## 5 Conclusions  
This paper clarified the characteristics of SF-based robust filters, which filters can deal with outliers and shape components, and verified the cases in which problems arise. Consequently, it was confirmed that each RSF, RL2-RSF and FMSF, could remove the effect of spikes to a practically acceptable level when their height is more than twice the maximum of the normal roughness component. On the other hand, when the height of the spike is less than twice the height of the maximum roughness component, this spike is impossible for the human eye to distinguish between spike and roughness. In this case, the effect on the roughness profile is marginal, even when using SF. Therefore, RL2-RSF and FMSF have no practical problems with spike height.  
In the case of the widths of outliers (spike and step), RL2-RSF removes width 0.5\(\lambda\)c or less outlier as a spike. However, this criterion varies slightly depending on the primary profile (roughness component, waviness component, and shape component). When the width exceeds 0.5\(\lambda\)c, the RL2-RSF blunted the step around the boundary. Therefore, if the purpose is to extract as a step, the RL2-RSF cannot extract the step accurately and should be used with caution. On the other hand, when the width is less than 0.2\(\lambda\)c outlier, the FMSF removes it as a spike, whereas when the width of the outlier is more than 0.5\(\lambda\)c, the FMSF extracts the shape component as a step. Therefore, the FMSF may cause problems if the width of the outlier is between 0.2\(\lambda\)c and less than 0.5\(\lambda\)c.  
The arc was verified as another example of a realistic shape component likely to cause problems; no problems were encountered with either RSF.  
The primary profile, including all spikes, steps and arcs, is verified. As a result, the same characteristics were confirmed for each of them alone.  
From these results, a figure that shows the characteristics of RL2-RSF and FMSF (Figure 9) is created. And a flowchart regarding which RSF should be used in which  
Figure 10: Flow chart of RL2-RSF and FMSF for filter selection.  
situations (Figure 10) is created. Those outcomes did not exist prior to this paper in the authors' knowledge. These results are expected to contribute not only to the spread and use of each RSF in the industrial world but also to avoid confusion at the measurement site and to help establish new RSF standards.  
Conceptualization, I.Y.; methodology, I.Y. and Y.K.; software, Y.K.; validation, Y.K. and I.Y.; formal analysis, Y.K. and I.Y.; investigation, Y.K., I.Y., R.S. and K.F.; resources, Y.K., I.Y. and M.N.; data curation, Y.K., R.S. and K.F.; writing--original draft preparation, Y.K.; writing--review and editing, I.Y., Y.K., R.S., K.F., M.N. and H.K.; visualization, Y.K. and I.Y.; supervision, I.Y.; project administration, I.Y.; funding acquisition, I.Y. and M.N. All authors have read and agreed to the published version of the manuscript.  
This work was partly supported by the Precise Measurement Technology Promotion Foundation (PMTP-F).  
Not applicable.  
The data presented in this study are available in article.  
The authors declare no conflict of interest.