Scaling Uncertainty Quantification From Patches to Scenes Through Discontinuity-Aware Stitching

Reconstructing spatially continuous 2-D fields out of their individually derived building blocks typically introduces artifacts that decrease the overall perceptual quality of the field. Machine learning (ML) applications encounter such a challenge when patching a U-net-like architecture output. Numerous techniques have been developed to mitigate this problem. Yet, few are informed scalable solutions. The present work manages the stitching of Unet-inferred images using Bayesian deep learning (BDL) probabilistic output. The ability to preserve a Bayesian prediction's variance while effectively reducing the artifacts within a patched scene is presented through an example of predicting a field related to atmospheric radiance. In areas of high variance, adjacent patches of inferred atmospheric radiances may significantly vary in magnitude, leading to large undesirable spatial gradients in the combined (patched) product. Multiple weighted aggregation strategies and weighting schema are surveyed to investigate how to efficiently decrease artificial gradients in large images constructed by stitching several small predictions while maintaining naturally occurring gradients expected to appear in the mosaiced image. Structural similarity (SSIM) Index and visual information fidelity (VIF) are used to evaluate the perceptual quality of the resultant images and confirm the successful employment of Bayesian U-nets with well-calibrated uncertainty, yielding geospatial images with fewer artifacts than naive methods. Log-linear pooling (LLP) proved to be the optimal aggregation strategy tested for fusing patch uncertainties by retaining per-pixel Gaussian distributions and scaling uncertainties in a principled manner to maintain calibration across the spatial map.