Signature and Log-signature for the Study of Empirical Distributions Generated with GANs

In this paper, we develop a new and systematic method to explore and analyze samples taken by NASA Perseverance on the surface of the planet Mars. A novel in this context PCA adaptive t-SNE is proposed, as well as the introduction of statistical measures to study the goodness of fit of the sample distribution. We go beyond visualization by generating synthetic imagery using Stylegan2-ADA that resemble the original terrain distribution. We also conduct synthetic image generation using the recently introduced Scored-based Generative Modeling. We bring forward the use of the recently developed Signature Transform as a way to measure the similarity between image distributions and provide detailed acquaintance and extensive evaluations. We are the first to pioneer RMSE and MAE Signature and log-signature as an alternative to measure GAN convergence. Insights on state-of-the-art instance segmentation of the samples by the use of a model DeepLabv3 are also given.