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http://dx.doi.org/10.15701/kcgs.2016.22.5.1

Curve Reconstruction from Oriented Points Using Hierarchical ZP-Splines  

Kim, Hyunjun (Department of Computer Science and Engineering, University of Seoul)
Kim, Minho (Department of Computer Science and Engineering, University of Seoul)
Publication Information
Journal of the Korea Computer Graphics Society / v.22, no.5, 2016 , pp. 1-16 More about this Journal
Abstract
In this paper, we propose and efficient curve reconstruction method based on the classical least-square fitting scheme. Specifically, given planar sample points equipped with normals, we reconstruct the objective curve as the zero set of a hierarchical implicit ZP(Zwart-Powell)-spline that can recover large holes of dataset without loosing the fine details. As regularizers, we adopted two: a Tikhonov regularizer to reduce the singularity of the linear system and a discrete Laplacian operator to smooth out the isocurves. Benchmark tests with quantitative measurements are done and our method shows much better quality than polynomial methods. Compared with the hierarchical bi-quadratic spline for datasets with holes, our method results in compatible quality but with less than 90% computational overhead.
Keywords
curve reconstruction; Least-square fitting; Hierarchical spline; ZP-splines; Regularization;
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