The precise extraction of laser stripe centerlines is critical for line-laser 3D scanning systems. However, conventional methods relying on threshold segmentation and morphological operations face significant challenges when confronted with pervasive optical phenomena, including specular reflection, scattering, and bleeding, which are commonly observed in translucent optical components. These methods typically require complex preprocessing procedures and often yield poor precision in centerline extraction. In this paper, we introduce a novel learning-based approach, complemented by a meticulously curated dataset, explicitly designed to address these challenges. Our proposed method leverages a multi-scale attention U-Net-like architecture, initially tasked with the segmentation of laser stripes from the complex background environment. Subsequently, it employs the Steger algorithm for the precise extraction of laser stripe centerlines. The experimental results, obtained by comprehensively evaluating real-world captured images, clearly demonstrate the effectiveness of our deep neural network combined with the Steger algorithm. This combined approach exhibits exceptional accuracy even when challenged by the interferences from specular reflection, scattering, and bleeding artifacts. Specifically, our method achieves a mean intersection over union (mIoU) of 84.71% for the laser stripe detection task, accompanied by a mean square error (MSE) of 10.371 pixels. Also, the average execution time for the centerline extraction task is notably efficient at 0.125 s.