Measure-Based Supervision for Tiny Object Detection in Aerial Imagery

Detection breaks down on objects a few pixels wide for a structural reason: as box side length shrinks, intersection over union (IoU) degenerates toward an indicator of exact pixel coincidence, so a one-pixel error can rewrite both the label assignment and the regression gradient. We avoid this regime by discarding pairwise box matching altogether. A scene is treated instead as an unnormalized positive measure over object centers, log-scales, and categories, and training minimizes a debiased, uncertainty-aware unbalanced optimal transport divergence between the predicted measure and a Gaussian-smoothed annotation measure. Soft correspondences replace hard assignment, and because the marginals are left free, total confidence mass survives as count supervision. A second training-only signal is drawn from the image itself predicted instances are rendered back to pixels through anisotropic Gaussian footprints, a shared blur kernel, pixel integration, and a capacity limited background, then compared with the observation under a Poisson–Gaussian noise model. Scene priors enter through a clipped log-space gate that caps how far context may suppress appearance evidence, a bound we audit by reporting recall on atypical placements alongside aggregate gains. The method reaches 31.7 AP on the AI-TOD-v2 validation split, including 23.4 AP on 2–8-pixel objects, and 36.8, 37.1, and 31.2 AP on SODA-D, SODA-A, and AI-TOD-R, with 53.6 AP on tiny persons in TinyPerson. Ablations isolate the contribution of each component.