Counting Trees from Satellite Imagery with Noisy Supervision

Counting individual trees is a basic input to carbon, biodiversity and land-management monitoring, yet it remains largely unaddressed at satellite resolution. The difficulty is twofold. First, the object itself is ill-defined: isolated trees stay identifiable, but crown boundaries merge in dense forests, so no single annotation convention holds across a scene. Second, supervision does not scale: manual delineation of individual trees over large areas is prohibitively expensive, and the one scalable alternative, annotations derived from airborne LiDAR, is noisy, incomplete, and of uneven quality across sites. We cast counting as a spatial density matching problem supervised by Unbalanced Optimal Transport. Relaxing both marginals lets the model localize precisely where trees are separable and fall back to density estimation where they are not, without committing to a one-to-one assignment or to the exact annotated count. The transport residuals act as a per-annotation reliability signal, which we exploit in a self-correction mechanism that progressively refines the noisy supervision during training. We find that this formulation outperforms popular detection and density regression approaches by a significant margin, on imagery from three different sensors.