NUMERICAL ANALYSIS & FAST ALGORITHM

Acquisition, creation and processing of 3D digital objects is an important topic in various fields, e.g., medical imaging, computer graphics, and preservation of cultural heritage. A fundamental step is to reconstruct a surface from a set of point cloud data. We explored fast algorithms for minimizing the surface-to-point-cloud weighted surface area, which greatly improve the computational efficiency compared to the original gradient descent scheme. Specifically, we investigated a semi-implicit scheme that allows for larger time step and an ADMM-type approach. For the ADMM method, we also analyzed the choice of algorithmic parameters.

[He et al. 2019, arXiv]