ThermalIoU: Physical Theory Empowered IoU Loss for Small Object Detection in Aerial Imagery

Object detection in aerial imagery faces significant challenges caused by extreme scale variation, dense object layouts, and the prevalence of tiny instances. Standard Intersection over Union (IoU) and its variants are sensitive to small localization errors: a minor coordinate deviation may cause a large IoU penalty for tiny objects, and non-overlapping boxes yield no gradients, which limits localization accuracy. To address these issues, we propose ThermalIoU, a heat-diffusion-inspired bounding-box regression loss that represents rigid boxes as continuous diffusive fields. A box is treated as a flat-top initial temperature distribution and diffused by the Gaussian heat kernel, preserving its rectangular geometry while providing smooth boundary support. We further introduce a scale-decoupled and epoch-annealed diffusion parameter, so that small objects obtain broader early-stage gradients whereas larger objects retain sharper localization fields. Experiments on AI-TOD and VisDrone, together with ablations, efficiency measurements, and qualitative visualizations, show that ThermalIoU is a practical training loss with overall gains over CIoU and competitive performance against Inner-IoU and MPDIoU.