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Smoothing of Partition of Unity Implicit Surfaces for Noise Robust Surface Reconstruction
Author(s) -
Nagai Yukie,
Ohtake Yutaka,
Suzuki Hiromasa
Publication year - 2009
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/j.1467-8659.2009.01511.x
Subject(s) - smoothing , partition of unity , laplace operator , partition (number theory) , grid , mathematics , surface (topology) , laplacian smoothing , noise (video) , algorithm , computer science , mathematical analysis , geometry , mesh generation , computer vision , image (mathematics) , physics , combinatorics , finite element method , thermodynamics
We propose a novel method for smoothing partition of unity (PU) implicit surfaces consisting of sets of non‐conforming linear functions with spherical supports. We derive new discrete differential operators and Laplacian smoothing using a spherical covering of PU as a grid‐like data structure. These new differential operators are applied to the smoothing of PU implicit surfaces. First, Laplacian smoothing is performed for the vector field defined by the gradient of the PU implicit surface, which is then updated to reflect the smoothing of the gradient field. This process achieves a method for noise robust surface reconstruction from scattered points.