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An, Y., Shao, C., Wang, X. and Li, Z. (2010). Geometric Properties Computation for Discrete Curves Based on Discrete Derivatives. 2010 International Conference on Intelligent Control and Information Processing, Dalian, 13-15 August 2010, 217-224.
https://doi.org/10.1109/icicip.2010.5564203

has been cited by the following article:

• TITLE: Gaussian Distance Weighted Algorithm for Geometric Characteristics of Three-Dimensional Discrete Curves

  AUTHORS: Liyan Zhang, Haiyi Ai, Shaohong Yan, Haili Chen, Jiali Zou, Junqing Zhang

  KEYWORDS: Discrete Curve, Angle Weight, Algorithm Comparison, Underground Pipeline Inspection

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.12 No.10, October 30, 2024

  ABSTRACT: Discrete curves are composed of a set of ordered discrete points distributed at the intersection of the scanning plane and the surface of the object. In order to accurately calculate the geometric characteristics of any point on the discrete curve, a distance-based Gaussian weighted algorithm is proposed to estimate the geometric characteristics of three-dimensional space discrete curves. According to the definition of discrete derivatives, the algorithm fully considers the relative position difference between a specific point and its neighboring points, introduces the distance weighting idea, and integrates the smoothing strategy. The experiment uses two spatial discrete curves for uniform and non-uniform sampling, and compares them with two commonly used estimation algorithms. The comparative analysis is carried out in terms of sampling density, neighborhood radius and noise resistance. The experimental results show that the Gaussian distance weighted algorithm is effective and provides an efficient algorithm for underground pipeline safety detection.