1 Introduction
Generating videos by animating objects in still images has countless applications across areas of interest including movie production, photography, and ecommerce. More precisely, image animation refers to the task of automatically synthesizing videos by combining the appearance extracted from a source image with motion patterns derived from a driving video. For instance, a face image of a certain person can be animated following the facial expressions of another individual (see Fig. 1). In the literature, most methods tackle this problem by assuming strong priors on the object representation (e.g. 3D model) blanz1999morphable and resorting to computer graphics techniques cao2014displaced ; thies2016face2face . These approaches can be referred to as objectspecific methods, as they assume knowledge about the model of the specific object to animate.
Recently, deep generative models have emerged as effective techniques for image animation and video retargeting balakrishnansynthesizing ; zablotskaia2019dwnet ; bansal2018recycle ; Zakharov_2019_CVPR ; Shysheya_2019_CVPR ; siarohin2018animating ; wang2018video ; wiles2018x2face ; hao2018Geaturegan ; liu2019gesture . In particular, Generative Adversarial Networks (GANs) goodfellow2014generative and Variational AutoEncoders (VAEs) kingma2013auto have been used to transfer facial expressions wang2018video or motion patterns bansal2018recycle between human subjects in videos. Nevertheless, these approaches usually rely on pretrained models in order to extract objectspecific representations such as keypoint locations. Unfortunately, these pretrained models are built using costly groundtruth data annotations balakrishnansynthesizing ; Shysheya_2019_CVPR ; hao2018Geaturegan and are not available in general for an arbitrary object category. To address this issues, recently Siarohin et al. siarohin2018animating
introduced MonkeyNet, the first objectagnostic deep model for image animation. MonkeyNet encodes motion information via keypoints learned in a selfsupervised fashion. At test time, the source image is animated according to the corresponding keypoint trajectories estimated in the driving video. The major weakness of MonkeyNet is that it poorly models object appearance transformations in the keypoint neighborhoods assuming a zeroth order model (as we show in Sec.
3.1). This leads to poor generation quality in the case of large object pose changes (see Fig. 4). To tackle this issue, we propose to use a set of selflearned keypoints together with local affine transformations to model complex motions. We therefore call our method a firstorder motion model. Second, we introduce an occlusionaware generator, which adopts an occlusion mask automatically estimated to indicate object parts that are not visible in the source image and that should be inferred from the context. This is especially needed when the driving video contains large motion patterns and occlusions are typical. Third, we extend the equivariance loss commonly used for keypoints detector training jakabunsupervised ; zhao2018learning , to improve the estimation of local affine transformations. Fourth, we experimentally show that our method significantly outperforms stateoftheart image animation methods and can handle highresolution datasets where other approaches generally fail. Finally, we release a new high resolution dataset, ThaiChiHD, which we believe could become a reference benchmark for evaluating frameworks for image animation and video generation.
















































2 Related work
Video Generation.
Earlier works on deep video generation discussed how spatiotemporal neural networks could render video frames from noise vectors
vondrick2016generating ; saito2017temporal . More recently, several approaches tackled the problem of conditional video generation. For instance, Wang et al. wang2018everycombine a recurrent neural network with a VAE in order to generate face videos. Considering a wider range of applications, Tulyakov
et al. tulyakov2017mocogan introduced MoCoGAN, a recurrent architecture adversarially trained in order to synthesize videos from noise, categorical labels or static images. Another typical case of conditional generation is the problem of future frame prediction, in which the generated video is conditioned on the initial frame finn2016unsupervised ; oh2015action ; srivastava2015unsupervised ; van2017transformation ; zhao2018learning . Note that in this task, realistic predictions can be obtained by simply warping the initial video frame babaeizadeh2017stochastic ; finn2016unsupervised ; van2017transformation . Our approach is closely related to these previous works since we use a warping formulation to generate video sequences. However, in the case of image animation, the applied spatial deformations are not predicted but given by the driving video.Image Animation. Traditional approaches for image animation and video retargeting cao2014displaced ; thies2016face2face ; geng20193d were designed for specific domains such as faces zollhofer2018state ; Zakharov_2019_CVPR , human silhouettes chan2018everybody ; wang2018video ; Shysheya_2019_CVPR or gestures hao2018Geaturegan and required a strong prior of the animated object. For example, in face animation, method of Zollhofer et al. zollhofer2018state produced realistic results at expense of relying on a 3D morphable model of the face. In many applications, however, such models are not available. Image animation can also be treated as a translation problem from one visual domain to another. For instance, Wang et al. wang2018video
transferred human motion using the imagetoimage translation framework of Isola
et al. pix2pix2016 . Similarly, Bansal et al. bansal2018recycle extended conditional GANs by incorporating spatiotemporal cues in order to improve video translation between two given domains. Such approaches in order to animate a single person require hours of videos of that person labelled with semantic information, and therefore have to be retrained for each individual. In contrast to these works, we neither rely on labels, prior information about the animated objects, nor on specific training procedures for each object instance. Furthermore, our approach can be applied to any object within the same category (e.g., faces, human bodies, robot arms etc).Several approaches were proposed that do not require priors about the object. X2Face wiles2018x2face uses a dense motion field in order to generate the output video via image warping. Similarly to us they employ a reference pose that is used to obtain a canonical representation of the object. In our formulation, we do not require an explicit reference pose, leading to significantly simpler optimization and improved image quality. Siarohin et al. siarohin2018animating introduced MonkeyNet, a selfsupervised framework for animating arbitrary objects by using sparse keypoint trajectories. In this work, we also employ sparse trajectories induced by selfsupervised keypoints. However, we model object motion in the neighbourhood of each predicted keypoint by a local affine transformation. Additionally, we explicitly model occlusions in order to indicate to the generator network the image regions that can be generated by warping the source image and the occluded areas that need to be inpainted.
3 Method
We are interested in animating an object depicted in a source image based on the motion of a similar object in a driving video . Since direct supervision is not available (pairs of videos in which objects move similarly), we follow a selfsupervised strategy inspired from MonkeyNet siarohin2018animating . For training, we employ a large collection of video sequences containing objects of the same object category. Our model is trained to reconstruct the training videos by combining a single frame and a learned latent representation of the motion in the video. Observing frame pairs, each extracted from the same video, it learns to encode motion as a combination of motionspecific keypoint displacements and local affine transformations. At test time we apply our model to pairs composed of the source image and of each frame of the driving video and perform image animation of the source object.
An overview of our approach is presented in Fig. 2. Our framework is composed of two main modules: the motion estimation module and the image generation module. The purpose of the motion estimation module is to predict a dense motion field from a frame of dimension of the driving video to the source frame . The dense motion field is later used to align the feature maps computed from with the object pose in . The motion field is modeled by a function that maps each pixel location in with its corresponding location in . is often referred to as backward optical flow. We employ backward optical flow, rather than forward optical flow, since backwarping can be implemented efficiently in a differentiable manner using bilinear sampling jaderberg2015spatial . We assume there exists an abstract reference frame . We independently estimate two transformations: from to () and from to (). Note that unlike X2Face wiles2018x2face the reference frame is an abstract concept that cancels out in our derivations later. Therefore it is never explicitly computed and cannot be visualized. This choice allows us to independently process and . This is desired since, at test time the model receives pairs of the source image and driving frames sampled from a different video, which can be very different visually. Instead of directly predicting and , the motion estimator module proceeds in two steps.
In the first step, we approximate both transformations from sets of sparse trajectories, obtained by using keypoints learned in a selfsupervised way. The locations of the keypoints in and are separately predicted by an encoderdecoder network. The keypoint representation acts as a bottleneck resulting in a compact motion representation. As shown by Siarohin et al. siarohin2018animating , such sparse motion representation is wellsuited for animation as at test time, the keypoints of the source image can be moved using the keypoints trajectories in the driving video. We model motion in the neighbourhood of each keypoint using local affine transformations. Compared to using keypoint displacements only, the local affine transformations allow us to model a larger family of transformations. We use Taylor expansion to represent by a set of keypoint locations and affine transformations. To this end, the keypoint detector network outputs keypoint locations as well as the parameters of each affine transformation.
During the second step, a dense motion network combines the local approximations to obtain the resulting dense motion field . Furthermore, in addition to the dense motion field, this network outputs an occlusion mask that indicates which image parts of can be reconstructed by warping of the source image and which parts should be inpainted, i.e.inferred from the context.
Finally, the generation module renders an image of the source object moving as provided in the driving video. Here, we use a generator network that warps the source image according to and inpaints the image parts that are occluded in the source image. In the following sections we detail each of these step and the training procedure.
3.1 Local Affine Transformations for Approximate Motion Description
The motion estimation module estimates the backward optical flow from a driving frame to the source frame . As discussed above, we propose to approximate by its first order Taylor expansion in a neighborhood of the keypoint locations. In the rest of this section, we describe the motivation behind this choice, and detail the proposed approximation of .
We assume there exist an abstract reference frame . Therefore, estimating consists in estimating and . Furthermore, given a frame , we estimate each transformation in the neighbourhood of the learned keypoints. Formally, given a transformation , we consider its first order Taylor expansions in keypoints . Here, denote the coordinates of the keypoints in the reference frame . Note that for the sake of simplicity in the following the point locations in the reference pose space are all denoted by while the point locations in the , or pose spaces are denoted by . We obtain:
(1) 
In this formulation, the motion function is represented by its values in each keypoint and its Jacobians computed in each location:
(2) 
Furthermore, in order to estimate , we assume that is locally bijective in the neighbourhood of each keypoint. We need to estimate near the keypoint in , given that is the pixel location corresponding to the keypoint location in . To do so, we first estimate the transformation near the point in the driving frame , e.g. . Then we estimate the transformation near in the reference . Finally is obtained as follows:
(3) 
After computing again the first order Taylor expansion of Eq. (3) (see Sup. Mat.), we obtain:
(4) 
with:
(5) 
In practice, and in Eq. (4) are predicted by the keypoint predictor. More precisely, we employ the standard UNet architecture that estimates heatmaps, one for each keypoint. The last layer of the decoder uses softmax activations in order to predict heatmaps that can be interpreted as keypoint detection confidence map. Each expected keypoint location is estimated using the average operation as in siarohin2018animating ; robinson2019laplace . Note if we set ( is identity matrix), we get the motion model of MonkeyNet. Therefore MonkeyNet uses a zerothorder approximation of .
For both frames and , the keypoint predictor network also outputs four additional channels for each keypoint. From these channels, we obtain the coefficients of the matrices and in Eq. (5) by computing spatial weighted average using as weights the corresponding keypoint confidence map.
Combining Local Motions. We employ a convolutional network to estimate from the set of Taylor approximations of in the keypoints and the original source frame . Importantly, since maps each pixel location in with its corresponding location in , the local patterns in , such as edges or texture, are pixeltopixel aligned with but not with . This misalignment issue makes the task harder for the network to predict from . In order to provide inputs already roughly aligned with , we warp the source frame according to local transformations estimated in Eq. (4). Thus, we obtain transformed images that are each aligned with in the neighbourhood of a keypoint. Importantly, we also consider an additional image for the background.
For each keypoint we additionally compute heatmaps indicating to the dense motion network where each transformation happens. Each is implemented as the difference of two heatmaps centered in and :
(6) 
In all our experiments, we employ following Jakab et al. jakabunsupervised .
The heatmaps and the transformed images are concatenated and processed by a UNet ronneberger2015u . is estimated using a partbased model inspired by MonkeyNet siarohin2018animating . We assume that an object is composed of rigid parts and that each part is moved according to Eq. (4). Therefore we estimate +1 masks that indicate where each local transformation holds. The final dense motion prediction is given by:
(7) 
Note that, the term is considered in order to model nonmoving parts such as background.
3.2 Occlusionaware Image Generation
As mentioned in Sec.3, the source image is not pixeltopixel aligned with the image to be generated . In order to handle this misalignment, we use a feature warping strategy similar to siarohin2018deformable ; siarohin2018animating ; grigorev2019coordinate . More precisely, after two downsampling convolutional blocks, we obtain a feature map of dimension . We then warp according to . In the presence of occlusions in , optical flow may not be sufficient to generate . Indeed, the occluded parts in cannot be recovered by imagewarping and thus should be inpainted. Consequently, we introduce an occlusion map to mask out the feature map regions that should be inpainted. Thus, the occlusion mask diminishes the impact of the features corresponding to the occluded parts. The transformed feature map is written as:
(8) 
where denotes the backwarping operation and denotes the Hadamard product. We estimate the occlusion mask from our sparse keypoint representation, by adding a channel to the final layer of the dense motion network. Finally, the transformed feature map is fed to subsequent network layers of the generation module (see Sup. Mat.) to render the sought image.
3.3 Training Losses
We train our system in an endtoend fashion combining several losses. First, we use the reconstruction loss based on the perceptual loss of Johnson et al. johnson2016perceptual using the pretrained VGG19 network as our main driving loss. The loss is based on implementation of Wang et al. wang2018video . With the input driving frame and the corresponding reconstructed frame , the reconstruction loss is written as:
(9) 
where is the
channel feature extracted from a specific VGG19 layer and
is the number of feature channels in this layer. Additionally we propose to use this loss on a number of resolutions, forming a pyramid obtained by downsampling and , similarly to MSSSIM wang2003multiscale ; tang2018dual . The resolutions are , , and . There are 20 loss terms in total.Imposing Equivariance Constraint. Our keypoint predictor does not require any keypoint annotations during training. This may lead to unstable performance. Equivariance constraint is one of the most important factors driving the discovery of unsupervised keypoints jakabunsupervised ; Zhang_2018_CVPR . It forces the model to predict consistent keypoints with respect to known geometric transformations. We use thin plate splines deformations as they were previously used in unsupervised keypoint detection jakabunsupervised ; Zhang_2018_CVPR and are similar to natural image deformations. Since our motion estimator does not only predict the keypoints, but also the Jacobians, we extend the wellknown equivariance loss to additionally include constraints on the Jacobians.
We assume that an image undergoes a known spatial deformation . In this case can be an affine transformation or a thin plane spline deformation. After this deformation we obtain a new image . Now by applying our extended motion estimator to both images, we obtain a set of local approximations for and . The standard equivariance constraint writes as:
(10) 
After computing the first order Taylor expansions of both sides, we obtain the following constraints (see derivation details in Sup. Mat.):
(11) 
(12) 
Note that the constraint Eq. (11) is strictly the same as the standard equivariance constraint for the keypoints jakabunsupervised ; Zhang_2018_CVPR . During training, we constrain every keypoint location using a simple loss between the two sides of Eq. (11). However, implementing the second constraint from Eq. (12) with would force the magnitude of the Jacobians to zero and would lead to numerical problems. To this end, we reformulate this constraint in the following way:
(13) 
where is identity matrix. Then, loss is employed similarly to the keypoint location constraint. Finally, in our preliminary experiments, we observed that our model shows low sensitivity to the relative weights of the reconstruction and the two equivariance losses. Therefore, we use equal loss weights in all our experiments.
3.4 Testing Stage: Relative Motion Transfer
At this stage our goal is to animate an object in a source frame using the driving video . Each frame is independently processed to obtain . Rather than transferring the motion encoded in to , we transfer the relative motion between and to . In other words, we apply a transformation to the neighbourhood of each keypoint :
(14) 
with
(15) 
Detailed mathematical derivations are provided in Sup. Mat.. Intuitively, we transform the neighbourhood of each keypoint in according to its local deformation in the driving video. Indeed, transferring relative motion over absolute coordinates allows to transfer only relevant motion patterns, while preserving global object geometry. Conversely, when transferring absolute coordinates, as in X2Face wiles2018x2face , the generated frame inherits the object proportions of the driving video. It’s important to note that one limitation of transferring relative motion is that we need to assume that the objects in and have similar poses (see siarohin2018animating ). Without initial rough alignment, Eq. (14) may lead to absolute keypoint locations physically impossible for the object of interest.
4 Experiments
Datasets. We train and test our method on four different datasets containing various objects. Our model is capable of rendering videos of much higher resolution compared to siarohin2018animating in all our experiments.

[noitemsep,topsep=0pt,wide=0pt]

The VoxCeleb dataset Nagrani17 is a face dataset of 22496 videos, extracted from YouTube videos. For preprocessing, we extract an initial bounding box in the first video frame. We track this face until it is too far away from the initial position. Then, we crop the video frames using the smallest crop containing all the bounding boxes. The process is repeated until the end of the sequence. We filter out sequences that have resolution lower than and the remaining videos are resized to preserving the aspect ratio. It’s important to note that compared to X2Face wiles2018x2face , we obtain more natural videos where faces move freely within the bounding box. Overall, we obtain 12331 training videos and 444 test videos, with lengths varying from 64 to 1024 frames.

The UvANemo dataset dibekliouglu2012you is a facial analysis dataset that consists of 1240 videos. We apply the exact same preprocessing as for VoxCeleb. Each video starts with a neutral expression. Similar to Wang et al. wang2018every , we use 1116 videos for training and 124 for evaluation.

The BAIR robot pushing dataset ebert2017self contains videos collected by a Sawyer robotic arm pushing diverse objects over a table. It consists of 42880 training and 128 test videos. Each video is 30 frame long and has a resolution.

Following Tulyakov et al. tulyakov2017mocogan , we collected 280 taichi videos from YouTube. We use 252 videos for training and 28 for testing. Each video is split in short clips as described in preprocessing of VoxCeleb dataset. We retain only high quality videos and resized all the clips to pixels (instead of pixels in tulyakov2017mocogan ). Finally, we obtain 3049 and 285 video chunks for training and testing respectively with video length varying from 128 to 1024 frames. This dataset is referred to as the TaiChiHD dataset. The dataset will be made publicly available.
Evaluation Protocol. Evaluating the quality of image animation is not obvious, since ground truth animations are not available. We follow the evaluation protocol of MonkeyNet siarohin2018animating . First, we quantitatively evaluate each method on the "proxy" task of video reconstruction. This task consists of reconstructing the input video from a representation in which appearance and motion are decoupled. In our case, we reconstruct the input video by combining the sparse motion representation in (2) of each frame and the first video frame. Second, we evaluate our model on image animation according to a userstudy. In all experiments we use =10 as in siarohin2018animating . Other implementation details are given in Sup. Mat.
Metrics. To evaluate video reconstruction, we adopt the metrics proposed in MonkeyNet siarohin2018animating :

[noitemsep,topsep=0pt,wide=0pt]

. We report the average distance between the generated and the groundtruth videos.

Average Keypoint Distance (AKD). For the TaiChiHD, VoxCeleb and Nemo datasets, we use 3rdparty pretrained keypoint detectors in order to evaluate whether the motion of the input video is preserved. For the VoxCeleb and Nemo datasets we use the facial landmark detector of Bulat et al. Bulat_2017_ICCV . For the TaiChiHD dataset, we employ the humanpose estimator of Cao et al. cao2017realtime . These keypoints are independently computed for each frame. AKD is obtained by computing the average distance between the detected keypoints of the ground truth and of the generated video.

Missing Keypoint Rate (MKR). In the case of TaiChiHD, the humanpose estimator returns an additional binary label for each keypoint indicating whether or not the keypoints were successfully detected. Therefore, we also report the MKR defined as the percentage of keypoints that are detected in the ground truth frame but not in the generated one. This metric assesses the appearance quality of each generated frame.

Average Euclidean Distance (AED). Considering an externally trained image representation, we report the average euclidean distance between the ground truth and generated frame representation, similarly to Esser et al. esser2018variational . We employ the feature embedding used in MonkeyNet siarohin2018animating .
Ablation Study. We compare the following variants of our model. Baseline: the simplest model trained without using the occlusion mask (=1 in Eq. (8)), jacobians ( in Eq. (4)) and is supervised with at the highest resolution only; Pyr.: the pyramid loss is added to Baseline; Pyr.+: with respect to Pyr., we replace the generator network with the occlusionaware network; Jac. w/o Eq. (12) our model with local affine transformations but without equivariance constraints on jacobians Eq. (12); Full: the full model including local affine transformations described in Sec. 3.1.
In Fig. 3, we report the qualitative ablation. First, the pyramid loss leads to better results according to all the metrics except AKD. Second, adding to the model consistently improves all the metrics with respect to Pyr.. This illustrates the benefit of explicitly modeling occlusions. We found that without equivariance constraint over the jacobians, becomes unstable which leads to poor motion estimations. Finally, our Full model further improves all the metrics. In particular, we note that, with respect to the Baseline model, the MKR of the full model is smaller by the factor of 2.75. It shows that our rich motion representation helps generate more realistic images. These results are confirmed by our qualitative evaluation in Tab. 1 where we compare the Baseline and the Full models. In these experiments, each frame of the input video is reconstructed from its first frame (first column) and the estimated keypoint trajectories. We note that the Baseline model does not locate any keypoints in the arms area. Consequently, when the pose difference with the initial pose increases, the model cannot reconstruct the video (columns 3,4 and 5). In contrast, the Full model learns to detect a keypoint on each arm, and therefore, to more accurately reconstruct the input video even in the case of complex motion.
Comparison with State of the Art. We now compare our method with state of the art for the video reconstruction task as in siarohin2018animating . To the best of our knowledge, X2Face wiles2018x2face and MonkeyNet siarohin2018animating are the only previous approaches for modelfree image animation. Quantitative results are reported in Tab. 3. We observe that our approach consistently improves every single metric for each of the four different datasets. Even on the two face datasets, VoxCeleb and Nemo datasets, our approach clearly outperforms X2Face that was originally proposed for face generation. The better performance of our approach compared to X2Face is especially impressive X2Face exploits a larger motion embedding (128 floats) than our approach (60=K*(2+4) floats). Compared to MonkeyNet that uses a motion representation with a similar dimension (50=K*(2+3)), the advantages of our approach are clearly visible on the TaiChiHD dataset that contains highly nonrigid objects (i.e.human body).
TaiChiHD  VoxCeleb  Nemo  Bair  

(AKD, MKR)  AED  AKD  AED  AKD  AED  
X2Face wiles2018x2face  0.080  (17.654, 0.109)  0.272  0.078  7.687  0.405  0.031  3.539  0.221  0.065 
MonkeyNet siarohin2018animating  0.077  (10.798, 0.059)  0.228  0.049  1.878  0.199  0.018  1.285  0.077  0.034 
Ours  0.063  (6.862, 0.036)  0.179  0.043  1.294  0.140  0.016  1.119  0.048  0.027 
We now report a qualitative comparison for image animation. Generated sequences are reported in Fig. 4. The results are well in line with the quantitative evaluation in Tab. 3. Indeed, in both examples, X2Face and MonkeyNet are not able to correctly transfer the body notion in the driving video, instead warping the human body in the source image as a blob. Conversely, our approach is able to generate significantly better looking videos in which each body part is independently animated. This qualitative evaluation illustrates the potential of our rich motion description. We complete our evaluation with a user study. We ask users to select the most realistic image animation. Each question consists of the source image, the driving video, and the corresponding results of our method and a competitive method. We require each question to be answered by 10 AMT worker. This evaluation is repeated on 50 different input pairs. Results are reported in Tab. 4. We observe that our method is clearly preferred over the competitor methods. Interestingly, the largest difference with the state of the art is obtained on TaiChiHD: the most challenging dataset in our evaluation due to its rich motions.







X2Face wiles2018x2face 






MonkeyNet siarohin2018animating 






Ours 






























5 Conclusions
We presented a novel approach for image animation based on keypoints and local affine transformations. Our novel mathematical formulation describes the motion field between two frames and is efficiently computed by deriving a first order Taylor expansion approximation. In this way, motion is described as a set of keypoints displacements and local affine transformations. A generator network combines the appearance of the source image and the motion representation of the driving video. In addition, we proposed to explicitly model occlusions in order to indicate to the generator network which image parts should be inpainted. We evaluated the proposed method both quantitatively and qualitatively and showed that our approach clearly outperforms state of the art on all the benchmarks.
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A Detailed Derivations
a.1 Approximating Motion with Local Affine Transformations
Here, we detail the derivation leading to the approximation of near the keypoint in Eq. (4). Using first order Taylor expansion we can obtain:
(16) 
can be written as the composition of two transformations:
(17) 
In order to compute the zeroth order term, we estimate the transformation near the point in the driving frame , e.g . Then we can estimate the transformation near in the reference . Since and , we can write . Consequently, we obtain:
(18) 
Concerning the first order term, we apply the function composition rule in Eq. (17) and obtain:
(19) 
Since the matrix inverse of the Jacobian is equal to the Jacobian of the inverse function, and since , Eq. (19) can be rewritten:
(20) 
a.2 Equivariance Loss
At training time, we use equivariance constraints that enforces:
(22) 
After applying first order Taylor expansion on the lefthand side, we obtain:
(23) 
After applying first order Taylor expansion on the righthand side in Eq. (22), we obtain:
(24) 
We can further simplify this expression using derivative of function composition:
(25) 
Eq. (22) holds only when every coefficient in Taylor expansion of the right and left sides are equal. Thus, it leads us to the following constaints:
(26) 
and
(27) 
a.3 Transferring Relative Motion
In order to transfer only relative motion patterns, we propose to estimate near the keypoint by shifting the motion in the driving video to the location of keypoint in the source. To this aim, we introduce that is the 2D vector from the landmark position in to its position in . We proceed as follows. First, we shift point coordinates according to in order to obtain coordinates in . Second, we apply the transformation . Finally, we translate the points back in the original coordinate space using . Formally, it can be written:
Now, we can compute the value and Jacobian in the :
and:
Now using Eq. (21) and treating as source and as driving frame, we obtain:
(28) 
with
(29) 
Note that, here, canceled out.
B Implementation details
b.1 Architecture details
In order to reduce memory and computational requirements of our model, the keypoint detector and dense motion predictor both work on resolution of (instead of ). For the two networks of the motion module, we employ an architecture based on UNet ronneberger2015u with five    blocks in the encoders and five    blocks in the decoders. In the generator network, we use the Johnson architecture johnson2016perceptual with two downsampling blocks, six residualblocks and two upsampling blocks. We train our network using Adam kingma2014adam optimizer with learning rate and batch size 20. We employ learning decay by dropping the learning rate at and iterations, where T is total number of iteration. We chose for TaiChiHD and VoxCeleb, and for Nemo and Bair. The model converges in approximately 2 days using 2 TitanX gpus for TaiChiHD and VoxCeleb.
b.2 Equivariance loss implementation
As explained above our equivariance losses force the keypoint detector to be equivariant to some transformations . In our experiments
is implemented using randomly sampled thin plate splines. We sample spline parameters from normal distributions with zero mean and variance equal to 0.005 for deformation component and 0.05 for the affine component. For deformation component we use uniform
grid.C Additional experiments
c.1 Image Animation
In this section, we report additional qualitative results.
We compare our approach with X2face wiles2018x2face and MonkeyNet siarohin2018animating . In Fig. 5, we show three animation examples from the VoxCeleb dataset. First, X2face is not capable of generating realistic video sequences as we can see, for instance in the last frame of the last sequence. Then, MonkeyNet generates realistic frames but fails to generate specific facial expressions as in the third frame of the first sequence or in transferring the eye movements as in the last two frames of the second sequence.
In Fig. 6, we show three animation examples from the Nemo dataset. First, we observe that this dataset is simpler than VoxCeleb since the persons are facing a uniformly black background. With this simpler dataset, X2Face generates realistic videos. However, it is not capable of inpainting image parts that are not visible in the source image. For instance, X2Face does not generate the teeth. Our approach also perform better than MonkeyNet as we can see by comparing the generate teeth in the first sequence or the closed eyes in the fourth frames of the second and third sequences.
In Fig. 6, we report additional examples for the TaiChiHD dataset. These examples are well in line with what is reported in the main paper. Both X2Face and MonkeyNet completely fail to generate realistic videos. The source images are warped without respecting human body structure. Conversely, our approach is able to deform the person in foreground without affecting the background. Even though we can see few minor artifacts, our model is able to move each body part independently following the body motion in the driving video.
Finally, in Fig. 8 we show three image animation examples on the Bair dataset. Again, we see that X2Face is not able to transfer motion since it constantly returns frames almost identical with the source images. Compared to MonkeyNet, our approach performs slightly better since it preserves better the robot arm as we can see in the second frame of the first sequence or in the fourth frame of the last sequence.
c.2 Keypoint detection
We now illustrate the keypoints that are learned by our selfsupervised approach in Fig. 9. On the TaiChiHD dataset, the keypoints are semantically consistent since each of them corresponds to a body part: light green for the right foot, and blue and red for the face for instance. Note that, a light green keypoint is constantly located in the bottom left corner in order to model background or camera motion. On VoxCeleb, we observe that, overall, the obtained keypoints are semantically consistent except for the yellow and green keypoints. For instance, the red and purple keypoints constantly correspond to the nose and the chin respectively. We observe a similar consistency for the Nemo dataset. For the Bair dataset, we note that two keypoints (dark blue and light green) correspond to the robotic arm.
c.3 Visualizing occlusion masks
In Fig. 10, we visualize the predicted occlusion masks on the TaiChiHD, VoxCeleb and Nemo datasets. In the first sequence, when the person in the driving video is moving backward (second to fourth frames), the occlusion mask becomes black (corresponding to 0) in the background regions that are occluded in the source frame. It indicates that these parts cannot be generated by warping the source image features and must be inpainted. A similar observation can be made on the example sequence of VoxCeleb. Indeed, we see that when the face is rotating, the mask has low values (dark grey) in the neck region and in the right face side (in the lefthand side of the image) that are not visible in the source Frame. Then, since the driving video example from Nemo contains only little motion, the predicted mask is almost completely white. Overall, these three examples show that the occlusion masks truly indicate occluded regions even if no specific training loss is employed in order to lead to this behaviour. Finally, the predicted occlusion masks are more difficult to interpret in the case of the Bair dataset. Indeed, the robotic arm is masked out in every frame whereas we could expect that the model generates it by warping. A possible explanation is that, since in this particular dataset, the moving object is always the same, the network can generate without warping the source image. We observe also that masks have low values for the regions corresponding to the arm shadow. It is explained by the fact that shadows cannot be obtained by image warping and that they need to be added by the generator.
X2face wiles2018x2face  

MonkeyNet siarohin2018animating  
Ours 
X2face wiles2018x2face  

MonkeyNet siarohin2018animating  
Ours 
X2face wiles2018x2face  

MonkeyNet siarohin2018animating  
Ours 
X2face wiles2018x2face  

MonkeyNet siarohin2018animating  
Ours 
X2face wiles2018x2face  

MonkeyNet siarohin2018animating  
Ours 
X2face wiles2018x2face  

MonkeyNet siarohin2018animating  
Ours 
X2face wiles2018x2face  

MonkeyNet siarohin2018animating  
Ours 
X2face wiles2018x2face  

MonkeyNet siarohin2018animating  
Ours 
X2face wiles2018x2face  

MonkeyNet siarohin2018animating  
Ours 
X2face wiles2018x2face  

MonkeyNet siarohin2018animating  
Ours 
X2face wiles2018x2face  

MonkeyNet siarohin2018animating  
Ours 
X2face wiles2018x2face  

MonkeyNet siarohin2018animating  
Ours 
TaiChiHD  

VoxCeleb  
Nemo  
Bair  
Occlusion  

Output 
Occlusion  

Output 
Occlusion  

Output 
Occlusion  

Output 