Line-structured light measurement technology is widely used in the field of industrial inspection. In the measurement system, the center extraction accuracy of the laser stripe directly influences the final measurement accuracy. Unfortunately, some factors in the industrial environment significantly affect the center extraction of the laser stripe. For example, the rounded convexity on the surface of a detected object leads to a large change in the curvature of the collected laser stripe, and the reflections on the surface of the detected object lead to a laser stripe connected with reflective noise, resulting in severe interference. In these situations, existing algorithms, such as the geometric center, gray gravity, and Steger algorithms, cannot obtain proper extraction results. In case of a large curvature change, existing algorithms fail to accurately extract the center of the laser stripe along its normal direction, resulting in a large deviation from the actual center. In the case of severe interference, existing algorithms fail to efficiently avoid interference disturbances; thus, the interference is calculated as part of the laser stripe. Therefore, it is necessary to implement countermeasures to solve these problems and improve the applicability of the center extraction algorithm.

In this study, a center extraction algorithm for line-structured light based on unilateral tracking and midpoint prediction is proposed. The algorithm consists of three parts: laser stripe unilateral tracking, initial center-point determination based on the gray gravity and least-square algorithm, and center extraction based on the Hessian matrix. The upper boundary of the laser stripe is extracted using the proposed unilateral tracking algorithm according to the direction and grayscale of the laser stripe. The proposed unilateral tracking algorithm tracks only the upper boundary of the laser stripe and selectively searches the upper right, right, and lower right of the pixel eight-neighborhood when tracking each upper boundary point, thereby improving the processing speed of center extraction. In addition, the unilateral tracking algorithm can filter out small noises while performing unilateral tracking starting point searches. Simultaneously, the initial center point of the laser stripe is calculated using the gray gravity algorithm or least-square algorithm. In the laser stripe part without interference, the initial center point is calculated using the gray gravity algorithm. In the laser stripe part with serious interference (the signal-to-noise ratio is less than 15 dB, and the laser stripe is connected with noise), the initial center point is predicted by the least-square algorithm with a step length of 1 pixel. Finally, the Hessian matrix is used to modify the normal direction coordinates of the initial center point to improve the center extraction precision under large curvature change conditions. When constructing the Hessian matrix, the first-order and second-order partial derivatives are obtained from the pixel differential of the neighboring pixels at the initial center point, which reduces the complexity of the algorithm and ensures the accuracy of the center point.

Laser stripes with a large curvature change and serious interference are created to compare the accuracy and speed of the proposed algorithm with those of existing algorithms. Compared with the geometric center, gray gravity, and Steger algorithms, the laser stripe center extracted by the proposed algorithm is closer to the real direction (Figs.8 and 9), demonstrating that the proposed center-extraction algorithm for line-structured light based on unilateral tracking and midpoint prediction has the better center extraction accuracy. In the case of severe interference (the signal-to-noise ratio is 8.52 dB, and the laser stripe is connected with noise), the center extraction algorithm in this study shows the highest extraction accuracy, which is 65.19 times that of the geometric center algorithm, 8.89 times that of the gray gravity algorithm, and 5.76 times that of the Steger algorithm (Table 1). In the measurement accuracy experiment, the center extraction algorithm used in this study shows the best measurement accuracy, which is 2.44 times that of the geometric center algorithm, 2.32 times that of the gray gravity algorithm, and 2.06 times that of the Steger algorithm (Table 2 and Fig.14). In the processing speed experiment, the center extraction algorithm used in this study shows the fastest processing speed, which is 3.96 times that of the geometric center algorithm, 4.32 times that of the gray gravity algorithm, and 10.52 times that of the Steger algorithm (Table 3). Furthermore, the center extraction algorithm proposed in this study is applicable to different types of laser stripes, such as folded lines, arcs, diagonal arc tangents, and continuous variation curves (Fig.15).

This study proposes a center-extraction algorithm for line-structured light based on unilateral tracking and midpoint prediction, which proves that the proposed algorithm can deal with laser stripe under the conditions with large curvature change or serious interference and obtain proper results. In addition, the proposed algorithm is faster and more applicable than existing algorithms. These advantages enable the proposed algorithm to provide support for line-structured light measurements under non-ideal conditions.