Three-dimensional (3D) mapping of power lines is very important for power line inspection. Many remotely-sensed data products like light detection and ranging (LiDAR) have been already studied for power line surveys. More and more data are being obtained via photogrammetric measurements. This increases the need for the implementation of advanced processing techniques. In recent years, there have been several developments in visualisation techniques using UAV (unmanned aerial vehicle) platform photography. The most modern of such imaging systems have the ability to generate dense point clouds. However, image-based point cloud accuracy is very often various (unstable) and dependent on the radiometric quality of images and the efficiency of image processing algorithms. The main factor influencing the point cloud quality is noise. Such problems usually arise with data obtained via low-cost UAV platforms. Therefore, generated point clouds representing power lines are usually incomplete and noisy. To obtain a complete and accurate 3D model of power lines and towers, it is necessary to develop improved data processing algorithms. The experiment tested the algorithms on power lines with different voltages. This paper presents the wavelet-based method of processing data acquired with a low-cost UAV camera. The proposed, original method involves the application of algorithms for coarse filtration and precise filtering. In addition, a new way of calculating the recommended flight height was proposed. At the end, the accuracy assessment of this two-stage filtration process was examined. For this, point quality indices were proposed. The experimental results show that the proposed algorithm improves the quality of low-cost point clouds. The proposed methods improve the accuracy of determining the parameters of the lines by more than twice. About 10% of noise is reduced by using the wavelet-based approach.