Fast surface reconstruction algorithm with adaptive step size

In (Dai et al. 2023), the authors proposed a fast algorithm for surface reconstruction that converges rapidly from point cloud data by alternating Anderson extrapolation with implicit progressive iterative approximation (I-PIA). This algorithm employs a fixed step size during iterations to enhance convergence. To further improve the computational efficiency, an adaptive step size adjustment strategy for surface reconstruction algorithm is investigated. During each iteration, the step size is adaptively chosen based on the current residual—larger residuals may necessitate larger steps, while smaller ones might permit smaller steps. Numerical experiments indicate that, for equivalent reconstruction errors, the adaptive step size algorithm demands substantially fewer iterations and less computation time than the fixed step size approach. These improvements robustly enhance computational performance in surface reconstruction, offering valuable insights for further research and applications.