Multimodal Unsupervised Image-to-Image Translation-Supplementary Material

Proof. Let z1 denote the latent code, which is the concatenation of c1 and s1. We denote the encoded latent distribution by pE(z1), which is defined by z1 = E1(x1) and x1 sampled from the data distribution p(x1). We denote the latent distribution at generation time by p(z1), which is obtained by s1 ∼ q(s1) and c1 ∼ p(c2). The generated image distribution pG(x1) = p(x2→1) is defined by x1 = G1(z1) and z1 sampled from p(z1). According to the change of variable formula for probability density functions:

[1]  Bernhard Schölkopf,et al.  Wasserstein Auto-Encoders , 2017, ICLR.

[2]  拓海 杉山,et al.  “Unpaired Image-to-Image Translation using Cycle-Consistent Adversarial Networks”の学習報告 , 2017 .

[3]  Lawrence Carin,et al.  ALICE: Towards Understanding Adversarial Learning for Joint Distribution Matching , 2017, NIPS.

[4]  Eric P. Xing,et al.  Generative Semantic Manipulation with Contrasting GAN , 2017, ArXiv.

[5]  Ming-Hsuan Yang,et al.  Universal Style Transfer via Feature Transforms , 2017, NIPS.

[6]  Serge J. Belongie,et al.  Arbitrary Style Transfer in Real-Time with Adaptive Instance Normalization , 2017, 2017 IEEE International Conference on Computer Vision (ICCV).

[7]  Andrea Vedaldi,et al.  Improved Texture Networks: Maximizing Quality and Diversity in Feed-Forward Stylization and Texture Synthesis , 2017, 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[8]  Alexei A. Efros,et al.  Image-to-Image Translation with Conditional Adversarial Networks , 2016, 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[9]  Mark W. Schmidt,et al.  Fast Patch-based Style Transfer of Arbitrary Style , 2016, ArXiv.

[10]  Leon A. Gatys,et al.  Image Style Transfer Using Convolutional Neural Networks , 2016, 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[11]  Navdeep Jaitly,et al.  Adversarial Autoencoders , 2015, ArXiv.

[12]  Jimmy Ba,et al.  Adam: A Method for Stochastic Optimization , 2014, ICLR.

[13]  Yoshua Bengio,et al.  Generative Adversarial Nets , 2014, NIPS.

[14]  Xiaofeng Tao,et al.  Transient attributes for high-level understanding and editing of outdoor scenes , 2014, ACM Trans. Graph..