An Improved Moving Least Squares Method for Curve and Surface Fitting

Zhang, Lei; Gu, Tianqi; Zhao, Jun; Ji, Shijun; Hu, Ming; Li, Xiangbo

doi:10.1155/2013/159694

Cited by 14 publications

(8 citation statements)

References 20 publications

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“…Not only the calculation efficiency is faster, but also the order of the basis function is easier to change. The augmented matrix [33,36] can be expressed as…”

Section: Mtls Methodsmentioning

confidence: 99%

A trimmed moving total least-squares method for curve and surface fitting

Tang

et al. 2020

Meas. Sci. Technol.

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The Moving Least Squares (MLS) method has been developed for fitting of the measurement data contaminated with errors. The local approximants of the MLS method only take the random errors of the dependent variable into account, whereas the independent variables of measurement data always contain errors. To consider the influence of errors of dependent and independent variables, the Moving Total Least Squares (MTLS) offers a better choice. However, both MLS and MTLS method are sensitive to outliers, which greatly affects the fitting accuracy and robustness. This paper presents an improved method-Trimmed Moving Total Least Squares (TrMTLS) method, in which Total Least Squares (TLS) method with truncation procedure is adopted to determine the local coefficients in the influence domain. This method can deal with outliers and random errors of all variables without setting the threshold or adding small weights subjectively. The numerical simulation and measurement experiments results indicate that the proposed algorithm has better fitting accuracy and robustness compared with the MTLS and MLS method.

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“…Not only the calculation efficiency is faster, but also the order of the basis function is easier to change. The augmented matrix [33,36] can be expressed as…”

Section: Mtls Methodsmentioning

confidence: 99%

A trimmed moving total least-squares method for curve and surface fitting

Tang

et al. 2020

Meas. Sci. Technol.

Self Cite

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“…Since the initial edges extracted by fractional Gaussian differential are small line segments with noised fluctuations, they should be properly corrected and estimated to be a clear and accurate edge line. Based on moving least square regression (MLSR) [25,26], we improve the least square fitting used in previous work [14] for more accurate and robust solder panel edge estimation.…”

Section: Mlsr Based Edge Estimation Algorithmmentioning

confidence: 99%

“…As for solar panel position determination, accurate edges location is prerequisite. To achieve this, we extract the initial edge points by a novel signal processing method, fractional calculus [16,[22][23][24], and then utilize MLSR algorithm [25,26] to refine initial edges. Once the final edges of solder panel are acquired, the position parameters, position shift, deflection angle, and edge lengths, are easily determined.…”

Section: Introductionmentioning

confidence: 99%

Extreme Learning Machine and Moving Least Square Regression Based Solar Panel Vision Inspection

Liu

Zhang²,

Huang

2017

Journal of Electrical and Computer Engineering

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In recent years, learning based machine intelligence has aroused a lot of attention across science and engineering. Particularly in the field of automatic industry inspection, the machine learning based vision inspection plays a more and more important role in defect identification and feature extraction. Through learning from image samples, many features of industry objects, such as shapes, positions, and orientations angles, can be obtained and then can be well utilized to determine whether there is defect or not. However, the robustness and the quickness are not easily achieved in such inspection way. In this work, for solar panel vision inspection, we present an extreme learning machine (ELM) and moving least square regression based approach to identify solder joint defect and detect the panel position. Firstly, histogram peaks distribution (HPD) and fractional calculus are applied for image preprocessing. Then an ELM-based defective solder joints identification is discussed in detail. Finally, moving least square regression (MLSR) algorithm is introduced for solar panel position determination. Experimental results and comparisons show that the proposed ELM and MLSR based inspection method is efficient not only in detection accuracy but also in processing speed.

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“…This method has been shown to provide better approximation performance for irregular shape curves with its local control ability. 25,26 It starts with a weighted least squares formulation for an arbitrary fixed point and then move this point over the entire parameter domain, where a weighted least squares fit is calculated for each measured point individually.…”

Section: Geometric Error Parameter Modeling Based On Moving Least Squmentioning

confidence: 99%

An investigation on modeling and compensation of synthetic geometric errors on large machine tools based on moving least squares method

Feng

Yang

et al. 2016

Proceedings of the Institution of Mechanical Engineers, Part B:

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This article intends to provide an efficient modeling and compensation method for the synthetic geometric errors of large machine tools. Analytical and experimental examinations were carried out on a large gantry-type machine tool to study the spatial geometric error distribution within the machine workspace. The result shows that the position accuracy of the tool-tip is affected by all the translational axes synchronously, and the position error curve shape is non-linear and irregular. Moreover, the angular error combined with Abbe's offset during the motion of a translational axis would cause Abbe's error and generate significant influence on the spatial positioning accuracy. In order to identify the combined effect of the individual error component on the tool-tip position accuracy, a synthetic geometric error model is established for the gantry-type machine tool. Also, an automatic modeling algorithm is proposed to approximate the geometric error parameters based on moving least squares in combination with Chebyshev polynomials, and it could approximate the irregular geometric error curves with high-order continuity and consistency with a low-order basis function. Then, to implement real-time error compensation on large machine tools, an intelligent compensation system is developed based on the fast Ethernet data interaction technique and external machine origin shift, and experiment validations on the gantry-type machine tool showed that the position accuracy could be improved by 90% and the machining precision could be improved by 85% after error compensation.

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An Improved Moving Least Squares Method for Curve and Surface Fitting

Cited by 14 publications

References 20 publications

A trimmed moving total least-squares method for curve and surface fitting

A trimmed moving total least-squares method for curve and surface fitting

Extreme Learning Machine and Moving Least Square Regression Based Solar Panel Vision Inspection

An investigation on modeling and compensation of synthetic geometric errors on large machine tools based on moving least squares method

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