Implicit progressive-iterative approximation for curve and surface reconstruction

Abstract

Implicit curve and surface reconstruction attracts the attention of many researchers and gains a wide range of applications, due to its ability to describe objects with complicated geometry and topology. However, extra zero-level sets or spurious sheets arising in the reconstruction process make the reconstruction result challenging to be interpreted and damage the final result. In this paper, we propose an implicit curve and surface reconstruction method based on the progressive-iterative approximation, named implicit progressive-iterative approximation (I-PIA). The proposed method elegantly and naturally eliminates the spurious sheets without requiring any explicit minimization procedure, thus significantly reducing the computing cost and providing high-quality reconstruction results. Numerical examples are presented to demonstrate the efficiency and effectiveness of the proposed method.