Hardware-Oriented Algorithm for High-Speed Laser Centerline Extraction Based on Hessian Matrix

Centerline extraction is the basic and key procedure in line-structured laser 3-D scanners. In this article, we propose a hardware-oriented algorithm for fast and accurate extraction of a laser centerline based on the Hessian matrix. The algorithm is divided into three low-coupling modules that can be processed in parallel - coarse positioning, linewidth estimation, and precise positioning module. In the coarse positioning module, a window slider is used to traverse all image pixels in the raster-scan mode for collecting local image features, based on which the potential region of interest (ROI) containing laser lines is detected. In the linewidth estimation module, the second-order moment features in the detected ROI are calculated to estimate the linewidth according to the local rectangular similarity characteristics of the laser line. In the precise positioning module, the optimal Gaussian template estimated by the linewidth is convolved with the ROI to obtain the Hessian matrix. Based on the Hessian matrix, the normal direction of the laser line is obtained, and the second-order Taylor expansion is performed in that direction to determine the subpixel position of the center point. Finally, non-maximum suppression is used to remove noise points and obtain the most reliable single-pixel centerline. The proposed algorithm is evaluated using thousands of sample images with different materials, exposure times, and laser line shapes, and it presents high robustness for subpixel precision extraction. By implementing the proposed algorithm on a field-programmable gate array (FPGA), a high-speed, high-precision laser centerline extraction system is achieved, which operates at 1350 frames/s for a 1-million-pixel video stream.