=Paper=
{{Paper
|id=Vol-3084/paper4
|storemode=property
|title=Exploring the Asynchronous of the Frequency Spectra of GAN-Generated Facial Images
|pdfUrl=https://ceur-ws.org/Vol-3084/paper4.pdf
|volume=Vol-3084
|authors=Le Minh Binh,Simon S. Woo
}}
==Exploring the Asynchronous of the Frequency Spectra of GAN-Generated Facial Images==
https://ceur-ws.org/Vol-3084/paper4.pdf
Exploring the Asynchronous of the Frequency Spectra of
GAN-Generated Facial Images
Le Minh Binh1 , Simon S. Woo2
1
Department of Software, Sungkyunkwan University, South Korea
2
Department of Applied Data Science, Sungkyunkwan University, South Korea
Abstract
The rapid progression of Generative Adversarial Networks (GANs) has raised a concern of their misuses for malicious pur-
poses, especially in creating fake face images. Although many proposed methods succeed in detecting GAN-based synthetic
images, they are still limited by the need for large quantities of the training fake image dataset, and challenges for the detec-
torβs generalizability to unknown facial images. In this paper, we propose a new approach that explores the asynchronous
frequency spectra of color channels, which is simple but effective for training both unsupervised and supervised learning
models to distinguish GAN-based synthetic images. We further investigate the transferability of a training model that learns
from our suggested features in one source domain and validates on another target domains with prior knowledge of the
featuresβ distribution. Our experimental results show that the discrepancy of spectra in the frequency domain is a practical
artifact to effectively detect various types of GAN-based generated images.
Keywords
Asynchronous of frequency, GAN-based synthetic images
1. Introduction
In recent years, there has been tremendous progress in
Generative Adversarial Networks (GAN), in which two
Real images
modules (generator vs. discriminator), play a minimax
game to produce highly realistic data. Unfortunately, in
addition to several fruitful GAN applications, attackers
can exploit GANs for malicious purposes, such as spread-
ing fake news [1] or propagating fake pornography of
celebrities [2] as shown in the past. Meanwhile, several
efforts have been made by researchers [3, 4, 5] to re-
sist these nasty misuses. Wang et al. built a deep neural
network to classify GAN-based generated images and
empirically demonstrates that a classifier trained on one
single dataset can generalize to different GAN datasets[4].
Especially, Dzanic and Shah [6] empirically show the Fake images
systematic bias in high spatial frequencies and use this
characteristic to classify real and deep network generated
images. However, they did not explore the deeper sta-
tistical frequency features that we propose in our work,
and they simply focused on converting the RGB to gray
image, unlike ours.
Also, the checkerboard artifacts in spectrum generated Figure 1: The frequency spectra differences of real vs. fake
by up-sampling components of GAN model were also ex- images. Top: Real images and their corresponding concur-
tensively investigated by Zhang et al. [3] and Frank et al. rent spectra. Bottom: Fake images and their corresponding
[5]. While these techniques have shown success in terms (chaotic) spectra. It is difficult for human eyes to distinguish
of achieving high accuracy, they typically require a large between real and fake images, but after applying DFT on each
channel of images, the vital clues to distinguish real vs. fake
International Workshop on Safety & Security of Deep Learning, images can be discovered.
IJCAI 2021
" bmle@g.skku.edu (L. M. Binh); swoo@g.skku.edu (S. S. Woo)
0000-0002-4344-3421 (L. M. Binh); 0000-0002-8983-1542
(S. S. Woo) quantities of data to train and the incurred high computa-
Β© 2021 Copyright for this paper by its authors. Use permitted under Creative
Commons License Attribution 4.0 International (CC BY 4.0). tional complexity, which can be prohibitively expensive
CEUR
Workshop
Proceedings
http://ceur-ws.org
ISSN 1613-0073 CEUR Workshop Proceedings (CEUR-WS.org)
R 010
011
G 1010
B 011
Descriptive
Feature extraction features
Discrete Fourier transform
Figure 2: Illustration of our end-to-end pipeline. Unlike other research [6] that apply DFT on a grayscale image, we focus on
each channel information and utilize statistical methods to obtain discriminative features.
in many practical applications. As a consequence, there 2. Our Methods
is a strong need for detection methodologies that can
achieve comparable levels of performance with limited 2.1. Fourier Spectrum Analysis
training data, requiring low computational requirements
In this section, we construct our hypothesis on the channel-
and better generalization to unknown GAN-based gener-
wise asynchrony of GAN-based generated images. The
ated images.
convolutional operation at the ππ‘β layer of a generative
In this work, we first observe that the frequencies of
model is formulated as follows:
the channels in the real images are highly correlated as β β
πΆ(π)
shown in Fig. 1 and Fig. 3. In fact, the discriminator in the βοΈ
GAN model can make the generated synthesized images π΄π+1
π = πΆπππ£ππ (π΄π ) = π β π
πΉππ β π π(π΄ππ )β , (1)
highly realistic, close to real images. However, to the best π=1
of our knowledge, there has not been any attempt to where πΆ is the number of channels of the ππ‘β layerβs
(π)
apply direct correlation constraint between channels on
output π΄π , πΉ π β Rππ Γππ ΓπΆ(π+1) ΓπΆ(π) is a set of πΆ(π+1) Γ
the output images in the frequency domain in the GAN
πΆ(π) trainable 2π· filters that have size of ππ Γ ππ . And
models. From this observation, we hypothesize that the
π π(Β·), β and π(Β·) denote the up-sampling operator, con-
insufficiency of channel-dependent training in most of
volutional operator and activation function, respectively.
the current GAN models can produce the channel-wise
According to Khayatkhoei and Elgammal [11], we can
asynchrony in the frequency domain. The asynchronous
simplify the Eq. 1 by restricting π(Β·) to to rectified lin-
can be exposed in various GAN datasets, which can be ef-
ear units (ReLU), which makes the πΆπππ£ππ (π΄π ) become
fectively used to distinguish GAN-based synthetic images
locally piece-wise linear, and absorbing the up-sampling
by both unsupervised or supervised learning methods.
π π(Β·) into π΄ππ . In this way, we transform Eq. 1 to:
In order to demonstrate the effectiveness of our pro-
posed approach, we experiment with four types of datasets: βοΈπΆ
Fake Head Talker [7], StyleGAN [8], StarGAN [9], and π΄ π+1
π = πΆπππ£ π
π (π΄ π
) = π
πΉππ β π΄ππ . (2)
Adversarial Latent Auto Encoder (ALAE) [10]. Our main π=1
contributions in this work are summarized as follows: By applying the 2D discrete Fourier transform (DFT)
to π΄π+1π , it is now viewed in the frequency domain as
β’ We firstly introduce the asynchronous in the fre- follows:
quency domain for detecting GAN-generated fake (οΈ πΆ )οΈ
images. π+1 βοΈ π
Λ
π΄π = F(π΄π ) = F π+1
πΉππ β π΄π π
β’ We propose effective unsupervised and super- π=1
vised learning models using our discriminative πΆ (οΈ )οΈ
mining features to classify real and fake images.
βοΈ π
= F πΉππ β π΄ππ (linearity property of FT)
β’ We demonstrate the transferability of our pro- π=1
posed learning models across different GAN-based πΆ
βοΈ (οΈ )οΈ (οΈ )οΈ
π
synthetic datasets using our spectra features. = F πΉππ Γ F π΄ππ (conv. property of FT)
π=1
πΆ
Λ πππ Γ π΄
Λ ππ = β¨πΉΛππ , π΄
βοΈ
= πΉ Λπ β©, (3)
π=1
where πΉΛππ = (πΉ Λ ππ1 , ..., πΉ
Λ πππΆ )π , and π΄Λπ = (π΄ Λ π1 , ..., π΄
Λ ππΆ )π . Based on this important observation, we propose the
Equation 3 indicates that in the frequency domain, every following key statistical descriptive features to discrimi-
channel of in the next layer is decomposed into the com- nate the GAN images in the frequency domain: π πππ,
bination all previous layerβs channels with different sets π ππ₯, π ππ, ππΆππππ
πΊ , ππΆππππ
π΅ , and ππΆππππΊπ΅ , where
of coefficients. If we consider π΄π+1 as the synthesized the details are presented below:
output image and fix π΄ Λπ , every vector πΉΛ π is
π,π=1,..πΆ(π+1)
β’ π πππ. We take the average of the channel-wise
trained independently to minimized the loss that applied
spectrum differences:
on each π΄Λ π+1
π . When we consider π΄ Λπ as a basic and πΉΛππ as
π+1 ππ
πΊ + ππ
π΅ + ππΊπ΅
the coordinate of π΄ Λ π with respect to π΄ Λπ , to synthesize
π πππ = , (6)
a new image, the generative models expect that π΄ Λπ is 3
also good enough so that each independent coefficient Also, we use ππ
πΊ that is the average spectrum
vector πΉΛππ can produce corresponding single channel. In differences between the spectra of the Red and
addition, these output channels should become as natural Green channel in an image as follows:
as possible in spacial domain after being stacked together
in the order of three color channels: Red, Green and Blue. π π»
1 βοΈ βοΈ ββ
Small shifts of πΉΛπ,π=1,..πΆ in the frequency domain
π
β
ππ
πΊ = πππππ
(π’, π£)βπππππΊ (π’, π£)β,
(π+1) π π» π’=1 π£=1
may only change fine-grained details of visualization but
(7)
can produce frequency-bias when there is no direct con-
and ππ
π΅ and ππΊπ΅ can be similarly defined.
straint between channels.
β’ π ππ₯ and π ππ. We take the maximum and min-
imum values in {ππ
πΊ , ππ
π΅ , ππΊπ΅ }.
β’ ππΆππππ
πΊ . We calculate the correlation coefficient
2.2. Descriptive Features Extraction between πππππ
and πππππΊ and transform it to
Let β be a color image with three channels: Red, Green positive range value by adding 1 to its negative
and Blue, which has width of π and height of π». To values as follows:
create its frequency representation, we firstly apply 2D
ππΆππππ
πΊ = βπ(πππππ
, πππππΊ ) + 1, (8)
DFT on each channel as follows:
π βοΈ
βοΈ π»
π’π₯ π£π¦
where π is the Pearson correlation coefficient, and
Fβπ
/πΊ/π΅ (π’, π£) = βπ
/πΊ/π΅ (π₯, π¦)Β·πβπ2π( π + π» ) , ππΆππππ
π΅ and ππΆππππΊπ΅ can be similarly defined.
π₯=1 π¦=1
(4) Our end-to-end pipeline of extracting above frequency
where π₯ and π¦, and denote the π₯ and π¦ slice in the
π‘β π‘β descriptive features from a given image is visually illus-
width and height dimension of β. For convenience, we trated in Fig. 2.
use the notation Fβπ
/πΊ/π΅ to represent the function that
is independently applied for each channel of the image. 2.3. Binary Classifier
Note that Fβπ
/πΊ/π΅ (π’, π£) is now a complex number, i.e.
Fβπ
/πΊ/π΅ (π’, π£) β C, and the spectrum of each channel To demonstrate the characteristic-defining ability of the
is obtained as follows: spectrum disagreement, we first employ the simple clas-
(οΈ )οΈ sifiers to classify real and fake images as below:
πππππ
/πΊ/π΅ (π’, π£) = πππ Fβπ
/πΊ/π΅ (π’, π£) , (5)
β’ Gaussian Mixture Model (GMM). GMM is a
probabilistic model that assumes the distribution
where πππ(Β·) denotes the modulus of complex number.
of observed sampling data points is composed of
Although it would be challenging for human eyes to
a mixture of many Gaussian distributions, partic-
distinguish between real and GAN-generated fake im-
ularly, in our case is two distributions of real and
ages, we believe that their frequency spectra differences
fake class. To determine the means and variances
can be possibly exposed, when we stack the three chan-
of the two Gaussian distributions, Expectation-
nelsβ spectra of real vs. fake. Figure 1 presents our exam-
Maximization (EM) algorithm is used to itera-
ple of imagesβ spectra from VoxCeleb2 dataset [12] and
tively estimate these parameters. Our descriptive
Fake Head Talker dataset [13]. In particular, in the real
features populate in the way that the higher spec-
images, we empirically find that the spectra of three color
trum agreement of an image will have the lower
channels are mostly concurrent when stacking together,
descriptive values. Therefore, we can expect that
whereas they become noisy in the fake images, as shown
the Gaussian distribution in the mixture model,
in Fig. 1.
which has a smaller expectation will represent
the real imagesβ distribution, and the other repre- representations in the latent space with adversar-
sents the fake imagesβ distribution. By applying ial settings. The ALAE model can not only syn-
EM, we can classify real and fake images in an thesize high-resolution images comparing with
unsupervised manner in which the labels of a StyleGAN, but also can further manipulate or re-
training dataset are not required. construct the new input facial images.
β’ Support Vector Machine (SVM). SVM is a ro-
bust supervised learning method that maximizes Details of each dataset in our experiment are summa-
the margin of hyperplanes between different classes. rized in Table 1. In our experiment, the number of real
The samples that lie along the margins are called and GAN fake images are equal in both training and test
the support vectors. In our experiment, we use sets. We further provide the histograms to visualize the
SVM with the radial basis function (RBF) kernel distributions of six descriptive features of these datasets
to train with our six proposed features. in Supp. Section A.
3.2. Experimental Results
3. Experiment
To demonstrate the discriminative power of our proposed
3.1. Datasets features, we perform three different experiments.
Binary classification. Our experimental results are
To examine the effectiveness of our proposed frequency shown in Table 2. We can observe that both unsuper-
features, we experiment four types of dataset: Fake Head vised and supervised methods are able to produce high
Talker [7], StyleGAN [8], StarGAN [9], and Adversarial performance with our newly introduced frequency fea-
Latent Auto Encoder (ALAE) [10]. A brief description of tures. The accuracy scores of the unsupervised method
each dataset is provided below as well as in Table 1: on Fake Head Talker and ALAE dataset are competitive,
β’ Fake Head Talker dataset [7]. Fake Head Talker compared to the supervised approaches. At the same
is generated by the few-shot learning system that time, they are still higher than 80% on StyleGAN and
is pre-trained extensively on a large dataset (meta- StarGAN. Meanwhile, the supervised methodβs accuracy
learning). Particularly, their approach includes an scores are always higher than 95% on the four datasets.
embedder, a generator, and a discriminator. After We can conclude that our proposed features based on the
training on a large corpus of talking head videos asynchronous in the frequency spectrum can effectively
of different faces with adversarial training, their capture the characteristics of the GAN-generated images,
approach can transform facial landmarks from and provide the foundation for distinguishing fake from
a source frame into realistically-looking person- real images.
alized photographs with a few photos of a new Unbalanced training datasets. Furthermore, to study
target person, and further mimic the target. the feasibility of training with an unbalanced dataset us-
ing our features, we gradually reduce the number of fake
β’ StyleGAN dataset [8]. StyleGAN is a high-level
images in each training dataset to 25%, 5%, and 1% of
style controlling approach that governs its gen-
the total training data size. After that, we apply the SVM
erator through adaptive instance normalization
as our learning model. To demonstrate our approachβs ef-
(AdaIN) and Gaussian noise adding in each con-
fectiveness, we compare our method with FakeTalkerDe-
volutional layer. Furthermore, by proposing two
tect model [13], which deployed a pre-trained AlexNet
novel metrics such as perceptual path length and
and Siamese network trained on RGB images. The results
linear separability, the generated images are less
are presented in Table 3. We can observe that our method
entangled and have different factors of variation.
with the hand-crafted features outperforms the AlexNet
β’ StarGAN dataset [9]. StarGAN is a unified model
and FakeTalkerDetect on both balanced and unbalanced
architecture that is able to train on multiple datasets
datasets. Therefore, we can conclude that our simple yet
across different domains. By proposing a simple
effective features are capable to characterize the fake
mask vector, the StarGAN is able to flexibly uti-
image much better in the unbalanced training dataset
lize multiple datasets containing different label
scenario, as well.
sets, and achieve competitive results in the facial
Unsupervised domain adaptation. In this task, we
attribute transfer tasks. This new approach with
propose an algorithm using our proposed features that
only a single generator and a discriminator has
allows a pre-trained SVM model on one source dataset
addressed the scalability and robustness limita-
(e.g., StyleGAN) can detect fake images in a new target
tions of many previous research.
dataset (e.g., ALAE) with the only prior knowledge of the
β’ Adversarial Latent Auto Encoder (ALAE) datasettarget feature expectations.
[10]. ALAE is an autoencoder-based generative
model that is capable to learn the disentangled
Table 1
Details of datasets used in our experiment.
Training size Test size
Datasets Resolution Source datasets
(real+ fake) (real+ fake)
Fake Head Talker [7] 224 Γ 224 VoxCeleb2 [12] 18,800 18,800
StyleGAN [8] 1024 Γ 1024 FFHQ 1 2,000 2,000
StarGAN [9] 256 Γ 256 CelebA [14] 2,000 1,998
ALAE [10] 1024 Γ 1024 FFHQ 2,000 2,000
Table 2
Experimental results of GMM and SVM on four datasets with our discriminative features.
GMM SVM
Datasets
Accuracy Recall Precision F1 Accuracy Recall Precision F1
Fake Head Talker 0.996 1.000 0.991 0.996 0.9972 0.994 1.000 0.997
StyleGAN 0.849 0.762 0.915 0.831 0.951 0.938 0.963 0.950
StarGAN 0.903 0.807 1.000 0.893 0.972 0.949 0.994 0.971
ALAE 0.992 0.984 1.000 0.992 0.999 0.997 1.000 0.998
Table 3 Algorithm 1 Unsupervised domain adaptation with
Comparison between our approach using proposed descrip- SVM using our proposed descriptive features
tive features and AlexNet and FakeTalkerDetect method on Require: Labeled source set {π π , π π }, unlabeled tar-
Fake Head Talker dataset. The precision, recall and F1 scores
get set π π‘ , where π π and π π‘ includes the six
of AlexNet and FakeTalkerDetect from [13], and their values
are rounded to second decimal
proposed features [π1π , .., π6π ], respectively. The
Methods Accuracy Recall Precision F1 [οΈprior knowledge of Gaussian expectation values:
ππ π,0 , ππ π,1 π=1,...,6 and ππ‘π,0 , ππ‘π,1 π=1,...,6 .
]οΈ [οΈ ]οΈ
AlexNet (50% fake) 0.981 0.98 0.98 0.98
1: Step 1: Scale (οΈ each feature
)οΈ (οΈin π and π π‘)οΈ:
π
FakeTalkerDetect 0.984 0.98 0.98 0.98
SVM (ours) 0.997 0.994 1.00 0.997 Β―
ππ = ππ β ππ,0 / ππ,1 β ππ π,0 ,
π π π π
AlexNet (25% fake) 0.971 0.95 0.95 0.96 πΒ―ππ‘ = πππ‘ β ππ‘π,0 / ππ‘π,1 β ππ‘π,0
(οΈ )οΈ (οΈ )οΈ
FakeTalkerDetect 0.986 0.98 0.98 0.98
2: Step 2: Fit source set [πΒ―1 , .., πΒ―6 ], π with SVM
{οΈ π π π
}οΈ
SVM (ours) 0.998 0.995 1.000 0.997
model.
AlexNet (5% fake) 0.964 0.98 0.80 0.87
FakeTalkerDetect 0.988 0.99 0.91 0.94 3: Step 3: Use pre-trained SVM to predict target set label
SVM (ours) 0.997 0.997 0.997 0.997 from [πΒ―1π‘ , .., πΒ―6π‘ ].
AlexNet (1% fake) 0.963 0.98 0.61 0.67
FakeTalkerDetect 0.988 0.99 0.74 0.82
SVM (ours) 0.992 0.999 0.986 0.992
suggested features the pre-trained SVM shows its strong
detection ability in the new target domain, where all the
detection performance is above 80% of accuracy for any
In particular, we first take the two Gaussian expecta-
pair of source and target dataset. This preliminary exper-
tion values of two mixture distributions of each feature
iment shows that our proposed features can be utilized
from both source and target dataset. These expectation
in domain adaptation tasks with more complex learning
values are kept as our prior knowledge about the target
models in the future.
dataset. We then scale the source training set features
such that their two Gaussian expectation values are nor-
malized between 0 and 1 , to better fit the training dataset 4. Conclusion
with the SVM model. In the testing phase, with our prior
knowledge above, we can scale the testing features from Although GANs have significantly advanced in the past,
the target dataset using the known expectation values we discover that there are some areas that GANsβ can-
and feed them to the pre-trained SVM model to make pre- not mimic the real images effectively in the frequency
diction. This adaptation learning process is summarized domain. Thus, in this work, we propose a preliminary
in the Algorithm 1. approach that reveals the asynchronous in frequency do-
We experiment with the four fake dataset and present main of the three channels in GAN images. By mining
the results in Table 4. We can observe that with our statistical features in frequency domain, our simple yet
Table 4
Experimental results of domain adaptation task using our proposed features
Source dataset Target dataset Accuracy Recall Precision F1
StyleGAN 0.800 0.908 0.745 0.819
Fake Head Talker StarGAN 0.918 0.844 0.992 0.912
ALAE 0.994 0.995 0.993 0.994
Fake Head Talker 0.965 0.932 0.998 0.964
StyleGAN StarGAN 0.906 0.814 0.998 0.896
ALAE 0.991 0.982 1.000 0.991
Fake Head Talker 0.983 0.982 0.983 0.983
StarGAN StyleGAN 0.832 0.980 0.756 0.854
ALAE 0.996 0.997 0.994 0.996
Fake Head Talker 0.993 0.989 0.998 0.993
ALAE StyleGAN 0.890 0.955 0.845 0.897
StarGAN 0.929 0.871 0.985 0.925
effective unsupervised and supervised learning methods [2] S. Cole, We are truly fucked: Everyone is
can easily discriminate the real and GAN-based synthetic making ai-generated fake porn now, 2018.
facial images without utilizing deep learning methods. URL: https://www.vice.com/en/article/bjye8a/
Our extensive experiments demonstrates that the pro- reddit-fake-porn-app-daisy-ridley.
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and supervised binary classification, 2) unbalanced train- simulating artifacts in gan fake images, in: 2019
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D. Kolossa, T. Holz, Leveraging frequency analysis
This work was partly supported by Institute of Informa-
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A. Distribution of Statistical Descriptive Features
The histogram distributions of our six proposed statistical features in the frequency domains are present in the Fig.
3. We can observe that these feature distributions are highly separable between real and fake images across four
datasets.
Figure 3: The histogram distributions of our six statistical descriptive features from four datasets: Fake Head Talker, StyleGAN,
StarGAN and ALAE.
B. Example GAN-based Synthetic Images
We provide example images from four datasets used in our experiment.