Recent advances in machine learning and hardware have produced embedded devices capable of performing real-time object detection with commendable accuracy. We consider a scenario in which embedded devices rely on an onboard object detector, but have the option to offload detection to a more powerful edge server when local accuracy is deemed too low. Resource constraints, however, limit the number of images that can be offloaded to the edge. Our goal is to identify which images to offload to maximize overall detection accuracy under those constraints. To that end, the paper introduces a reward metric designed to quantify potential accuracy improvements from offloading individual images, and proposes an efficient approach to make offloading decisions by estimating this reward based only on local detection results. The approach is computationally frugal enough to run on embedded devices, and empirical findings indicate that it outperforms existing alternatives in improving detection accuracy even when the fraction of offloaded images is small.