Two decades have passed since the seminal work of Vetter and Blanz  that first showed how to reconstruct 3D facial geometry from a single image. Since then, 3D face reconstruction methods have rapidly advanced (for a comprehensive overview see ) enabling applications such as 3D avatar creation for VR/AR , video editing 5, 54], virtual make-up , or speech-driven facial animation . To make the problem tractable, most existing methods incorporate prior knowledge about geometry or appearance by leveraging pre-computed 3D face models [7, 20]. These models reconstruct the coarse face shape but are unable to capture geometric details such as expression-dependent wrinkles, which are essential for realism and for analysing human emotion.
Several methods recover detailed facial geometry [1, 9, 15, 30, 53, 73, 74], however, they require high-quality training scans [9, 15] or lack robustness to occlusions [1, 30, 53]. None of these works explore how the recovered wrinkles change with varying expressions. Previous methods that learn expression-dependent detail models [14, 82] either use detailed 3D scans as training data and, hence, do not generalize to unconstrained images , or model expression-dependent details as part of the appearance map rather than the geometry , preventing realistic mesh relighting.
We introduce DECA (Detailed Expression Capture and Animation), which learns an animatable displacement model from in-the-wild images without 2D-to-3D supervision. In contrast to prior work, these animatable expression-dependent wrinkles are specific to an individual and are regressed from an image. Specifically, DECA jointly learns 1) a geometric detail model that generates a UV displacement map from a low-dimensional representation that consists of subject-specific detail parameters and expression parameters, and 2) a regressor that predicts subject-specific detail, albedo, shape, expression, pose, and lighting parameters from an image. The detail model builds upon FLAME’s  coarse geometry, and we formulate the displacements as a function of subject-specific detail parameters and FLAME’s jaw pose and expression parameters.
To gain control over expression-dependent wrinkles of the reconstructed face, while preserving person-specific details (i.e. moles, pores, eyebrows, and expression-independent wrinkles), the person-specific details and expression-dependent wrinkles must be disentangled. Our key contribution is a novel detail consistency loss that enforces this disentanglement. Given two images of the same person with different expressions, we observe that their 3D face shape and their person-specific details are the same in both images, but the expression and the intensity of the wrinkles differ with expression. During training, this observation is exploited by swapping the detail codes between different images of the same identity and enforcing the newly rendered results to look similar to the original input images. Once trained, DECA reconstructs a detailed 3D face from a single image (Fig. 1 third row) in real time (about 120fps on a Nvidia Quadro RTX 5000), and is able to animate the reconstruction with realistic adaptive expression wrinkles (Fig. 1 bottom).
In summary, our main contributions are: 1) The first approach to learn an animatable displacement model from in-the-wild images that can synthesize plausible geometric details by varying expression parameters. 2) A novel detail consistency loss that disentangles identity-dependent and expression-dependent facial details. 3) Reconstruction of geometric details that is, unlike most competing methods, robust to occlusions, poses, and illumination variation. This is enabled by our low-dimensional detail representation, the detail disentanglement, and training from a large dataset of in-the-wild images. 4) State-of-the-art shape reconstruction accuracy on two different benchmarks. 5) Code and model will be made publicly available for research purposes.
2 Related work
The reconstruction of 3D faces from visual input has received significant attention over the last decades after the pioneering work of Parke , the first method to reconstruct 3D faces from multi-view images. While a large body of related work aims to reconstruct 3D faces from various input modalities such as multi-view images [4, 11, 50], video data [23, 33, 35, 62, 66], RGB-D data [41, 70, 80] or subject-specific image collections [37, 56], our main focus is on methods that use only a single RGB image. For a more comprehensive overview, see Zollhöfer et al. .
Coarse reconstruction: Many monocular 3D face reconstruction methods follow Vetter and Blanz 
by estimating coefficients of pre-computed statistical models in an analysis-by-synthesis fashion. Such methods can be categorized into optimization-based[2, 3, 5, 6, 26, 55, 71], or learning-based methods [13, 18, 25, 38, 52, 58, 69, 72, 75]. These methods estimate parameters of a statistical face model with a fixed linear shape space, which captures only low-frequency shape information. This results in overly-smooth reconstructions.
Several works are model-free and directly regress 3D faces (i.e. voxels  or meshes [19, 21, 28, 79]) and hence could capture more variation than the model-based methods. However, all these methods require explicit 3D supervision, which is provided either by an optimization-based model fitting [21, 28, 34, 79] or by synthetic data generated by sampling a statistical face model  and therefore also only capture coarse shape variations.
Instead of capturing high-frequency geometric details, some methods reconstruct coarse facial geometry along with high-fidelity textures [24, 57, 65, 81]. As this “bakes” shading details into the texture, lighting changes do not affect these details. To enable animation and relighting, DECA captures these details as part of the geometry.
Detail reconstruction: Another body of work aims to reconstruct faces with “mid-frequency” details. Common optimization-based methods fit a statistical face model to images to obtain a coarse shape estimate, followed by a shape from shading (SfS) method to reconstruct facial details from monocular images [36, 43] or videos [23, 66]. Unlike DECA, these approaches are slow, the results lack robustness to occlusions, and the coarse model fitting step requires facial landmarks, making them error-prone for large viewing angles and occlusions.
Most regression-based approaches [9, 15, 30, 53, 73] follow a similar approach by first reconstructing the parameters of a statistical face model to obtain a coarse shape, followed by a refinement step to capture localized details. Chen et al.  and Cao et al.  compute local wrinkle statistics from high-resolution scans and leverage these to constrain the fine-scale detail reconstruction from images  or videos . Guo et al.  and Richardson et al.  directly regress per-pixel displacement maps. All these methods only reconstruct fine-scale details in non-occluded regions, causing visible artifacts in the presence of occlusions. Tran et al.  gain robustness to occlusions by applying some face segmentation method  to determine occluded regions, and employ an example-based hole filling of the occluded regions. Further, model-free methods exist that directly reconstruct detailed meshes [60, 83] or surface normals that add detail to coarse reconstructions [1, 61].
Tran et al.  and Tewari et al. [67, 68] jointly learn a statistical face model and reconstruct 3D faces from images. While offering more flexibility than fixed statistical models, these methods capture limited geometric details compared to other detail reconstruction methods.
Unlike DECA, none of these detail reconstruction methods offer animatable details after reconstruction.
Animatable detail reconstruction: Most relevant to DECA are methods that reconstruct detailed faces while allowing animation of the result. Golovinski et al. , Shin et al.  and FaceScape  learn correlations between wrinkles and factors like age and gender  or expression [63, 82] from high-quality face scans. In contrast, DECA learns an animatable detail model solely from in-the-wild images without paired 3D training data. While FaceScape  predicts an animatable 3D face from a single image, the method is not robust to occlusions. This is due to a two step reconstruction process: first optimize the coarse shape, then predict a displacement map from the texture map extracted with the coarse reconstruction.
Chaudhuri et al.  learn identity and expression corrective blendshapes with dynamic (expression-dependent) albedo maps . They model geometric details as part of the albedo map, and therefore, the shading of these details does not adapt with varying lighting. This results in unrealistic renderings. In contrast, DECA models details as geometric displacements, which look natural when re-lit.
Geometry prior: FLAME  is a statistical 3D head model that combines separate linear identity shape and expression spaces with linear blend skinning (LBS) and pose-dependent corrective blendshapes to articulate the neck, jaw, and eyeballs. Given parameters of facial identity , pose (with joints for neck, jaw, and eyeballs), and expression , FLAME outputs a mesh with vertices. The model is defined as
with the blend skinning function that rotates the vertices in around joints , linearly smoothed by blendweights . The joint locations J are defined as a function of the identity . Further,
denotes the mean template T in “zero pose” with added shape blendshapes , pose correctives , and expression blendshapes , with the learned identity, pose, and expression bases and . See  for details.
Appearance model: FLAME does not have an appearance model, hence we convert Basel Face Model’s PCA albedo space  into the FLAME UV layout to make it compatible with FLAME. The appearance model outputs a UV albedo map for albedo parameters .
Camera model: Photographs in existing in-the-wild face datasets are often taken from a distance. We, therefore, use an orthographic camera model c to project the 3D mesh into image space. Face vertices are projected into the image as , where is a vertex in , is the orthographic 3D-2D projection matrix, and and denote isotropic scale and 2D translation, respectively. The parameters , and are summarized as .
Illumination model: For face reconstruction, the most frequently-employed illumination model is based on Spherical Harmonics (SH) . By assuming that the light source is distant and the face’s surface reflectance is Lambertian, the shaded face image is computed as:
where the albedo, , surface normals, , and shaded texture, , are represented in UV coordinates and where , , and denote pixel in the UV coordinate system. The SH basis and coefficients are defined as and , with , and denotes the Hadamard product.
Texture rendering: Once we have the geometry parameters (), albedo (), lighting (l) and camera information , we can recover the 2D image by rendering as , where denotes the rendering function.
FLAME is able to generate a face geometry with various poses, shapes and expressions from a low-dimensional latent space. However, the representational power of the model is limited by the low mesh resolution and therefore mid-frequency details are mostly missing in FLAME’s surface. The next section introduces our expression-dependent displacement model that augments FLAME with mid-frequency details, and it demonstrates how to reconstruct detailed geometry from a single image and animate it.
4 Proposed method
The goal of DECA is to learn a parameterized face model with geometric detail solely from in-the-wild images (Fig. 2 left). Once trained, DECA reconstructs the 3D head with detailed face geometry from a single face image . The learned parametrization of the reconstructed details enables us then to animate the detail reconstruction by controlling FLAME’s expression and jaw pose parameters (Fig. 2 right). This synthesizes new wrinkles while keeping person-specific details unchanged.
Key idea: The key idea of DECA is grounded in the observation that an individual’s face shows different details (i.e. wrinkles), depending on their facial expressions but that other properties of their shape remain unchanged. Consequently, facial details should be separated into static person-specific details and dynamic expression-dependent details such as wrinkles . However, disentangling static and dynamic facial details is a non-trivial task. Static facial details are different across people, whereas dynamic expression dependent facial details even vary for the same person. Thus, DECA learns an expression-conditioned detail model to infer facial details from both the person-specific detail latent space and the expression space.
The main difficulty of learning a detail displacement model is the lack of training data. Prior work uses specialized camera systems to scan people in a controlled environment to obtain detailed facial geometry. However, this approach is expensive and impractical for capturing large numbers of identities with varying expressions and diversity in ethnicity and age. Therefore we propose an approach to learn detail geometry from in-the-wild images.
4.1 Coarse reconstruction
We first learn a coarse reconstruction (i.e. in FLAME’s model space) in an analysis-by-synthesis way: given a 2D image as input, we encode the image to a latent code, decode this to synthesize a 2D image , and minimize the difference between the synthesized image and the input. As shown in Fig. 2, we train an encoder , which consists of a ResNet50  network followed by a fully connected layer, to regress a low-dimensional latent code. This latent code consists of FLAME parameters , , (i.e. representing the coarse geometry), albedo coefficients , camera , and lighting parameters l. More specifically, the coarse geometry uses the first 100 FLAME shape parameters (), 50 expression parameters (), and 50 albedo parameters (). In total, predicts a dimensional latent code.
Given a dataset of face images with multiple images per subject, corresponding identity labels , and keypoints per image, the coarse reconstruction branch is trained by minimizing
with landmark loss , eye closure loss , photometric loss , identity loss , shape consistency loss and regularization .
Landmark re-projection loss: The landmark loss measures the difference between ground-truth face landmarks and the corresponding landmarks in the FLAME’s surface , projected into the image by the estimated camera model. The landmark loss is defined as
Eye closure loss: The eye closure loss computes the relative offset of landmarks and on the upper and lower eyelid, and measures the difference to the offset of the corresponding landmarks in the FLAME’s surface and projected into the image. Formally, the loss is given as
where is the set of upper/lower eyelid landmark pairs.
Photometric loss: The photometric loss computes the error between the input image and the rendering as . Here, is a face mask with value in the face skin region, and value elsewhere obtained by an existing face segmentation method , and denotes the Hadamard product. Computing the error in the face region only provides robustness to common occlusions by e.g. hair, clothes, sunglasses, etc.
Identity loss: Recent 3D face reconstruction methods demonstrate the effectiveness of utilizing an identity loss to produce more realistic face shapes [18, 24]. Motivated by this, we also use a pretrained face recognition network , to employ an identity loss during training.
The face recognition network
outputs feature embeddings of the rendered images and the input image, and the identity loss then measures the cosine similarity between the two embeddings. Formally, the loss is defined as
Shape consistency loss: Given two images and of the same subject (i.e. ), the coarse encoder should output the same shape parameters (i.e. ). Previous work encourages shape consistency by enforcing the distance between and to be smaller by a margin than the distance to the shape coefficients corresponding of a different subject . However, choosing this fixed margin is challenging in practice. Instead, we propose a different strategy by replacing with while keeping all other parameters unchanged. Given that and represent the same subject, this new set of parameters must reconstruct well. Formally, we minimize
Regularization: regularizes shape , expression , and albedo .
4.2 Detail reconstruction
The detail reconstruction aims at augmenting the coarse FLAME geometry with a detailed UV displacement map (see Fig. 2). Similar to the coarse reconstruction, we train an encoder (with the same architecture as ) to encode to a -dimensional latent code , representing subject-specific details. The latent code is then concatenated with FLAME’s expression and jaw pose parameters , and decoded by to .
Detail decoder: The detail decoder is defined as
where the detail code controls the static person-specific details. We leverage the expression and jaw pose parameters from the coarse reconstruction branch to capture the dynamic expression wrinkle details. For rendering, is converted to a normal map.
Detail rendering: The detail displacement model allows us to generate images with fine-scale surface details. To reconstruct the detailed geometry , we convert and its surface normals to UV space, denoted as and , and combine them with as
By calculating normal from , we obtain the detail rendering by rendering with applied normal map as
The detail reconstruction is trained by minimizing
with photometric detail loss , ID-MRF loss , soft symmetry loss , and detail regularization .
Detail photometric losses: With the applied detail displacement map, the rendered images contain some geometric details. Equivalent to the coarse rendering, we use a photometric loss , where, recall, is a mask representing the visible skin pixels.
ID-MRF loss: We add an Implicit Diversified Markov Random Fields (ID-MRF) loss  to reconstruct geometric details. Given two images of the same person, the ID-MRF loss extracts feature patches from different layers of a pre-trained network, and then minimizes the difference between corresponding nearest neighbor feature patches from both images. Following Wang et al. , the loss is computed on layers and of VGG19  as
where denotes the ID-MRF loss which is employed on the feature patches extracted from and with layer of VGG19. As for the photometric losses, we compute only for the face skin region in UV space.
Soft symmetry loss: To add robustness to occlusions, we add a soft symmetry loss to regularize non-visible face parts. Specifically, we minimize
where denotes the face skin mask in UV space, and is the horizontal flip operation.
Detail regularization: The detail displacements are regularized by to reduce noise.
4.3 Detail disentanglement
Optimizing enables us to reconstruct faces with mid-frequency details. Making these detail reconstructions animatable however requires us to disentangle person specific details (i.e. moles, pores, eyebrows, and expression-independent wrinkles) controlled by from expression-dependent wrinkles (i.e. wrinkles that change for varying facial expression) controlled by FLAME’s expression and jaw pose parameters, and . Our key observation is that the same person in two images should have both similar coarse geometry and personalized details. So for the rendered detail image, exchanging the detail codes between two images of the same subject should have no effect on the rendered image.
5 Implementation Details
Data: We train DECA on three publicly available datasets: VGGFace2 , BUPT-Balancedface  and VoxCeleb2 . VGGFace2  contains images of over subjects, with an average of more than images per subject. BUPT-Balancedface  offers subjects per ethnicity (i.e. Caucasian, Indian, Asian and African), and VoxCeleb2  contains videos of subjects. In total, DECA is trained on 2 Million images.
All datasets provide an identity label for each image. We use FAN  to predict 2D landmarks on each face. To improve the robustness of the predicted landmarks, we run FAN for each image twice with different face crops, and discard all images with non-matching landmarks. See Sup. Mat. for details on data selection and data cleaning.
6.1 Qualitative evaluation
Reconstruction: Given a single face image, DECA reconstructs the 3D face shape with mid-frequency geometry details. The second row of Fig. 1 shows that the coarse shape (i.e. in FLAME space) well represents the overall face shape, and the learned DECA detail model reconstructs subject-specific details and wrinkles of the input identity (Fig. 1 row three), while being robust to partial occlusions.
Figure 4 qualitatively compares DECA results with state-of-the-art coarse face reconstruction methods, namely PRNet , RingNet , Deng et al. , FML  and 3DDFA-V2 . Compared to these methods, DECA better reconstructs the overall face shape with details like the nasolabial fold (rows 1, 2, 3, 4, and 6) and forehead wrinkles (row 3). DECA better reconstructs the mouth shape and the eye region than all other methods. DECA further reconstructs a full head while PRNet , Deng et al. , FML  and 3DDFA-V2  reconstruct tightly cropped faces. While RingNet , like DECA, is based on FLAME , DECA better reconstructs the face shape and the facial expression.
Figure 5 compares DECA visually to existing detail face reconstruction methods, namely Extreme3D , Cross-modal , and FaceScape . Extreme3D  and Cross-modal  reconstruct more details than DECA but at the cost of being less robust to occlusions (rows 1, 2, 3). Unlike DECA, Extreme3D and Cross-modal only reconstruct static details. However, using static details instead of DECA’s animatable details leads to visible artifacts when animating the face (see Fig. 6). While FaceScape  provides animatable details, unlike DECA, the method is trained on high-resolution scans while DECA is solely trained on in-the-wild images. Also, with occlusion, FaceScape produces artifacts (rows 1, 2) or effectively fails (row 3).
In summary, DECA produces high-quality reconstructions, outperforming previous work in terms of robustness, while enabling animation of the detailed reconstruction. To demonstrate the quality of DECA and the robustness to variations in head pose, expression, occlusions, image resolution, lighting conditions, etc., we show results for 200 randomly selected ALFW2000  images in the Sup. Mat. along with more qualitative coarse and detail reconstruction comparisons to the state-of-the-art.
Detail animation: DECA models detail displacements as a function of subject-specific detail parameters and FLAME’s jaw pose and expression parameters . This formulation allows us to animate detailed facial geometry such that wrinkles are specific to the source shape and expression as shown in Fig. 1. Using static details instead of DECA’s animatable details (i.e. by using the reconstructed details as a static displacement map) and animating only the coarse shape by changing the FLAME parameters results in visible artifacts as shown in Fig. 6 (top), while animatable details (middle) look similar to the reference shape (bottom) of the same identity. The Sup. Mat. shows more comparisons of animatable and static details.
6.2 Quantitative evaluation
NoW benchmark: The NoW challenge  consists of 2054 face images of 100 subjects, split into a validation set (20 subjects) and a test set (80 subjects), with a reference 3D face scan per subject. The images consist of indoor and outdoor images, neutral expression and expressive face images, partially occluded faces, and varying viewing angles ranging from frontal view to profile view, and selfie images. The challenge provides a standard evaluation protocol that measures the distance from all reference scan vertices to the closest point in the reconstructed mesh surface, after rigidly aligning scans and reconstructions. For details, see .
We found that the tightly cropped face meshes predicted by Deng et al.  are smaller than the NoW reference scans, which would result in a high reconstruction error in the missing region. For a fair comparison to the method of Deng et al. , we use the Basel Face Model (BFM)  parameters they output, reconstruct the complete BFM mesh, and get the NoW evaluation for these complete meshes. As shown in Tab. 1
and the cumulative error plot in the Sup. Mat., DECA gives state-of-the-art results on NoW, providing the reconstruction error with the lowest mean, median, and standard deviation.
|Deng et al.19 ||1.23||1.54||1.29|
Feng et al. benchmark: The Feng et al. challenge  contains 2000 face images of 135 subject, and a reference 3D face scan for each subject. The benchmark consists of 1344 low-quality (LQ) images extracted from videos, and 656 high-quality (HQ) images taken in controlled scenarios. A protocol similar to NoW is used for evaluation that measures the distance between all reference scan vertices to the closest points on the reconstructed mesh surface, after rigidly aligning scan and reconstruction. As shown in Tab. 2 and the cumulative error plot in the Sup. Mat., DECA provides state-of-the-art performance.
6.3 Ablation experiment
Detail consistency loss: To evaluate the importance of our novel detail consistency loss (Eq. 15), we train DECA with and without . Figure 7 (left) shows the DECA details for detail code from the source identity, and expression and jaw pose parameters from the source expression. For DECA trained with (top), wrinkles appear in the forehead as a result of the raised eyebrows of the source expression, while for DECA trained without (bottom), no such wrinkles appear. This indicates that without , person-specific details and expression-dependent wrinkles are not well disentangled. See Sup. Mat. for more disentanglement results.
ID-MRF loss: Figure 7 (right) shows the effect of on the detail reconstruction. Without (middle), wrinkle details (e.g. in the forehead) are not reconstructed, resulting in an overly smooth result. With (right), DECA captures the details.
7 Conclusion and discussion
We have presented DECA, which enables detailed expression capture and animation from single images by learning an animatable detail model from in-the-wild images. In total, DECA is trained from about 2M in-the-wild face images without 2D-to-3D supervision. DECA reaches state-of-the-art shape reconstruction performance enabled by a shape consistency loss. A novel detail consistency loss helps DECA to disentangle expression-dependent wrinkles from person-specific details. The low-dimensional detail latent space makes the fine-scale reconstruction robust to noise and occlusions, and the novel loss leads to disentanglement of identity and expression-dependent wrinkle details. This enables applications like animation, shape change, wrinkle transfer, etc. DECA is publicly available for research purposes. Due to the reconstruction accuracy, the reliability, and the speed, DECA is useful for applications like face reenactment or virtual avatar creation.
DECA opens the door for future work. First, our albedo model is dependent on the Basel face model, which lacks ethnic diversity and facial hair. This pushes skin tone into the lighting model and causes facial hair to be explained by shape deformations. We believe that we can learn a more diverse albedo model from in-the-wild images using our system. Second, we want to extend the model over time, both for tracking and to learn more personalized models of individuals from video where we could enforce continuity of intrinsic wrinkles over time. Third, while robust, our method can still fail due to extreme head pose and lighting. This suggests the need for more diverse training data.
We thank S. Sanyal for providing us the RingNet PyTorch implementation, support with paper writing, and fruitful discussions, and M. Kocabas, N. Athanasiou, and V. Fernández Abrevaya for the helpful suggestions. We further thank all Perceiving Systems department members for the feedback. This work was partially supported by the Max Planck ETH Center for Learning Systems.
Disclosure: MJB has received research gift funds from Intel, Nvidia, Adobe, Facebook, and Amazon. While MJB is a part-time employee of Amazon, his research was performed solely at, and funded solely by, MPI. MJB has financial interests in Amazon and Meshcapade GmbH.
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Appendix A Implementation Details
Data: DECA is trained on 2 Million images from VGGFace2  and BUPT-Balancedface  and VoxCeleb2 . From VGGFace2 , we randomly select images such that images are of resolution higher than , and are of lower resolution. From BUPT-Balancedface  we randomly sample with Asian or African ethnicity labels to reduce the ethnicity bias of VGGFace2. From VoxCeleb2  we choose frames, with multiple samples from the same video clip per subject to obtain data with variation only in the facial expression and head pose. We also sample images from the VGGFace2  test set for validation.
Data cleaning: We generate a different crop for the face image by shifting the provided bounding box by to the bottom right (i.e. shift by , where and denote the bounding box width and height). Then we expand the original and the shifted bounding boxes by to the top, and by to the left, right, and bottom. We run FAN , providing the expanded bounding boxes as input and discard all images with , where and are the th landmarks for the original and the shifted bounding box, respectively, and D denote the normalization matrix .
Training details: We pre-train the coarse model (i.e.
) for two epochs with a batch size ofwith , , , and . Then, we train the coarse model for epochs with a batch size of , with images per subject with , , , , , , and . The landmark loss uses different weights for individual landmarks, the mouth corners and the nose tip landmarks are weighted by a factor of , other mouth and nose landmarks with a factor of , and all remaining landmarks have a weight of . This is followed by training the detail model (i.e. and ) on VGGFace2 and VoxCeleb2 with a batch size of , with images per subject, and parameters , , , , and . The coarse model is fixed while training the detail model.
Appendix B Evaluation
b.1 Detail animation
As described in Section 6.1 and shown in Figure 6 of the main paper, using a static displacement map to model geometric details instead of DECA’s animatable details results in visible artifacts. Figure 8 shows more examples where using static details results in artifacts in the mouth corner or the forehead region, while DECA’s animated results look plausible.
b.2 Quantitative evaluation
|NoW ||Feng et al.  LQ||Feng et al.  HQ|
As described in Section 6.2 of the main paper, we quantitatively compare DECA with publicly available methods, namely 3DDFA-V2 , Deng et al. , RingNet , PRNet , 3DMM-CNN  and Extreme3D  on two existing 3D face reconstruction benchmarks, the NoW challenge  and the Feng et al.  benchmark. The left of Figure 9 shows the cumulative errors for Table 1 of the main paper, the middle and right of Figure 9 show the cumulative errors for Table 2 of the main paper. Note that in all cases, the DECA curve in dark blue is aboth that of the other methods. This demonstrates that DECA gives state-of-the-art reconstruction performance for both benchmarks.
b.3 Qualitative comparisons
Figure 10 shows additional qualitative comparisons to existing coarse and detail reconstruction methods. DECA better reconstructs the overall face shape than all existing methods, it reconstructs more details than existing coarse reconstruction methods (e.g. (b), (e), (f)), and it is more robust to occlusions compared to existing detail reconstruction methods (e.g. (c), (d), (g)).
As promised in the main paper (e.g. Section 6.1), we show results for more than 200 randomly selected ALFW2000  samples in Figures 11, 12, 13, 14, 15, 16, and 17. For each sample, we compare the DECA’s detail reconstruction (e) with the state-of-the-art coarse reconstruction method 3DDFA-V2  (see (b)) and existing detail reconstruction methods, namely FaceScape  (see (c)), and Extreme3D  (see (e)). In total, DECA reconstructs more details then 3DDFA-V2, and it is more robust to occlusions than FaceScape and Extreme3D. Further, the DECA retargeting results appear realistic.