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3D profile filter algorithm based on parallel generalized B-spline approximating Gaussian

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Abstract

Currently, the approximation methods of the Gaussian filter by some other spline filters have been developed. However, these methods are only suitable for the study of one-dimensional filtering, when these methods are used for three-dimensional filtering, it is found that a rounding error and quantization error would be passed to the next in every part. In this paper, a new and high-precision implementation approach for Gaussian filter is described, which is suitable for three-dimensional reference filtering. Based on the theory of generalized B-spline function and the variational principle, the transmission characteristics of a digital filter can be changed through the sensitivity of the parameters (t 1, t 2), and which can also reduce the rounding error and quantization error by the filter in a parallel form instead of the cascade form. Finally, the approximation filter of Gaussian filter is obtained. In order to verify the feasibility of the new algorithm, the reference extraction of the conventional methods are also used and compared. The experiments are conducted on the measured optical surface, and the results show that the total calculation by the new algorithm only requires 0.07 s for 480×480 data points; the amplitude deviation between the reference of the parallel form filter and the Gaussian filter is smaller; the new method is closer to the characteristic of the Gaussian filter through the analysis of three-dimensional roughness parameters, comparing with the cascade generalized B-spline approximating Gaussian. So the new algorithm is also efficient and accurate for the implementation of Gaussian filter in the application of surface roughness measurement.

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Authors and Affiliations

  1. School of Mechanical Engineering and Automation, Fuzhou University, Fuzhou, 350108, China

    Zhiying Ren & Chenghui Gao

  2. Tribology Research Institute, Fuzhou University, Fuzhou, 350108, China

    Zhiying Ren & Chenghui Gao

  3. Fujian Institute of Metrology, Fuzhou, 35000, China

    Ding Shen

Authors
  1. Zhiying Ren
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  2. Chenghui Gao
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  3. Ding Shen
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Corresponding author

Correspondence to Chenghui Gao.

Additional information

Supported by National Natural Science Foundation of China (Grant Nos. 51175085, 51375094), Fujian Provincial Education Department Foundation of China (Grant No. JA13059), Open Fund of State Key Laboratory of Tribology of Tsinghua University, China (Grant No. SKLTKF13B02), and Fuzhou Science and Technology plan Fund of China (Grant No. 2014-G-74)

REN Zhiying, born in 1980, is currently a PhD candidate at School of Mechanical Engineering and Automation, Fuzhou University, China. She received her master degree from Fuzhou University, China, in 2006. Her research interests include tribological and signal processing.

GAO Chenghui, born in 1953, is currently a professor at Fuzhou University, China. He received his PhD degree from Mechanical Science Research Institute, China, in 1990. His research interests include mechachonics engineering, tribological, digital design.

SHEN Ding, born in 1988, is currently an engineer at Fujian Institute of Metrology, China. He received his master degree on mechanical design and theory from Fuzhou University, China, in 2014.

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Ren, Z., Gao, C. & Shen, D. 3D profile filter algorithm based on parallel generalized B-spline approximating Gaussian. Chin. J. Mech. Eng. 28, 148–154 (2015). https://doi.org/10.3901/CJME.2014.1106.163

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  • DOI: https://doi.org/10.3901/CJME.2014.1106.163

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