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 arise in the reconstruction process makes the reconstruction result challenging to be interpreted and damage the final result. In this paper, we proposed an implicit curve and surface reconstruction method based on the progressive-iterative approximation method, named implicit progressive-iterative approximation (I-PIA). The proposed method elegantly eliminates the spurious sheets naturally without requiring any explicit minimization procedure, thus reducing the computational cost greatly and providing high-quality reconstruction results. Numerical examples are provided to demonstrate the efficiency and effectiveness of the proposed method.

High-Precision 3D Reconstruction for Small-to-Medium-Sized Objects Utilizing Line-Structured Light Scanning: A Review

“…Meanwhile, Hamza et al applied the progressive iterative approximation (PIA) method to the implicit curve and surface reconstruction process for the first time, where the convergence is proved. This algorithm can solve the minimization problem with regularization terms, improving the reconstruction efficiency of implicit curves and surfaces [110].…”

New Progressive Iterative Approximation Techniques for Shepard-Type Curves

“…We compare the same helix example for variant 2 of PIA process (15). In Figure 3 corresponding curves at the initial step and after 1, 2, and 3 iterations are presented.…”

“…[10,11]). Applications of PIA techniques to image super-resolution, video data compression, online handwritten synthesis, implicit curve reconstruction, fairing curve generation, local modeling, offset of planar curves, conversion of rational curves into nonrational curves, and least squares fitting are also studied [12][13][14][15][16][17][18][19][20].…”

Approximating triangular meshes by implicit, multi-sided surfaces

“…There is a vast range of algorithms for creating implicit surfaces interpolating or approximating point data. These can be categorized into several classes, such as methods based on local approximations [6,14], algebraic splines [7,4], radial basis functions [2,15], moving least squares [17], Poisson surface reconstruction [8], or even neural networks [19]. All of these methods are very general, and can be used on unorganized point sets.…”