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UAVs (unmanned aerial vehicles) or drones are promising instruments for video-based surveillance. Various applications of aerial surveillance use object detection programs to detect target objects. In such applications, three parameters influence a drone deployment strategy: the area covered by the drone, the latency of target (object) detection, and the quality of the detection output by the object detector. Previous works have focused on improving Pareto optimality along the area-latency frontier or the area-quality frontier, but not on the combined area-latency-quality frontier, because of which these solutions are sub-optimal for drone-based surveillance. We explore a three way tradeoff between area, latency, and quality in the context of autonomous aerial surveillance of targets in an area using drones with cameras and an object detection program. We propose Vega, a drone deployment framework that captures these tradeoffs to deploy drones efficiently. We make three contributions with Vega. First, we characterize the ability of the state-of-the-art mobile object detector, EfficientDet [CPVR '20], to detect objects from varying drone altitudes using confidence and IoU curves vs. drone altitude. Second, based on these characteristics of the detector, we propose a set of two algorithmic primitives for drone-based maneuvers, namely DroneZoom and DroneCycle. Using these two primitives, we obtain a more optimal Pareto frontier between our three target parameters - coverage area, detection latency, and detection quality for a single drone system. Third, we scale out our findings to a swarm deployment using higher-order Voronoi tessellations, where we control the swarm's spatial density using the Voronoi order to further lower the detection latency while maintaining detection quality.