Detecting overfitting in GANs with a metric based on the Fourier spectrum

Recent progress in generative image modeling is leading to a new era of highresolution fakes visually indistinguishable from real life images. However, the development of metrics capable of discerning whether images are synthetic or not runs behind the race of achieving the best generator, thus bringing potential threats. We propose a rotation invariant metric capable of distinguishing real and generated images and prove its performance and correlation with subjective evaluation on a brain MRI dataset to generate synthetic white matter lesion images. We name this metric CSD (Circular Spectrum Distance) due to its circular nature and its inherent relation to the Fourier Spectrum. We find that this metric, as opposed to Frechet Inception Distance or Inception Score, detects overfitting during training in terms of generator memorisation without making use of any pretrained network. The conclusions are generalized to CelebA-HQ as a benchmark dataset.