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Informed secure watermarking using optimal transport

Patrick Bas
2011 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)  
The minimization of the embedding distortion is afterwards casted into an optimal transport problem.  ...  This paper presents several watermarking methods preventing the estimation of the secret key by an adversary.  ...  In the sequel, we use (7) to compute the optimal mapping, it is based on F X (x) = 0.5(1 + erf(x/ 2σ 2 x )).  ... 
doi:10.1109/icassp.2011.5946865 dblp:conf/icassp/Bas11 fatcat:mr5bufkmtrbthkaoi7k33flyc4

Adversarial Risk via Optimal Transport and Optimal Couplings [article]

Muni Sreenivas Pydi, Varun Jog
2020 arXiv   pre-print
We show that the optimal adversarial risk for binary classification with 0-1 loss is determined by an optimal transport cost between the probability distributions of the two classes.  ...  In this paper, we analyze adversarial risk and adversarial classifiers from an optimal transport perspective.  ...  The transport maps used in these K problems may be arbitrary; however, we shall often use versions of the monotone optimal transport map [36] .  ... 
arXiv:1912.02794v2 fatcat:j6tqdeo2pvdglob2ubvf6udvii

Adversarial Optimal Transport Through The Convolution Of Kernels With Evolving Measures [article]

Daeyoung Kim, Esteban G. Tabak
2020 arXiv   pre-print
The optimal transport also follows a flow that, by duality, must follow the gradient of the test function.  ...  A novel algorithm is proposed to solve the sample-based optimal transport problem.  ...  Adversarial optimal transport This section elaborates on the specifics of the problem and proposes the new method in detail.  ... 
arXiv:2006.04245v2 fatcat:6gldumhaibc4vdkw32tpjkk74y

Connecting adversarial attacks and optimal transport for domain adaptation [article]

Arip Asadulaev, Vitaly Shutov, Alexander Korotin, Alexander Panfilov, Andrey Filchenkov
2022 arXiv   pre-print
If samples with the same labels in two domains are c-cyclically monotone, the optimal transport map between these domains preserves the class-wise structure, which is the main goal of domain adaptation  ...  In our method, we use optimal transport to map target samples to the domain named source fiction. This domain differs from the source but is accurately classified by the source domain classifier.  ...  This work was supported by the Analytical Center for the Government of the Russian Federation (IGK 000000D730321P5Q0002), agreement No. 70-2021-00141.  ... 
arXiv:2205.15424v2 fatcat:btvlfsqhl5ayzd3jdtklqdxi7u

On making optimal transport robust to all outliers [article]

Kilian Fatras
2022 arXiv   pre-print
Optimal transport (OT) is known to be sensitive against outliers because of its marginal constraints.  ...  To decrease the influence of these outliers in the transport problem, we propose to either remove them from the problem or to increase the cost of moving them by using the classifier prediction.  ...  Acknowledgments and Disclosure of Funding This work was partially supported by NSERC Discovery grant (RGPIN-2019-06512), a Samsung grant and a Canada CIFAR AI chair.  ... 
arXiv:2206.11988v1 fatcat:gojiyuotczcxldkuudm3dzdrpy

Optimal Transport Based Generative Autoencoders [article]

Oliver Zhang, Ruei-Sung Lin, Yuchuan Gou
2019 arXiv   pre-print
Instead, we propose two novel generative autoencoders, AE-OTtrans and AE-OTgen, which rely on optimal transport instead of adversarial training.  ...  The field of deep generative modeling is dominated by generative adversarial networks (GANs). However, the training of GANs often lacks stability, fails to converge, and suffers from model collapse.  ...  Acknowledgements The authors of this paper would like to acknowledge Zach Gaslowitz of Proof School for the many fruitful discussions along the way. We would also like to thank Dr.  ... 
arXiv:1910.07636v1 fatcat:6kqc3sowyrdvdi3ux4xvxck64q

Optimization of natural watermarking using transportation theory

Benjamin Mathon, Patrick Bas, François Cayre, Benoît Macq
2009 Proceedings of the 11th ACM workshop on Multimedia and security - MM&Sec '09  
Contrarily to another technique presented in [13] , the embedding does not depend on computationally demanding pre-computed mapping.  ...  Because security of watermarking schemes relies on the distribution of marked contents in a private subspace, we use the transportation theory in order to derive a mapping that will minimize the global  ...  The computation of the optimal transport map T0 for embedding the message (0, . . . , 0) is given by: T0 : R Nc → R Nc zx → zy = T0(zx), (16) where T0 0 B @ zx(0) . . . zx(Nc − 1) 1 C A = 0 B @ P −1 ν  ... 
doi:10.1145/1597817.1597824 dblp:conf/mmsec/MathonBCM09 fatcat:badvq4b4nzd7blfmin3uxkynnu

OTAdapt: Optimal Transport-based Approach For Unsupervised Domain Adaptation [article]

Thanh-Dat Truong, Naga Venkata Sai Raviteja Chappa, Xuan Bac Nguyen, Ngan Le, Ashley Dowling, Khoa Luu
2022 arXiv   pre-print
This paper presents a novel approach to unsupervised domain adaptations based on the optimal transport-based distance.  ...  Unsupervised domain adaptation is one of the challenging problems in computer vision.  ...  Optimal Transport has been widely used to compute the distance between two probability distributions, which has been first introduced in middle of the 19th century.  ... 
arXiv:2205.10738v1 fatcat:g3sqezlqabdcfjga2htluytjjq

Gromov-Wasserstein Alignment of Word Embedding Spaces [article]

David Alvarez-Melis, Tommi S. Jaakkola
2018 arXiv   pre-print
In this paper, we cast the correspondence problem directly as an optimal transport (OT) problem, building on the idea that word embeddings arise from metric recovery algorithms.  ...  Current state-of-the-art methods, however, involve multiple steps, including heuristic post-hoc refinement strategies.  ...  The work was partially supported by MIT-IBM grant "Adversarial learning of multimodal and structured data", and Graduate Fellowships from Hewlett Packard and CONACYT.  ... 
arXiv:1809.00013v1 fatcat:4njieo6spjhc5ouft6rgxy3pfe

Gromov-Wasserstein Alignment of Word Embedding Spaces

David Alvarez-Melis, Tommi Jaakkola
2018 Proceedings of the 2018 Conference on Empirical Methods in Natural Language Processing  
In this paper, we cast the correspondence problem directly as an optimal transport (OT) problem, building on the idea that word embeddings arise from metric recovery algorithms.  ...  Current state-of-theart methods, however, involve multiple steps, including heuristic post-hoc refinement strategies.  ...  The work was partially supported by MIT-IBM grant "Adversarial learning of multimodal and structured data", and Graduate Fellowships from Hewlett Packard and CONACYT.  ... 
doi:10.18653/v1/d18-1214 dblp:conf/emnlp/Alvarez-MelisJ18 fatcat:e2qsf2fwafaupg437ruygdtd54

Guiding the One-to-One Mapping in CycleGAN via Optimal Transport

Guansong Lu, Zhiming Zhou, Yuxuan Song, Kan Ren, Yong Yu
2019 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
We propose to solve an optimal transport mapping restrained by a task-specific cost function that reflects the desired properties, and use the barycenters of optimal transport mapping to serve as references  ...  CycleGAN is capable of learning a one-to-one mapping between two data distributions without paired examples, achieving the task of unsupervised data translation.  ...  Due to the lack of computation power, we use L2 barycenter instead of accurate barycenter to obtain the barycentric mapping out of the previously-obtained optimal transport plan, which can be simplified  ... 
doi:10.1609/aaai.v33i01.33014432 fatcat:jcbkum4ehrc6lhnuyyry3k7fy4

Learning Adversarially Robust Representations via Worst-Case Mutual Information Maximization [article]

Sicheng Zhu, Xiao Zhang, David Evans
2020 arXiv   pre-print
To better understand adversarial robustness, we consider the underlying problem of learning robust representations.  ...  Training machine learning models that are robust against adversarial inputs poses seemingly insurmountable challenges.  ...  a specific task on which adversarially robust learning is computationally intractable.  ... 
arXiv:2002.11798v2 fatcat:figlnvzcazcfli3g3bw2wzm4cy

Guiding the One-to-one Mapping in CycleGAN via Optimal Transport [article]

Guansong Lu, Zhiming Zhou, Yuxuan Song, Kan Ren, Yong Yu
2018 arXiv   pre-print
We propose to solve an optimal transport mapping restrained by a task-specific cost function that reflects the desired properties, and use the barycenters of optimal transport mapping to serve as references  ...  CycleGAN is capable of learning a one-to-one mapping between two data distributions without paired examples, achieving the task of unsupervised data translation.  ...  Due to the lack of computation power, we use L2 barycenter instead of accurate barycenter to obtain the barycentric mapping out of the previously-obtained optimal transport plan, which can be simplified  ... 
arXiv:1811.06284v1 fatcat:hodmonjn5zdpnboeu2l77nhglq

Large-Scale Optimal Transport via Adversarial Training with Cycle-Consistency [article]

Guansong Lu, Zhiming Zhou, Jian Shen, Cheng Chen, Weinan Zhang, Yong Yu
2020 arXiv   pre-print
It models the transport map via stochastic neural networks and enforces the constraint on the marginal distributions via adversarial training.  ...  In this paper, we propose an end-to-end approach for large-scale optimal transport, which directly solves the transport map and is compatible with general cost function.  ...  .: Adversarial computation of optimal transport maps. arXiv preprint arXiv:1906.09691 (2019) 23. Liu, M.Y., Breuel, T., Kautz, J.: Unsupervised image-to-image translation networks.  ... 
arXiv:2003.06635v1 fatcat:e7jxq54lpzfqvl6i63aijauwdq

Optimal Transport for Secure Spread-Spectrum Watermarking of Still Images

Benjamin Mathon, Francois Cayre, Patrick Bas, Benoit Macq
2014 IEEE Transactions on Image Processing  
This article studies the impact of secure watermark embedding in digital images by proposing a practical implementation of secure spread-spectrum watermarking using distortion optimization.  ...  The use of transportation theory also provides an average PSNR gain of 3.6 dB on PSNR with respect to the previous embedding for a set of 2, 000 images.  ...  For any m ∈ F Nc 2 , the optimal transport map T m is given by: T m (x) = R −1 (T 0 (Rx)), (22) with: R ∈ M Nc,Nc (R), R(i, j) =    0 if i = j, (−1) m(i) otherwise. (23) This optimal transport map allows  ... 
doi:10.1109/tip.2014.2305873 pmid:24808340 fatcat:rwqgzqdtwfahfi4walaswddqzm
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