We observe only small performance decrease for noise level equal to 30% which is greater than the level of noise that the network was trained with.

Conclusion: Initialization is not a major issue for 3D-FAN.

在构成性能。根据曲线下面积(AUC)(阈值为7%)，我们报告了3D-FAN在LS3D-W上的表现。我们只观察到在非常大的位姿([60o - 90o])下性能有轻微的下降。我们认为这在某种程度上是可以预期的，因为3D-FAN主要是使用这些姿势的合成数据进行训练的(300-W-LP-3D)。这些数据是通过将正面图像(即300-W的图像)扭曲成非常大的姿态产生的，这会导致面部变形，尤其是靠近耳朵的面部区域。

结论:面部姿势不是3d风扇的主要问题。

在分辨率性能。我们重复了之前的实验，但是对于不同的人脸分辨率(分辨率相对于紧边界框定义的人脸尺寸减小)，并在图7中以AUC的形式报告了3D-FAN的性能。请注意，我们并没有对3D-FAN进行再培训，使其特别适合如此低分辨率的工作。我们观察到，只有当面部尺寸低至30像素时，所有姿势的表现才会显著下降。

结论:解决问题并不是3D-FAN的主要问题。

跨有噪声的初始化的性能。对于到目前为止所有报告的结果，我们使用10%的噪音添加到地面真实边界框。注意3D-FAN的训练噪音等级为20%。在此，我们重复了之前的实验，但是在不同的噪声水平下，我们用AUC来报告3D-FAN的性能如表4所示。我们观察到，当噪声水平大于网络训练时的噪声水平时，当噪声水平等于30%时，系统的性能只有很小的下降。

结论:初始化不是3D-FAN的主要问题。