A mathematical model-driven algorithm for inverse precision measurement and error evaluation of complex surfaces

Abstract Point cloud data acquired from complex surface measurements often contain noise and incompleteness due to equipment and registration errors. To address these challenges, this study proposes a mathematical model-driven inverse precision measurement and error evaluation method aimed at improving the accuracy and robustness of surface reconstruction. The approach enhances normal vector consistency through anisotropic normal vector smoothing, removes small-scale noise using bilateral filtering while preserving feature edges, and generates high-quality manifold point clouds using moving least squares (MLS) smoothing. Surface reconstruction is then performed using greedy projection triangulation with Delaunay triangulation to ensure mesh regularity. Experimental results show that the proposed method achieves RMSE values of 0.025 mm, 0.029 mm, and 0.022 mm on the Bunny, Dragon, and Blade models, respectively, outperforming Poisson reconstruction (0.049 mm, 0.057 mm, and 0.053 mm). In noise robustness testing, the method achieves an RMSE of 0.049 mm at 0.1 mm noise level, surpassing comparable techniques. Ablation analysis reveals that removing MLS smoothing increases the reconstruction error by 72 %, confirming its significance. The method also achieved an engineer subjective score of 90.5 points, and scalability experiments on the Lucy model maintained high accuracy (RMSE 0.062 mm). Overall, the proposed method provides a highly accurate, robust, and practical mathematical model-driven solution for reverse engineering of complex surfaces, significantly improving measurement reliability in real-world applications.