Least square geometric iterative fitting method for generalized B-spline curves with two different kinds of weights

Zhang, Li; Ge, Xianyu; Tan, Jieqing

doi:10.1007/s00371-015-1170-3

Cited by 27 publications

(9 citation statements)

References 20 publications

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“…]. By replacing the B-spline basis with the generalized B-spline basis, it is generalized in [9] to the weighted least square fitting curve, and, by replacing the tensor product B-spline basis with the non-tensor product bivariate B-spline basis, extended in [13] to the regularized least square fitting surface.…”

Section: Related Workmentioning

confidence: 99%

“…To compare with the LSPIA method, the other trivial choice is to use the same initial control points as that used by another authors in numerical experiments. Since the initial control point set is selected as a subset of the given data set in [7,9], we choose them as initial control points, too, and let…”

Section: Initial Control Pointsmentioning

confidence: 99%

“…Since it is linear, the construction of the method may be simpler. One can look for more details about these two kinds of fittings, for examples, in [1][2][3][4][5][6][7][8][9][10][11][12][13][14] and references therein.…”

Section: Introductionmentioning

confidence: 99%

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On a progressive and iterative approximation method with memory for least square fitting

Huang

Wang

2019

Preprint

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In this paper, we present a progressive and iterative approximation method with memory for least square fitting (MLSPIA). It adjusts the control points and the weighted sums iteratively to construct a series of fitting curves (surfaces) with three weights. For any normalized totally positive basis even when the collocation matrix is of deficient column rank, we obtain a condition to guarantee that these curves (surfaces) converge to the least square fitting curve (surface) to the given data points. It is proved that the theoretical convergence rate of the method is faster than the one of the progressive and iterative approximation method for least square fitting (LSPIA) in [Deng C-Y, Lin H-W. Progressive and iterative approximation for least squares B-spline curve and surface fitting. Computer-Aided Design 2014;47:32-44] under the same assumption. Examples verify this phenomenon.

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Section: Related Workmentioning

confidence: 99%

Section: Initial Control Pointsmentioning

confidence: 99%

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On a progressive and iterative approximation method with memory for least square fitting

Huang

Wang

2019

Preprint

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“…2014 年, Deng 等 [10] 提出基于最小二乘的渐进迭代逼近方法(progressive iterative approximation for least squares, LSPIA), 与传统的最小二乘方法相比, LSPIA 不仅具备传统 PIA 的优良性质, 还可以高效、直观地处理大规模数据点集. Zhang 等 [11][12] 研究了广义 B 样条的 LSPIA 算法, 并给出可以减少拟合误差. 有大量文献 [16][17][18][19] 对此进行了研究, 现有参数的选择包括均匀参数化法、累加弦长法、向心参数法, 也可以通过一些其他方法对参数进行调整.…”

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Discrete Data Points Fitting Based on Optimization of B-Spline Parameters Using Step-Acceleration Method

Zhang¹,

Zhang²,

Yao³

et al. 2021

J Comput-Aided Design Comput Graphics

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When fitting discrete data points by iterative method, the parameterization of data points will affect the approximation effect and speed at the same time. A method of optimizing the parameters of control vertices and data points by iterative adjustment is proposed, which converges faster and fits the original data points better.Firstly, the initial control vertices are selected, and the adaptive BFGS method is used to optimize the control vertices and obtain the fitting curve. Secondly, the parameters corresponding to data points are optimized by the step-size acceleration method while the control vertices are kept unchanged. Finally, the new parameters are used to re-optimize the control vertices and a new fitting curve is obtained. Numerical examples show that the convergence speed in the early iteration stage of the given algorithm is faster than most existing iterative methods. Furthermore, the optimized curves are much closer to discrete data points and fitting error are much smaller.

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“…Lu [11] 提出了加权 PIA 算法来加快经典 PIA 的收敛速度. 基于广义 B 样条, 另一种具有不同权重的 LSPIA 算法被提出以拟合更复杂的数据点 [12][13] . 此外, Liu 等 [14] 提出了用于正则化最小二乘双变量 B 样条曲面拟合算法 (progressive iterative approximation for regularized least square bivariate B-spline surface fitting, RLSPIA), 将单变量 NTP 的 PIA 性质推广至线性相关的非张量积型二元 B 样条基.…”

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Gauss-Seidel Progressive and Iterative Approximation for Least Squares Fitting

Yusuf¹,

Jiang²,

Lin³

2021

J Comput-Aided Design Comput Graphics

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Progressive-iterative approximation (PIA) is an efficient method for data fitting that attracts the attention of many researchers and has a wide range of applications. However, the convergence rate of LSPIA is prolonged. In this study, we design a fast PIA format based on the Gauss-Seidel iterative method named Gauss-Seidel progressive and iterative approximation for least squares curve and surface fitting (GS-LSPIA). Firstly, the control points of the fitting curve (surface) are selected from the given data points.Then, the chord length method is used to assign the parameters of the given data points. GS-LSPIA generates a series of fitting curves (surfaces) by refining the control points iteratively, and the limit of the generated curve (surface) is the least square fitting result to the given data points. Several experimental results presented in this paper demonstrate that, to achieve the same accuracy for GS-LSPIA and LSPIA, GS-LSPIA required fewer steps and shorter running time compared with LSPIA. Thus, the proposed GS-LSPIA is efficient and has a faster convergence rate compared with the LSPIA algorithm.

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Least square geometric iterative fitting method for generalized B-spline curves with two different kinds of weights

Cited by 27 publications

References 20 publications

On a progressive and iterative approximation method with memory for least square fitting

On a progressive and iterative approximation method with memory for least square fitting

Discrete Data Points Fitting Based on Optimization of B-Spline Parameters Using Step-Acceleration Method

Gauss-Seidel Progressive and Iterative Approximation for Least Squares Fitting

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