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A novel algorithm: fitting a spatial arc to noisy point clouds with high accuracy and reproducibility

Fitting a spatial arc to noisy point clouds with high accuracy and reproducibility is challenging, although it is important in many applications, such as precise measurement, computerized numerical control machining and robotic path planning. In optical measuring applications, an arc-shaped object is usually first scanned as point clouds by a 3D camera or multiple charge-coupled device cameras, and arc fitting is then invoked to fit these point clouds, obtaining the measuring radius and center. The accuracy of the arc-fitting algorithm plays an important role in the arc-measuring precision. In this paper, a novel algorithm is proposed to fit a spatial arc of high accuracy and reproducibility to noisy point clouds. This method combines the repeated least trimmed squares idea with the smoothing fairness function, i.e. discrete curvature, to devise the objective function, which is solved iteratively. This algorithm can successfully filter noise and fit a highly accurate arc to noisy point clouds with high reproducibility. Seven popular arc-fitting algorithms are implemented as benchmarks and both simulated and real data scanned from physical objects are tested to validate that the proposed algorithm performs best. The proposed algorithm is efficient and can be easily implemented in industrial applications.