Implicit Uniform Rational Spline Reconstruction Method With Regularization Term

To improve the accuracy of implicit curve reconstruction and reduce the occurrence of supplementary zero-level sets during the reconstruction process, we propose an implicit curve fitting method with a regularization term based on uniform rational B-splines. First, an implicit uniform rational spline reconstruction model is established using an implicit B-spline reconstruction method. Second, by introducing internal and external offset points during reconstruction, the occurrence of supplementary zero-level sets is reduced, and a regularization term is added to adjust the structure of the reconstructed surface during iteration. Finally, a comparison is made with the I-PIA(implicit progressive iterative approximation) method under the same iteration steps and the same iteration accuracy. The proposed method demonstrates enhanced reconstruction precision and effectively ameliorates the characteristics of the reconstructed surface, which shows robustness in noisy datasets.