Delineating farm boundaries through segmentation of satellite images is a fundamental step in many agricultural applications. The task is particularly challenging for smallholder farms, where accurate delineation requires the use of high resolution (HR) imagery which are available only at low revisit frequencies (e.g., annually). To support more frequent (sub-) seasonal monitoring, HR images could be combined as references (ref) with low resolution (LR) images – having higher revisit frequency (e.g., weekly) – using reference-based super-resolution (Ref-SR) methods. However, current Ref-SR methods optimize perceptual quality and smooth over crucial features needed for downstream tasks, and are unable to meet the large scale-factor requirements for this task. Further, previous two-step approaches of SR followed by segmentation do not effectively utilize diverse satellite sources as inputs. We address these problems through a new approach, SEED-SR, which uses a combination of conditional latent diffusion models and large-scale multi-spectral, multi-source geo-spatial foundation models. Our key innovation is to bypass the explicit SR task in the pixel space and instead perform SR in a segmentation-aware latent space. This unique approach enables us to generate segmentation maps at an unprecedented 20× scale factor, and rigorous experiments on two large, real datasets demonstrate up to 25.5% and 12.9% relative improvement in instance and semantic segmentation metrics respectively over approaches based on state-of-the-art Ref-SR methods.

Generative adversarial nets (GANs) and variational auto-encoders have significantly improved our distribution modeling capabilities, showing promise for dataset augmentation, image-to-image translation and feature learning. However, to model high-dimensional distributions, sequential training and stacked architectures are common, increasing the number of tunable hyper-parameters as well as the training time. Nonetheless, the sample complexity of the distance metrics remains one of the factors affecting GAN training. We first show that the recently proposed sliced Wasserstein distance has compelling sample complexity properties when compared to the Wasserstein distance. To further improve the sliced Wasserstein distance we then analyze its `projection complexity' and develop the max-sliced Wasserstein distance which enjoys compelling sample complexity while reducing projection complexity, albeit necessitating a max estimation. We finally illustrate that the proposed distance trains GANs on high-dimensional images up to a resolution of 256x256 easily.

Generative Adversarial Nets (GANs) are very successful at modeling distributions from given samples, even in the high-dimensional case. However, their formulation is also known to be hard to optimize and often not stable. While this is particularly true for early GAN formulations, there has been significant empirically motivated and theoretically founded progress to improve stability, for instance, by using the Wasserstein distance rather than the Jenson-Shannon divergence. Here, we consider an alternative formulation for generative modeling based on random projections which, in its simplest form, results in a single objective rather than a saddle-point formulation. By augmenting this approach with a discriminator we improve its accuracy. We found our approach to be significantly more stable compared to even the improved Wasserstein GAN. Further, unlike the traditional GAN loss, the loss formulated in our method is a good measure of the actual distance between the distributions and, for the first time for GAN training, we are able to show estimates for the same.