Fréchet inception distance

The Fréchet inception distance (FID) is a metric used to assess the quality of images created by the generator of a generative adversarial network (GAN).[1] Unlike the earlier inception score (IS), which evaluates only the distribution of generated images, the FID compares the distribution of generated images with the distribution of real images that were used to train the generator.[1][2]

The FID metric is the Fréchet distance between two multidimensional Gaussian distributions: ${\displaystyle {\mathcal {N}}(\mu ,\Sigma )}$, the distribution of the Inception v3 features of the images generated by the GAN and ${\displaystyle {\mathcal {N}}(\mu _{w},\Sigma _{w})}$, the distribution of the Inception v3 features from the "world" or real images used to train the GAN. As a result, it can be computed from the mean and the covariance of the activations when the synthesized and real images are fed into the Inception network as: [1][2][3]

${\displaystyle {\text{FID}}=|\mu -\mu _{w}|^{2}+\operatorname {tr} (\Sigma +\Sigma _{w}-2(\Sigma \Sigma _{w})^{1/2}).}$

Rather than directly comparing images pixel by pixel (for example, as done by the L2 norm), the FID compares the mean and standard deviation of one of the deeper layers in Inception v3, a Convolutional neural network. These layers are closer to output nodes that correspond to real-world objects such as a specific breed of dog or an airplane, and further from the shallow layers near the input image. As a result, they tend to mimic human perception of similarity in images.

The FID metric is the current standard metric for assessing the quality of GANs as of 2020. It has been used to measure the quality of many recent GANs[2] including the high-resolution StyleGAN1[4] and StyleGAN2[5] networks

History

The FID metric was introduced in 2017.[1] It is inspired by the Fréchet distance introduced in 1957 by M. Frechet.[6]

References

1. Heusel, Martin; Ramsauer, Hubert; Unterthiner, Thomas; Nessler, Bernhard; Hochreiter, Sepp (12 January 2018). "GANs Trained by a Two Time-Scale Update Rule Converge to a Local Nash Equilibrium". arXiv:1706.08500 [cs.LG].
2. Jean, Neal (15 July 2018). "Fréchet Inception Distance". Neal Jean. Retrieved 3 July 2020.
3. Dowson, D. C; Landau, B. V (1 September 1982). "The Fréchet distance between multivariate normal distributions". Journal of Multivariate Analysis. 12 (3): 450–455. doi:10.1016/0047-259X(82)90077-X. ISSN 0047-259X.
4. Karras, Tero; Laine, Samuli; Aila, Timo (2020). "A Style-Based Generator Architecture for Generative Adversarial Networks". IEEE Transactions on Pattern Analysis and Machine Intelligence. PP: 1. arXiv:1812.04948. doi:10.1109/TPAMI.2020.2970919. PMID 32012000.
5. Karras, Tero; Laine, Samuli; Aittala, Miika; Hellsten, Janne; Lehtinen, Jaakko; Aila, Timo (23 March 2020). "Analyzing and Improving the Image Quality of StyleGAN". arXiv:1912.04958 [cs.CV].
6. Fréchet., M (1957). "Sur la distance de deux lois de probabilité". C. R. Acad. Sci. Paris. 244: 689–692.