Currently, the approximation methods of the Gaussian filter by some other spline filters have been developed. However, thesc methods are only suitable for the study of one-dimensional filtering, when these methods are...Currently, the approximation methods of the Gaussian filter by some other spline filters have been developed. However, thesc 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 （t1, t2）, 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.展开更多
基金Supported by National Natural Science Foundation of China(Grant Nos51175085,51375094)Fujian Provincial Education Department Foundation of China(Grant No.JA13059)+1 种基金Open Fund of State Key Laboratory of Tribology of Tsinghua University,China(Grant No.SKLTKF13B02)Fuzhou Science and Technology plan Fund of China(Grant No.2014-G-74)
文摘Currently, the approximation methods of the Gaussian filter by some other spline filters have been developed. However, thesc 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 （t1, t2）, 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.
