HNC: a heatmap-guided normal centroid method for multi-line laser stripe centerline extraction with geometry-based ground truth.

In complex industrial 3D measurement, multi-line laser stripes are often degraded by specular reflection, low exposure, noise, and abrupt surface-curvature variation, leading to unstable centerline extraction. We present the heatmap-guided normal centroid (HNC) method for subpixel extraction of multi-line laser stripe centerlines. A physics-based Blender simulation is constructed, and accurate centerline ground truth computed from the geometric intersections between the laser planes and the mesh model is used to generate Gaussian energy-distribution heatmap supervision for network training and evaluation. A lightweight regression network predicts the heatmaps, from which subpixel centerline coordinates are decoded by structure-tensor normal estimation, normal-direction non-maximum suppression, and centroid refinement. For heatmap prediction, the method achieves Dice and IoU scores of 96.67% and 93.56%, respectively. With only 0.71 M parameters, EDR-Net averages 11.04 ms for heatmap prediction on a 768 × 768 input, while the complete HNC pipeline averages 209.97 ms on high-resolution real images. On real images without ground-truth centerlines, it achieves a point-to-spline RMSE of 0.2804 px for centerline-stability assessment, with reductions of 38.68% and 68.50% relative to the second-best method and the Steger algorithm. In train wheel measurement, the errors of wheel diameter, flange height, and flange thickness are reduced by 10.22%, 49.05%, and 71.43%, respectively. These results demonstrate the potential of the proposed method to provide robust and efficient multi-line laser stripe centerline extraction for high-precision industrial 3D measurement.