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As part of a novel approach to automatic sewer inspection, this paper presents a robust algorithm for automatic flow line detection. A large image repository is obtained from about 50,000 m sewers to represent the high variability of real world sewer systems. Automatic image processing combines Canny edge detection, Hough transform for straight lines and cost minimization using Dijkstra's shortest path algorithm. Assuming that flow lines are mostly smoothly connected horizontal structures, piecewise flow line delineation is reduced to a process of selecting adjacent line candidates. Costs are derived from the gap between adjacent candidates and their reliability. A single parameter α enables simple control of the algorithm. The detected flow line may precisely follow the segmented edges (α = 0.0) or minimize gaps at joints (α = 1.0). Both, manual and ground truth-based analysis indicate that α = 0.8 is optimal and independent of the sewer's material. The algorithm forms an essential step to further automation of sewer inspection.