# Image Translation to Mixed-Domain

using Sym-Parameterized Generative Network

###### Abstract

Recent advances in image-to-image translation have led to some ways to generate multiple domain images through a single network. However, there is still a limit in creating an image of a target domain without a dataset on it. We propose a method to expand the concept of ‘multi-domain’ from data to the loss area, and to combine the characteristics of each domain to create an image. First, we introduce a sym-parameter and its learning method that can mix various losses and can synchronize them with input conditions. Then, we propose Sym-parameterized Generative Network (SGN) using it. Through experiments, we confirmed that SGN could mix the characteristics of various data and loss, and it is possible to translate images to any mixed-domain without ground truths, such as 30% Van Gogh and 20% Monet.

figureResults of image translation to mixed-domains. These images are obtained by learning the SGN for three losses (reconstruction, adversarial, perceptual) and then by inferring the input of a test image in a single generator with only changing the sym-parameter. The numbers in the parentheses are sym-parameters for each A, B, and C domain.

## 1 Introduction

Recently, literature on multi-domain deep image translation has introduced many methods that learn the joint distribution of two or more domains and find transformations among them. Particularly, a single generator is able to translate images to multiple domains based on training data distributions [3, 20, 26]. However, translating style features across domains seen by the model is different from ‘creativeness’. Consider a case of generating a translated image with a style that is 20% of Van Gogh, 50% of Picasso and 30% of the original image. Since the ground truths for learning such a translation do not exist, the target distribution to approximate can not explicitly be provided for conventional deep generative networks.

If we construe that the optimum of the target style is a weighted sum of optima of the candidate styles, then the objective function can be defined by a weighted sum of objective functions of those. In this end, if the weights are set as hyper-parameters, they can be preselected and learned to generate images outside of a domain even without ground truths [5]. Even in such a case, not only a criterion on selections of the parameters is vague, but every training for cross-domain translations must also be impractically done with a unique set of weights. Therefore, it would be more efficient to dynamically control them during inferences for desired translations. We, in this paper, present a concept of sym-parameters that enable human users to control them so that influences of candidate domains on final translations can be heuristically adjusted during inferences.

Along with inputs, sym-parameters are inputted as a condition into our proposed generator network, Sym-parameterized Generative Network (SGN). And also, these sym-parameters are synchronously set as weights for the linear combination of multiple loss functions. With the proposed setting, we have verified that a single network is able to generate corresponding images of a mixed-domain based on an arbitrarily weighted combination of loss functions without direct ground truths. While an SGN utilizes multiple loss functions that conventional image-to-image translation models use (e.g. reconstruction loss, GAN (adversarial) loss, perceptual loss), the sym-parameter conditions the weights of these losses for variously purposed translations. If an SGN, as an exemplar case depicted in Figure Image Translation to Mixed-Domain using Sym-Parameterized Generative Network, uses GAN loss for training Van Gogh style and perceptual loss for Udnie of Francis Picabia, sym-parameters allow adjusting the ratio of the styles to create correspondingly styled images. Through experiments, we found that sym-parameters conditioned within a model in the ways performed in typical conditional methods [3, 15, 30], fail to yield our intended generations. To overcome this, we additionally propose Conditional Channel Attention Module (CCAM) that allows our method to have a fully convolutional structure for handling variously sized images and gating channels conditionally with sym-parameters for similar effects as SENet [8]. The channel attention module also enables our generator network structurally irrelevant to the size of an image.

To summarize, our contributions are as follows:

(1) We propose the concept of sym-parameter and its learning method that can control the weight between losses during inferences.

(2) We introduce SGN, a novel generative network that expands the concept of ‘multi-domain’ from data to the loss area using sym-parameters.

(3) Experimental results show that SGN could translate images to mixed-domain without ground truths.

## 2 Related work

Generative Adversarial Networks Recently, Generative Adversarial Networks (GANs) [6] have been actively adapted to many image generation tasks [1, 11, 16, 21]. GANs are typically composed of two networks: a generator and a discriminator. The discriminator is trained to distinguish the generated samples (fake samples) from the ground-truth images (real samples), while the generator learns to generate samples so that the discriminator misjudges. This training method is called adversarial training which our method uses for both the generator and the discriminator to learn the distribution of a real dataset.

Conditional Image Synthesis By conditioning concurrently with inputs, image generation methods learn conditional distribution of a domain. CVAE [24] uses conditions to assign intentions to VAEs [13]. Conditional image generation methods that are based on GANs also have been developed [2, 4, 18, 19, 20, 28], using class labels or other characteristics. Conditional GANs are also used in domain transfers [12, 25] and super-resolution [16]. While the methods from [3, 20] use discrete conditioning (either 0 or 1), our method uses continuous values for input conditioning.

Image to Image Translation While there exist generative models that generate images based on sampling (i.e. GANs, VAEs), models that generate images for given base input images are also studied. They mostly use autoencoders [14] and among them, one of the most representative and recent works is [9], which uses adversarial training with conditions. CycleGAN [29] and DiscoGAN [12] translate either style or domain of input images. Johnson et al. [10] have proposed perceptual loss in order to train feed-forward network for image style transformation. Since most of them use convolutional autoencoders with ResBlocks [7] or U-Net [22] structure, we also utilize the structure of CycleGAN [29], but additionally apply sym-parameters to image-to-image translation tasks in the form of continuous valued conditions. We also adopt the perceptual loss harmonized with the GAN loss and the reconstruction loss terms.

One generator to multiple domains Many have extended the study of image-to-image translations to multiple domains with a single generator network. IcGAN [20], StarGAN [3] and SingleGAN [26] address the problem of previously reported generative models that they are stuck with two domains, and achieve meaningful results on their extended works by using hard labels of each domain. Methods regarding image generation problems also have been proposed. ACGAN [19] uses auxiliary classifier to generate images by providing class information as a condition in the input. In different perspective, CAN [5] tries generating artworks by blending multiple domains. The method trains the generator of GAN to confuse the auxiliary classifier to judge fake samples in forms of uniform-distribution. In this study, we make a good use of conditions synchronized with loss functions not only to transfer to multiple domains, but also to mix each styles simultaneously by using expandable loss terms.

## 3 Proposed Method

Our goal is to learn distributions from multiple domains by varying weighted loss functions in order to dynamically translate images into a mixed-domain. In order to control mixing ratio during inferences, the corresponding conditions must be inputted and trained with the model. For such purpose, we present sym-parameters which are symmetrically set inside (as condition inputs) as well as outside (as weights of multiple loss functions) of a generator. The sym-paraemters allow transitive learning without explicit ground truth images among diverse mixtures of multiple domains and loss functions. The generator of sym-parameterized generative networks (SGN) can thus be controlled during inferences unlike conventional generators that infer strictly as optimized for a specific dataset or a particular loss function.

### 3.1 Sym-parameter

By trying to find not only the optimum of each candidate objective function but also the optima for various combinations of them, we desire to control the mixing weights during inferences. We propose human controllable parameters, sym-parameters, that can replace typical hyper-parameters for weighing multiple loss functions. As the prefix “sym-” is defined in dictionaries as “with; along with; together; at the same time”, sym-parameters are fed into a generative model, symmetrically set as weights of the candidate loss functions and synchronized after training. If number of different loss functions, , are engaged, then the sym-parameter is defined as a -dimensional vector . The total loss of a model that takes inputs and sym-parameters is:

(1) |

Having the total sum of sym-parameters to be 1, the total loss defined by the function and sym-parameters is a weighted sum of sub-loss functions, each of which is weighed by the corresponding element of .

Figure 1 depicts the concept showing the difference between a sym-parametrized model and conventional models using multiple loss functions weighted by hyper-parameters. While a new model is required for learning each combination of weights if conventional methods are used, our method allows a single model to manage various combination of weights through one learning. We, in the experiment section, verify that not only each sub-objective function is optimized but various linear sums of them also are. For example, if a neural model wants to perform both the regression and the classification tasks, the optimization is processed towards minimizing the regression loss when , the classification loss when and the weighted sum of the losses when .

Training with Dirichlet Distribution As mentioned above, a sym-parameter is represented as a vector which has the same number of dimensions as the number of loss functions. The vector’s values are randomly selected during training in order to synchronize accordingly with sym-parameterized combinations of loss functions. To do so, the sym-parameter values are sampled based on Dirichlet distribution. The probability distribution of a -dimensional vector with the sum of positively valued elements being 1, can be written as:

(2) |

Here, is a normalization constant and represents Gamma function. When , the distribution boils down to Beta distribution. Using Dirichlet distribution allows the sum of sym-parameter values to be 1 and enables adjusting the distribution with the concentration vector .

### 3.2 Sym-parameterized Generative Networks

Using sym-parameters that allow inferences of various mixtures of losses, we propose sym-parametrized generative networks (SGN) that translate images to mixed-domain. Our method is able to either generate images from latent inputs or translate styles with image inputs as long as sym-parameters are inputted along with the inputs and define a linear combination of loss functions. Figure 2 illustrates the structure of SGN for image-to-image translation purpose. Selection of loss functions are not necessarily limited for image generation tasks, and the following is a representative loss for a generator with reconstruction loss , adversarial loss and perceptual loss weighted by sym-parameters :

(3) |

Here, each loss function may cope with different objective and dataset for more diverse image generations such as using two of adversarial losses one of which for Van Gogh and another for Monet style domain.

While either reconstruction loss or perceptual loss does not require to train an additional network, a discriminator must be trained along with an SGN model for the adversarial loss, and a distinct training criterion of the discriminator is needed for SGN. Because our method generates images based on linearly combined losses with sym-parametrized weights, the weight on the loss of a discriminator must be also set accordingly. Therefore, discriminator must be trained with the weight assigned on the generator loss in an adversarial manner:

(4) |

A trained SGN can translate images with specific sym-parameters, or generate random images from random variables sampled from Dirichlet distribution defined by an input image.

#### 3.2.1 Conditional Channel Attention Module

SGN takes a continuous valued sym-parameter vector along with inputs and generates images reflecting characteristics of various parts of a mixed-domain, which covers wider range of target distribution than multi-domain models do with discrete conditions. Since domain injection used in conventional conditional generators is empirically shown to be inadequate for our purpose, we propose another injection method for sym-parameterized conditionings, named Conditional Channel Attetion Module (CCAM). Inspired by SENet [8], CCAM is a channel attention model that selectively gates feature channels based on sigmoid attentiveness. CCAM also allows SGN to have a fully convolutional structure and manage various spatial sizes. CCAM’s structural details are depicted in Figure 3, and the module can be written as:

(5) |

where represents feature maps outputted from a preceding layer and denotes the concatenation operation. The features are shrunk to through an average pooling, and the sym-parameters are represented in the same size as the pooled features through . After creates attention maps based on the concatenation of input features and sym-parameters, a sigmoid function activates to produce the channel attention map, . The output features of CCAM is then created by channel-wise multiplication of the channel attention map and the original feature map . For such a continuous conditioning case, CCAM allows superior efficiency of image generations over channel-wise inclusion of domain information along with RGB channels [3] or domain code injection through central biasing normalization [26].

## 4 Implementation of SGN

Network Architecture The base architecture of SGN has adopted the autoencoder layers from [3, 10, 29], which consists of two downsampling convolution layers, two upsampling transposed convolution layers with strides of two and nine residual blocks in between them. In this architecture, CCAM modules are inserted for conditioning at three positions, before the downsampling convolutions, after the downsampling convolutions and lastly, before the upsampling convolutions. For , we use PatchGAN discriminator, introduced by Isole et al. [9] where discriminator is applied at each image patch separately. The choice of feed-forward CNN for is VGG16 with consensus on the work of Johnson et al. [10]. More details of the architecture will be handled on supplementary materials.

Training Details For three loss terms, , and , we use norm for the reconstruction loss , and have applied a technique of LSGAN [17] for the adversarial loss in which an MSE (mean squared error) loss is used. Additionally, the identity loss introduced by Taigman et al. [25] and used in CycleGAN [29] is used in for regularizing the generator, combined with the LSGAN loss. The implementation of the perceptual loss follow the implementation of Johnson et al. [10], adopting both feature reconstruction loss and style reconstruction loss. At the training phase, all three loss terms were weighted by numbers sampled from Dirichlet distribution with all the valued 0.5

## 5 Experiments

In this section, we first investigate the behavior of sym-parameters based on different loss functions through a 1-D toy problem. We then experiment an SGN on image translations to mixed-domains. Since there are no direct baselines for image translation to an arbitrary mixed-domain, we perform qualitative and quantitative experiments on how well SGN translates images to mixed-domains. And lastly, CCAM’s role within the SGN is reviewed.

Weights | Sym-parameter model | Hyper-parameter models | ||||
---|---|---|---|---|---|---|

(, ) | ||||||

(1.00, 0.00) | 0.0001 | 0.0001 | 0.2148 | 0.0000 | 0.0000 | 0.2167 |

(0.75, 0.25) | 0.0483 | 0.0063 | 0.1743 | 0.0481 | 0.0062 | 0.1737 |

(0.50, 0.50) | 0.0824 | 0.0347 | 0.1302 | 0.0815 | 0.0353 | 0.1277 |

(0.25, 0.75) | 0.0878 | 0.1674 | 0.0613 | 0.0846 | 0.1597 | 0.0592 |

(0.00, 1.00) | 0.0062 | 0.4113 | 0.0062 | 0.0013 | 0.4254 | 0.0013 |

### 5.1 Toy Example: Regression and Classification with Single Network

In order to understand sym-parameters, a single network is designed to perform both regression and classification for an 1-D toy problem. We have defined a polynomial function that takes one dimensional vector and outputs . Also, with and a linear function , is represented as a binary class label of 1 if or 0 otherwise. We have created a dataset consisting of () tuples. A sym-parametrized network concisely structured with three hidden layers of MLP is trained with the dataset to perform regression and classification in terms of and respectively. The total loss is defined as with a sym-parameter . The results are illustrated in Figure 4 and more experimental details are reported in the supplementary materials.

Three sub-figures on the right side in Figure 4 demonstrate ’s outputs (white lines) and computed loss values (color-maps) when sym-parameters are and , respectively. The figures clearly show a sym-parametrized model properly minimizes losses according to sym-parameter values. Also, the same sym-parametrized model is compared against an equivalently structured model that is separately trained with various hyper-parameter weights. As can be seen in Table 1, the loss values of the models separately trained with hyper-parameterized weights do not differ much from the values of the model trained with sym-parametrized weights. This implies that a single training of a model using sym-parameters may replace the models trained in multiple cases of hyper-parameters.

A | B | C | |
---|---|---|---|

Model 1 | , Photo | , Van Gogh | , Udnie |

Model 2 | , Photo | , Ukiyo-e | , Rain |

Model 3 | , Summer | , Winter | , Monet |

### 5.2 Image Translation to Mixed-Domain

We have set up three SGN models for experiments on image translations to mixed-domain.
With the use of sym-parameters, SGN extends the concept of multi-domain to loss functions,
and each domain is thus defined with combinations of loss functions and data.
For our experiments, the datasets used in [10, 29] are combined with loss criteria of , and from Section 4 to train each model as presented in Table 2.

Qualitative Result
Figure Image Translation to Mixed-Domain using Sym-Parameterized Generative Network illustrates translation results of Model 1 with various sym-parameters.
Not only inter-translations among A, B and C domains are well generated,
but the model also produces mixed generations with weighted characteristics of candidate domains.
Especially, the successful image translations between domain B with adversarial loss and domain C with perceptual loss should be noticed; the generated images are influenced more by colors and styles of Van Gogh than by the test image input.
As the numbers in the parentheses represent sym-parameter values, correspondingly styled images are well produced when mixed with 3 types of domains.
Lastly, generated image with is an extrapolated result with a sym-parameter that is set outside of the trained range, and Van Gogh’s style is still bolstered accordingly.

Figure 5 shows image translations yielded by two other models. While an SGN can be trained with different loss functions and datasets as done for Model 1 and 2, it can also be trained with domains defined with two GAN losses for different datasets. As it can be seen in the figure, Model 3 is able to translate a summer Yosemite image not only to a winter Yosemite image but also to a winter image with Monet style with . This result well depicts how weighted optima of multiple objective functions can be expressed. More test results of each model are provided in the supplementary material.

(1.0, 0.0, 0.0) | 0.164 | 0.164 | 0.829 | 0.209 |
---|---|---|---|---|

(0.5, 0.5, 0.0) | 0.305 | 0.285 | 0.323 | 0.253 |

(0.0, 1.0, 0.0) | 0.211 | 0.756 | 0.211 | 0.311 |

(0.0, 0.5, 0.5) | 0.171 | 0.718 | 0.256 | 0.085 |

(0.0, 0.0, 1.0) | 0.040 | 0.443 | 0.525 | 0.040 |

(0.5, 0.0, 0.5) | 0.139 | 0.201 | 0.889 | 0.077 |

Quantitative Result It is generally known to be difficult to define quantitatively evaluating metrics for generative models. Nonetheless, it is logical to quantitatively examine by checking loss values for different values since our aim is to find optimal of variously weighted sum of losses. If trained sufficiently in terms of (1) and (3), the corresponding domain’s loss should be minimized when a domain’s weight is 1, and when the weight is mid-valued as 0.5, resultant loss of the domain should be valued in between the values when the weight is 1 and 0.

Loss values of trained Model 1 are measured with a test dataset and enumerated in Table 3. The numbers in the table represent averaged loss values of each loss function the generator uses. In the table, each domain yields its minimum loss value when weighted with 1. Relatively large loss values appear when zero-weighted while loss values within the range between the minimum and maximum values are recorded for the weight of 0.5. When the weight of a domain is valued either 0.5 or 0, the loss value of the domain vary according to weights of other domains. As similarly resulted in Table 1 from Section 5.1, this is because each loss function differs from other losses in terms of its scope and optimization range, which precludes absolute comparisons among the values. Through the experiment, it is proven that our SGN enables the optimization of multiple loss functions with weighted losses as we intend.

Random Sampled Image Translation As mentioned in Section 3.2, SGN creates random images of mixed-domain through Dirichlet distribution of which concentration parameters define the sampling distribution. Figure 6 shows images generated by SGN Model 1 with an input image using to sample more from domain B and C than from domain A. Because images are generated by mixing 3 types of domain based on single input image, generations notably share mutual information, but multiple domains are differently mixed depending on the sampling distribution.

Continuous Translation Since the sym-parameter is represented as a -dimensional continuous vector, continuous inter-domain translations are achieved during mixed-domain image translations. Such characteristics of SGN allows seamless mixed-domain transitions among candidate domains through video. The video demo is available on YouTube (https://youtu.be/i1XsGEUpfrs) and detailed in supplementary material.

### 5.3 Conditional Channel Attention Module

We perform sym-parameter injections into SGN through CCAM since conventional condition injecting methods are empirically shown inefficient for our method. We have thus experimentally compared the performance results among different cases of condition injections, which is depicted in Figure 7. The injection method labeled CONCAT represents the method of depth-wise concatenations with a latent coded vector repeated to be in the same spatial size as features. Central biasing normalization (CBN) [27] is also experimented for comparisons. We have adjusted the instance normalization of the down-sampling layers and the residual blocks of the generator network as similarly used in [26].

CONCAT method produces outputs that are alike despite of various combinations of sym-parameters and fails to generate images in mixed-domain correspondingly. This method works promisingly for discrete condition injections as reported in [3, 15, 30] but struggles in the SGN using continuous conditions. This phenomenon is reasonable considering that the normalization within the generator perturbs the values of the sym-parameter and differences in the values are susceptible. CBN method performs better than CONCAT, generating comparably more various images with given sym-parameters. Yet, its generations are rather biased to one domain than a mixed-domain targeted by sym-parameters, and also follow with some artifacts. Since CBN uses bias and thus is hard to exclude the possibility on influence of a particular channel, additional interferences among candidate domains may occur. Among the experimented condition injecting methods, our proposed CCAM is more suitable for the sym-parameter and SGN.

Figure 8 summarizes channel activation trends of CCAM when changing sym-parameters for a given test image. As can be seen in the plots, channels are activated differently for three cases of sym-parameter. First layer of CCAM is mainly responsible for scaling with no blocked channel. Considering the number of closed channels with zero activations are increased at deeper layers, CCAM selectively excludes channels and reduces influence of unnecessary channels to generate images in a mixed-domain conditioned by sym-parameters. This is the major difference of our CCAM and the CBN which utilizes bias in controlling each domain’s influence.

## 6 Conclusion

In this paper, we propose a sym-parameter that can extend the concept of domain from data to loss and adjust the weight among multiple domains at inference. We then introduce SGN, which is a novel network that can translate image into mixed-domain as well as each domain using this sym-parameter. It is hard to say which method is proper and optimal when it comes to making a valid result for a mixed-domain without ground truth. However, if optimizing to the weighted objective of each domain is one of the effective methods for this purpose, SGN performs well to translate image to a target mixed-domain as shown in the experiments. Using our proposed method, users can create more diverse images beyond specific data or loss.

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Supplementary Material

## Appendix A Experiment Settings

### a.1 1D Toy Example

The polynomial and the linear function are defined such that the output is between 0 and 1 when the range of is -1 to 1.

(6) |

(7) |

The sym-parametrized network is an MLP network that has three hidden layers with the size of 64 and ReLU activations. It takes a tuple of as an input and outputs a single value for either classification or regression. The mean squared error function is used for regression loss , and binary cross entropy is used for the classification loss . is scaled down to 20% to balance the losses. In the training phase, the sym-parameter is sampled from Dirichlet distribution with valued (0.5, 0.5). We use ADAM with a batch size of 16, and learning rates of 0.01 during the first 200 epochs, 0.001 during the next 200 epochs and 0.0001 during the last 100 epochs.

### a.2 Sym-Parameterized Generative Network

The architecture details of an SGN generator is provided in Table 4 of this supplementary. The discriminator is equivalently set as CycleGAN [29]. To regulate the imbalance between the losses, and are respectively weighted with 2 and 1. And for , GAN loss and the identity loss are respectively weighted by 1 and 5. For the perceptual loss , we have used the pretrained Pytorch model of VGG16 [23] without batch-normalization layers. is composed of a content loss and a style loss, computed at first 4 blocks of VGG16, which means it uses output features from Conv1-2, Conv2-2, Conv3-3, Conv4-3, and do not use the fifth block, following the work of Johnson et al. [10]. The content loss is weighted with 0.001 and the style losses at 4 layers are weighted as (0.1, 1.0, 10, 5.0) for the Model 1, (0.1, 1.0, 10, 5.0) for the other models. We use the ADAM optimizer with a batch size of 4. Then Model 1 and Model 2 are trained for 20 epochs and Model 3 is trained for 60 epochs. We keep the learning rate of 0.0002 for the first half of epochs and linearly decay it to zero for the remaining epochs.

Layer Configuration | Input Dimension | Layer Information | Output Dimension |

Input convolution | (, , 3) | Convolution (K:7x7, S:1, P:3), IN, ReLU | (, , 64) |

CCAM (Reduction Rate : 4) | |||

Down-sampling | (, , 64) | Convolution (K:3x3, S:2, P:1), IN, ReLU | (, , 128) |

(, , 128) | Convolution (K:3x3, S:2, P:1), IN, ReLU | (, , 256) | |

CCAM (Reduction rate : 4) | |||

Residual Blocks | (, , 256) | Convolution (K:3x3, S:1, P:1), IN, ReLU | (, , 256) |

(, , 256) | Convolution (K:3x3, S:1, P:1), IN, ReLU | (, , 256) | |

(, , 256) | Convolution (K:3x3, S:1, P:1), IN, ReLU | (, , 256) | |

(, , 256) | Convolution (K:3x3, S:1, P:1), IN, ReLU | (, , 256) | |

(, , 256) | Convolution (K:3x3, S:1, P:1), IN, ReLU | (, , 256) | |

(, , 256) | Convolution (K:3x3, S:1, P:1), IN, ReLU | (, , 256) | |

(, , 256) | Convolution (K:3x3, S:1, P:1), IN, ReLU | (, , 256) | |

(, , 256) | Convolution (K:3x3, S:1, P:1), IN, ReLU | (, , 256) | |

(, , 256) | Convolution (K:3x3, S:1, P:1), IN, ReLU | (, , 256) | |

CCAM (Reduction Rate : 4) | |||

Up-sampling | (, , 256) | Transposed Convolution (K:3x3, S:2, P:1), IN, ReLU | (, , 128) |

(, , 128) | Transposed Convolution (K:3x3, S:2, P:1), IN, ReLU | (, , 64) | |

Output Convolution | (, , 64) | Convolution (K:7x7, S:7, P:3), Tanh | (, , 3) |

## Appendix B Additional Experimental Results

### b.1 Continuous Translation

The video (https://youtu.be/i1XsGEUpfrs) is created by extracting images from the original and translating it through SGN. ORIGINAL VIDEO and VIDEO WITH SGN represent original video and SGN translated video, respectively. We use SGN models trained in the paper and translated images changing only the sym-parameters. The color bar above VIDEO WITH SGN represents the sym-parameter values for each domain. If the entire bar is red, then the sym-parameter is (1,0,0). Since all the images are translated through SGN, reconstructed images may differ in some colors and appearance from the original ones.