A Proposal of a Spline Filter that Achieves Both Robustness and Lower Compatibility
A Proposal of a Spline Filter that Achieves Both Robustness and Lower Compatibility
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一种兼具鲁棒性和低兼容性的样条滤波器的提案
DOI：
10.1007/s41871-020-00092-1
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发表时间：
2021
影响因子：
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通讯作者：
Hiroyasu Koshimizu
中科院分区：
文献类型：
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作者：
Yuki Kondo;Munetoshi Numada;Keiya Takahashi;Ichiro Yoshida; Hiroyasu Koshimizu
样条滤波器用于提取粗糙度轮廓，用于测量表面纹理，并且在无法获得原始轮廓之前和之后的足够部分时非常有用。这是因为样条滤波器可以防止端部效应，端部效应是在主轮廓的两端周围发生的输出数据的波动，并且取决于滤波器的加权函数的宽度。样条滤波器是基于逆矩阵的计算，而不是滤波器的加权函数的卷积。当输入数据中含有异常值时，样条滤波器的输出会产生很大的波动。为了解决这个问题，我们提出了一种鲁棒样条滤波器。然而，当输入数据不包括异常值时，鲁棒样条滤波器的输出与样条滤波器的输出不一致。因此，鲁棒样条滤波器不具有较低的兼容性。本文提出了一种快速M估计样条滤波器（FMSF）。FMSF使用快速M估计方法。FMGF对含有野值的输入数据具有较强的鲁棒性，对不含野值的输入数据，其输出与一般样条滤波器相同。在不存在离群值的情况下，用该方法估计的值与用最小二乘法估计的值是一致的。为了将快速M估计方法应用到样条滤波器中，用权函数的卷积代替求逆矩阵。并对剪切拉伸和点对称拉伸的输入几何进行了预处理，以防止端部效应。
A spline filter is used to extract roughness profiles for the measurement of surface texture and is useful when sufficient sections before and after a primary profile could not be secured. This is because a spline filter could prevent the end effect, which is the fluctuation of output data that occurs around both ends of the primary profile and depends on the width of the weighting function of a filter. The spline filter is based on the calculation of an inverse matrix instead of the convolution of the weighting function of the filters. When input data include outliers, the output of a spline filter greatly fluctuates. To solve this problem, we propose a robust spline filter. However, output of the robust spline is not in agreement with that of the spline filter when input data do not include outliers. Thus, the robust spline filter has no lower compatibility. In this paper, the "Fast M-estimation Spline Filter (FMSF)" is proposed. FMSF uses the fast M-estimation method. FMGF performs robust to input data including outliers, and gives the same output as that of general spline filters to input data without outliers. The value estimated by this method is in agreement with that estimated by the least squares method if no outlier exists. In order to apply the fast M-estimation method to the spline filter, convolution of weight function is used instead of the inverse matrix. And the input geometry with shear and point-symmetric extensions is pre-processed to prevent the end effect.
一种基于快速M估计方法的鲁棒高斯滤波器的提出
影响因子：
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作者：
M. Numada;T. Fujiwara;T. Funahashi;H. Koshimizu;K. Kamiya;T. Nomura
通讯作者：
T. Nomura
粗糙度轮廓的鲁棒过滤算法
影响因子：
0.5
作者：
B. N. Markov;A. V. Shulepov
通讯作者：
A. V. Shulepov
DOI：
10.1098/rspa.2013.0150
发表时间：
2013
期刊：
Mathematical, Physical and Engineering Sciences
影响因子：
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作者：
Lou S
通讯作者：
Lou S