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Welding is a fabrication process used to join or fuse two mechanical parts. Modern welding machines have automated lasers that follow a pre-defined weld seam path between the two parts to create a bond. Previous efforts have used simple computer vision edge detectors to automatically detect the weld seam edge on an image at the junction of two metals to be welded. However, these systems lack reliability and accuracy resulting in manual human verification of the detected edges. This paper presents a neural network architecture that automatically detects the weld seam edge between two metals with high accuracy. We augment this system with a pre-classifier that filters out anomalous workpieces (e.g., incorrect placement). Finally, we justify our design choices by evaluating against several existing deep network pipelines as well as proof through real-world use. We also describe in detail the process of deploying this system in a real-world shop floor including evaluation and monitoring. We make public a large, well-labeled laser seam dataset to perform deep learning-based edge detection in industrial settings.