Spatial Radius and Group Coverage of Conformal Image Sets under Covariate Shift

Reconstructing a high-resolution image from coarse measurements leaves uncertainty about regional averages. A prediction set can contain the true image with high probability while allowing large differences between accepted images. In this article, we study the smallest and largest averages over all accepted images that match the observed coarse measurements. These ranges give simultaneous bounds for every region whenever the set contains the true image. We derive exact ranges for nested regions and construct an accepted reconstruction with the smallest worst-case regional error. Standard calibration within observed groups preserves coverage when group proportions change and within-group distributions remain unchanged. This guarantee does not require an accurate predictor. For smoothly varying images, a fixed number of regional averages controls approximation error independently of resolution. The calibrated threshold also contributes to the image radius. In controlled chest X-ray experiments, calibrating regional averages without individual pixels reduces the largest regional range by 20% to 44% compared with calibrating both. Retinal experiments show that calibration within grades improves the smallest mean group coverage over marginal calibration.