Fast Surface Reconstruction Technique Based on Anderson Accelerated I-PIA Method

For curve and surface reconstruction, the implicit progressive-iterative approximation (I-PIA) is widely used in many applications because it is efficient in data fitting and handling noise and missing data. By introducing Anderson extrapolation to the I-PIA, in this paper we exploit an accelerated method, namely AA-I-PIA, for the I-PIA of the B-spline function. For noisy point cloud data, we have exploited the regularized I-PIA and its accelerated version. We have shown that the AA-I-PIA method converges for appropriate parameters. Numerical results show that regardless of missing or noisy data, the (regularized) AA-I-PIA outperforms the classical I-PIA method regarding the number of iterations and elapsed CPU time.