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 filt...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.展开更多
基金This study is supported by a Grant-in-Aid for Scientific Research No.20K04202 from Japan Society for the Promotion of Science(JSPS).We would like to thank Editage(www.editage.com)for English language editing.
文摘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.
