Arc sag is an important parameter in the design and operation and maintenance of transmission lines and is directly related to the safety and reliability of grid operation. The current arc sag measurement method is inefficient and costly, which makes it difficult to meet the engineering demand for fast inspection of transmission lines. In view of this, this paper proposes an automatic spacer bar segmentation algorithm, CM-Mask-RCNN, that combines the CAB attention mechanism and MHSA self-attention mechanism, which automatically extracts the spacer bars and calculates the center coordinates, and combines classical algorithms such as beam method leveling, spatial front rendezvous, and spatial curve fitting, based on UAV inspection video data, to realize arc sag measurement with a low cost and high efficiency. It is experimentally verified that the CM-Mask-RCNN algorithm proposed in this paper achieves an AP index of 73.40% on the self-built dataset, which is better than the Yolact++, U-net, and Mask-RCNN algorithms. In addition, it is also verified that the adopted approach of fusing CAB and MHSA attention mechanisms can effectively improve the segmentation performance of the model, and this combination improves the model performance more significantly compared with other attention mechanisms, with an AP improvement of 2.24%. The algorithm in this paper was used to perform arc sag measurement experiments on 10 different transmission lines, and the measurement errors are all within ±2.5%, with an average error of −0.11, which verifies the effectiveness of the arc sag measurement method proposed in this paper for transmission lines.