This study developed an algorithm capable of detecting a reference line (a 0.2 mm thick piano wire) to accurately determine the position of an automated installation robot within an elevator shaft. A total of 3,245 images were collected from the experimental tower of H Company, the leading elevator manufacturer in South Korea, and the detection performance was evaluated using four experimental approaches (GCH, GSCH, GECH, FCH). During the initial image processing stage, Gaussian blurring, sharpening filter, embossing filter, and Fourier Transform were applied, followed by Canny Edge Detection and Hough Transform. Notably, the method was developed to accurately extract the reference line by averaging the x-coordinates of the lines detected through the Hough Transform. This approach enabled the detection of the 0.2 mm thick piano wire with high accuracy, even in the presence of noise and other interfering factors (e.g., concrete cracks inside the elevator shaft or safety bars for filming equipment). The experimental results showed that Experiment 4 (FCH), which utilized Fourier Transform in the preprocessing stage, achieved the highest detection rate for the LtoL, LtoR, and RtoL datasets. Experiment 2(GSCH), which applied Gaussian blurring and a sharpening filter, demonstrated superior detection performance on the RtoR dataset. This study proposes a reference line detection algorithm that enables precise position calculation and control of automated robots in elevator shaft installation. Moreover, the developed method shows potential for applicability even in confined working spaces. Future work aims to develop a line detection algorithm equipped with machine learning-based hyperparameter tuning capabilities.