Fast-growing trees pose risks to the operational safety of overhead power lines. Traditional methods of inspecting tree growth, such as ground inspection, are time-consuming and not accurate. Latest development employs drones equipped with either light detection and ranging (LiDAR) or camera for accurate inspections. However, those methods are expensive and cannot be used all the time. They are also susceptible to severe weather conditions. Therefore, in this paper, an online method for measuring and calculating the horizontal distances between the power lines and trees in a mobile edge computing architecture is proposed by taking into account a unique property of power systems. Firstly, two-dimensional images are taken by a standard optical camera mounted on the tower. Secondly, the power lines and the surrounding trees in the images are discovered by processing the images. Finally, the distances between the power lines and trees are calculated based on a reference distance. Furthermore, the applications that control the cameras and image processing are implemented on a mobile edge server for real-time monitoring and system updates. Experiment results in real-world scenarios show that the measurement error is less than 10%, which indicates that the proposed approach can reliably estimate the distances and the edge computing-based architecture can improve the efficiency.