Estimating differential quantities from point cloud based on a linear fitting of normal vectors |
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Authors: | ZhangLin Cheng XiaoPeng Zhang |
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Affiliation: | (1) Sino-French Laboratory LIAMA, National Laboratory of Pattern Recognition, Institute of Automation, Chinese Academy of Sciences, Beijing, 100080, China |
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Abstract: | Estimation of differential geometric properties on a discrete surface is a fundamental work in computer graphics and computer
vision. In this paper, we present an accurate and robust method for estimating differential quantities from unorganized point
cloud. The principal curvatures and principal directions at each point are computed with the help of partial derivatives of
the unit normal vector at that point, where the normal derivatives are estimated by fitting a linear function to each component
of the normal vectors in a neighborhood. This method takes into account the normal information of all neighboring points and
computes curvatures directly from the variation of unit normal vectors, which improves the accuracy and robustness of curvature
estimation on irregular sampled noisy data. The main advantage of our approach is that the estimation of curvatures at a point
does not rely on the accuracy of the normal vector at that point, and the normal vectors can be refined in the process of
curvature estimation. Compared with the state of the art methods for estimating curvatures and Darboux frames on both synthetic
and real point clouds, the approach is shown to be more accurate and robust for noisy and unorganized point cloud data.
Supported in part by the National Natural Science Foundation of China (Grant Nos. 60672148, 60872120), the National High-Tech
Research & Development Program of China (Grant Nos. 2006AA01Z301, 2008AA01Z301), and Beijing Municipal Natural Science Foundation
(Grant No. 4062033) |
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Keywords: | differential geometric properties point cloud normal fitting Weingarten matrix |
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