The Effect of Surface Topography Feature Size Density and Distribution on the Results of a Data Processing and Parameters Calculation with a Comparison of Regular Methods

In this paper, the influence of occurrence of surface texture features on the values of surface topography parameters calculated after the application of various data processing techniques was presented. Different types of surface topographies were considered, as follows: cylinder liners, some with additionally burnished dimples, turned, ground, milled, laser-textured, composite, ceramic, or isotropic in general. The effects of feature size on the areal form removal, noise suppressions, or end-effect reducing in surface texture measurements were studied. The variations of the ISO 25178 standard surface topography parameters were taken into consideration in detail. It was assumed that some of the feature sizes, distributions, and densities have a substantial impact on the values of surface topography parameters calculated after applications of regular (commonly used) algorithms and procedures, defined as basic operations, provided for raw surface texture data obtained directly from the measurement process. In the end, some of the practical applications for receiving the relevant values of surface topography parameters were proposed.


Introduction
The surface topography (ST) is created in the last stages of the manufacturing process. The results of its analysis, including calculating the values of ST parameters, can affect the classification of the produced parts as those suitable for efficient operation. In fact, the ST is often called a fingerprint of the manufacturing process that many valuable and accurate information, e.g., wear resistance [1,2], lubricant retention [3], sealing [4], friction [5], fatigue [6], material contact in general, can be gained directly from its studies. Moreover, ST analysis is often an integral part of process control.
Even the precise method (technique) of ST measurement may not produce accurate results when the processes of data analysis are not provided in a conscious way. Necessary ST parameters for evaluating the tribological behavior of 'engineering surfaces' [7] are calculated after form removal [8]. Processes of shape and waviness separation have been studied in many research papers that the improper selection of reference planes may affect the values of surface texture parameters and the accuracy of detail applications. Very popular in the process of areal form removal are polynomials. It was found that oil pockets occurrence can be caused by a significant inaccuracy in the selection of reference planes by the polynomials [9]. Polynomials of various degrees are commonly used (available in the commercial software) algorithms for the separation of form in surface topography measurements [10]. Very often, the process of areal form removal is performed, the distortions of some of the features from surface texture are received, such as dimple (valley) flatness [11], when the degree of polynomials is too high. On the other hand, the form cannot be entirely removed from the raw measured data as the too-small degree is applied. The valley distortion can radically affect the process of calculation of ST parameters that

Analyzed Surfaces
To confirm the suitability of the analyzed, commonly used procedures (approaches and filters), various types of surface topographies were taken into consideration. More than 10 surfaces (modeled and measured in particular) were studied, but only some of them, consistent with general observations to all analyzed data, are presented in detail. In Figure 1, examples of each type of analyzed detail (surfaces) are presented with an isometric view and selected surface topography parameters. The first type of surface is the plateau-honed cylinder liners (a), some with additionally burnished oil pockets (b). Cylinder liner texture can be presented as a representative example of functional surfaces. The progress from surface engineering to the functional surface was one of the main objectives in many types of research [28]. Liners have surface topographies with a cross-hatch pattern generated in a finishing process known as honing, which is an abrasive machining process in which material is cut away from the workpiece using abrasive grains that are bound together with an adhesive to form a honing stone [29]. A plateauhoned cylinder surface, generated in a finishing process, establish simultaneously both the sliding properties of a smooth surface and a great ability to maintain oil on a porous surface; therefore, it is believed that a plateau-honed surface improves the lubrication and reduces friction and wear [30]. Consequently, multi-process topographies, which bear traces of two or more processes, are becoming increasingly important from a functional point of view. A typical example of the textured surface is the plateau-honed cylinder liner surfaces with networks of micro reservoirs, also correctly named as dimple, cavities, or, simply, oil pockets. Previous studies prove that this type of surface texture has great sliding properties and an outstanding ability to preserve the oil in its rough topography. Analysis of both types of surface topographies, plateau-honed cylinder liners, some after the process of oil pockets burnishing, may be particularly significant in the tribological point of view. Other types of tribologically important details are those after the turning (c) or grinding (d) processes. Turned piston skirts work with plateau-honed cylinder liners. It was found that the waviness layout is largely disrupted when surfaces contain curvature and, consequently, imperfections in the manufacturing process cause many of such disruptions [31]. Analysis of the turned surfaces can be performed when the topographies of brake pads are thoroughly evaluated [32]. Analysis of the milled textures (e) is especially crucial in the last stage (end) of the milling process. Milling is a widely employed material removal process for different materials that are characterized by high material removal rate and, generally, machining leads to high friction between tool and workpiece that can result in high temperatures, impairing the dimensional accuracy and the surface quality of products [33]. simply, oil pockets. Previous studies prove that this type of surface texture has great sliding properties and an outstanding ability to preserve the oil in its rough topography. Analysis of both types of surface topographies, plateau-honed cylinder liners, some after the process of oil pockets burnishing, may be particularly significant in the tribological point of view. Other types of tribologically important details are those after the turning (c) or grinding (d) processes. Turned piston skirts work with plateau-honed cylinder liners. It was found that the waviness layout is largely disrupted when surfaces contain curvature and, consequently, imperfections in the manufacturing process cause many of such disruptions [31]. Analysis of the turned surfaces can be performed when the topographies of brake pads are thoroughly evaluated [32]. Analysis of the milled textures (e) is especially crucial in the last stage (end) of the milling process. Milling is a widely employed material removal process for different materials that are characterized by high material removal rate and, generally, machining leads to high friction between tool and workpiece that can result in high temperatures, impairing the dimensional accuracy and the surface quality of products [33].  Laser texturing is one of the machining methods used to prepare a workpiece surface with various microstructures. The tribological behavior [34] of the contact surface can be affected by surface roughness if the liquid film is formed to have a thickness with the same order of magnitude [35] and, simultaneously, that can be affected by the texturing of the surface topography. Selected STs produced with laser melting methods (SLM), which improves the surface quality [36], can be classified within a group of complex textures. They usually feature significant topographic details in multiple scales, with a mixture of high and low aspect-ratio formations, high slopes, undercuts and deep recesses, etc. Therefore these types of surface topographies (f) are challenging to measure or analyze, e.g., the small cavities may become protrusions, while regular hemispheric shapes (e.g., spatter particles) may seem to be irregular.
Generally different from the metal surface after machining is the engineering, isotropic composite (g), or ceramic surfaces (h). The surface quality of workpiece during ceramic grinding is an ever-increasing concern in industries nowadays that the importance of the surface finish of a product depends upon its functional requirements. Since the surface finish is governed by many factors, its experimental determination is laborious (timeconsuming), so the establishment of a model for the reliable prediction of surface roughness is still a key issue for ceramic grinding [37]. Measurement and analysis of this type of ground surface seem to be still a mammoth task to be solved.

Procedures for an Areal form Removal
Algorithms and procedures proposed in the paper can be roughly divided into two groups, based on the issue taken to solve. The first group of approaches implemented was those for the separation of the form from the results of surface topography measurements. Areal form removal in surface metrology can be provided with plenty of Gaussian filters. Moreover, the Gaussian filters were proposed according to the ISO 16610-21 [38], providing the official standard defining the Gaussian filter for open or closed profiles. For surfaces, the equivalent definition is given in ISO 16610-61 [39]. A robust Gaussian regression filter, defined in ISO 16610-31, has its mean plane (line) correctly following the general trend of the surface (profile) without being disaggregated by outliers, outlier-like errors, or other extraordinary values. The robust Gaussian filter is an iterative algorithm that calculates local weights based on the distance between the primary profile and the waviness profile [40]. All the commonly used Gaussian filters proposed, e.g., in the commercial software, can allow receiving relevant results in the surface topography filtering process that make the analysis of the results obtained more qualitative.
Contrary to the Gaussian filtering techniques, the least-square fitted polynomial plane of a different (n-th) order is proposed in plenty of software appliances. This type of data processing method is more robust from the end-effect than the regular Gaussian algorithms. Nevertheless, it was found in the previous studies that the valley size has a huge impact on the areal form removal. Generally, when the surface contained the dimples, the form removal by the commonly used procedures, e.g., least-square fitted polynomial plane of n-th order or regular Gaussian filters, was not provided. To resolve the problem of valley sizes (depth, width), the valley excluding method (VEM) [41], based on the extraction and fulfilling of valleys, was suggested. This technique provided better results, especially when the valleys (oil pockets) were edge-located.
Regardless of the above statement, the effect of feature (e.g., oil pockets, dimples, scratches, valleys in general) distribution, its density and sizes (especially widths) on the results of areal form removal by the regular, often-used algorithms was not comprehensively studied and, simultaneously, only a few hints appeared in this topic.

Algorithms and Approaches for Characterizations of the High-Frequency Errors
Generally, the process of suppression of the high-frequency noise can be effectively separated into two different, albeit dependent, processes such as definition (detection) Materials 2021, 14, 4077 6 of 28 and removal (extraction and reduction). Therefore, the procedures for the high-frequency measurement errors characterizations were classified into those applied for detection of the S-components of the received measurement signal and, correspondingly, those with the suppression performance.
Approaches Considered for the Detection of the High-Frequency Noise The detection of high-frequency noise can be provided considering various techniques. In general, the high-frequency components of the measurement signal should be visible on the Power Spectral Density (PSD) graphs that the PSD describes how the power of a signal or time series is distributed over the different frequencies [42]. The PSD, in its two-dimensional form, has been designated as the preferred means of specifying the surface roughness on the draft international drawing standard for surface texture [43] and can be freely applied in many surface studies. For example, the surface quality can be favorably compared using PSD, e.g., for dry and Minimum Quantity Cooling Lubrication (MQCL) turning process [44]. Furthermore, the PSD technique provides the average frequency spectrum of the acquired signals, making possible the determination of the actual contribution of the tool wear mechanisms. Finally, the average PSD, which is the area of the PSD signal curve that gives the energy of the signal, can be obtained. Therefore, a methodology for the detection of wear mechanisms and determination of the end of life of the cutting tool based on the acoustic emission signals was proposed using PSD. Based on the definition of the PSD technique, which can be described as the estimation of the distribution of the total power of the signal in the frequency domain from a finite recording of a sequence of stationary data [45], the detection of some of the frequency errors, e.g., those in the high-frequency domain, can be proceeded with the PSD appliances. When the high-frequency noise was detected, it was found that the profile (2D) PSD analysis might be more convincing than the areal (3D) studies [46]. Examples of PSD detection procedures of high-frequency errors from the raw surface texture measurement data of turned details are presented in Figure 2. Generally, the process of suppression of the high-frequency noise can be effectively separated into two different, albeit dependent, processes such as definition (detection) and removal (extraction and reduction). Therefore, the procedures for the high-frequency measurement errors characterizations were classified into those applied for detection of the S-components of the received measurement signal and, correspondingly, those with the suppression performance.
Approaches Considered for the Detection of the High-Frequency Noise The detection of high-frequency noise can be provided considering various techniques. In general, the high-frequency components of the measurement signal should be visible on the Power Spectral Density (PSD) graphs that the PSD describes how the power of a signal or time series is distributed over the different frequencies [42]. The PSD, in its two-dimensional form, has been designated as the preferred means of specifying the surface roughness on the draft international drawing standard for surface texture [43] and can be freely applied in many surface studies. For example, the surface quality can be favorably compared using PSD, e.g., for dry and Minimum Quantity Cooling Lubrication (MQCL) turning process [44]. Furthermore, the PSD technique provides the average frequency spectrum of the acquired signals, making possible the determination of the actual contribution of the tool wear mechanisms. Finally, the average PSD, which is the area of the PSD signal curve that gives the energy of the signal, can be obtained. Therefore, a methodology for the detection of wear mechanisms and determination of the end of life of the cutting tool based on the acoustic emission signals was proposed using PSD. Based on the definition of the PSD technique, which can be described as the estimation of the distribution of the total power of the signal in the frequency domain from a finite recording of a sequence of stationary data [45], the detection of some of the frequency errors, e.g., those in the high-frequency domain, can be proceeded with the PSD appliances. When the high-frequency noise was detected, it was found that the profile (2D) PSD analysis might be more convincing than the areal (3D) studies [46]. Examples of PSD detection procedures of high-frequency errors from the raw surface texture measurement data of turned details are presented in Figure 2.   The type of profile extraction technique was fitted to the type of surface studied. For turned cylindrical surfaces containing deep and wide dimples, the out-of-feature approach was applied. This method is based on the analysis of this part of the surface where the traces of manufacturing treatment, e.g., dimples, scratches, oil pockets, valleys in general, do not occur. The application of this technique provided better noise recognition by the PSD analysis. The detection process of high-frequency errors with autocorrelation function (ACF) characterization was useful regardless of the out-of-feature or treatment trace schemes.
Specification of the S-F surface can also be provided by the analysis of the results extracted from the raw measured data. For example, to determine the suitability of the F-operator algorithm, F-filter, or F-procedure in particular, the specification of the form surface (F-surface) and the short-wavelength noise surface (S-surface) [47] can become exceedingly valuable. Simplifying, analysis of the F-surface and the S-surface can be particularly significant for the selection of the procedures for removing irrelevant features, such as form (shape and waviness) or measurement noise in selected bandwidth, from the raw measured surface topography data.

Filters Applied for the Reduction in the Influence of High-Frequency Errors
There were many filters proposed for the removal of the measurement noise from the results of surface topography measurements. As it was mentioned before, surface metrology is often supported by plenty of Gaussian filtering algorithms. A denoising Gaussian S-filter [48] (DGS-F) is an example of S-filters for the removal of short components from the received measurement results (signal). Spatial oriented Gaussian filter was applied previously with convolution-based fringe pattern denoising method [49], the proposal has an outstanding performance against noise. Moreover, the Gaussian filter is ideally suited for smoothing surfaces with rich features. Both S-F surface and waviness surface can be obtained from a single filtering procedure without phase distortion in either of the separated components [50].
Generally, noise, especially in the high-frequency domain, can be effectively suppressed by the various averaging filters. Typical examples of this type of filter are denoising moving average (DMAF) and denoising median (DMF) algorithms. The DMAF is the easiest digital filter to understand and use. It is the most common filter in the analysis of a signal. In spite of its simplicity, the DMAF approach is optimal for a common task such as reducing noise [51]. In turn, it was found that the ranges of effective spatial frequency could be extended through DMF without destroying the properties of the fractal surface. The results of this research were particularly important for characterizing imaging optical systems accurately that the median filtering expands the effective spatial frequency, enhances the effective resolution, and significantly increases the use of the optical profiler without destroying the properties of the fractal surface [52].
Increasingly popular in the characterization of surface topography are wavelets. Wavelet transforms can divide functions into different scale-frequency components, and then each component can be studied with a resolution matched to its scale [53]. One of the classifications can divide wavelets into orthogonal [54] and biorthogonal [55]. Progress in wavelet analysis lets use orthogonal wavelets to decompose turned, milled, and ground surfaces, as well as evaluate tool marks, machining vibrations, and machine-tool errors [56]. The biorthogonal wavelet transform is very suitable for isotropic surfaces but has difficulty with surface topography with various scale scratches such as those in plateau-honed surfaces or worn biomedical surfaces. It is caused that in a discrete biorthogonal wavelet transform, small shifts in the position of the surface can result in a completely different distribution of 'energy' among the wavelet components. To extract and reconstruct a surface topography with various scales scratches, such as those in plateau-honed surfaces and worn biomedical surfaces, a complex wavelet model should be proposed [57]. Wavelet transforms can decompose a signal into several scales that represent different frequency bands, and at each scale, the position of the signal's instantaneous structures can be determined approximately. Such a property can be used for the denoising process [58]. According to the versatility of the wavelet applications, the wavelet denoising filter (DWF), based on the orthogonal Daubechies wavelet [59], was proposed.
All of the above filters, except the wavelet approaches, are available in the commercial software that the main purpose of their application was to determine its usage for the process of reduction in the high-frequency errors from the results of surface texture measurements. The effect of feature (dimples, valleys, scratches) size, density, and distribution on the results of areal form removal commonly used (available in commercial, TalyMap Gold software) procedures were taken into consideration. In Figure 3, contour map plots and surface texture parameters, correspondingly, of three plateau-honed cylinder liner topographies with different densities and distribution of the dimples (oil pockets) are presented. It was found that the value of the Sq and Sa parameters increased, but the values of the Sz parameter changed slightly when the density of oil pockets was larger. No significant changes in the maximum height parameter value are caused by the constant depth of the ST features, oil pockets in particular. Noteworthy is that the 'dominant' texture direction is related to the number (and density) of the features, such as dimples (oil pockets) and (relatively) deep scratches. When the number of dimples was greater than the number of deep scratches, the Std value was affected by the direction of the scratches. Otherwise, the texture direction parameter value was dependent on the direction of the oil pockets (dimples). Therefore, the density of the valleys can affects the value of the Std parameter more than the direction of the scratches created by the honing process. surfaces and worn biomedical surfaces, a complex wavelet model should be proposed [57]. Wavelet transforms can decompose a signal into several scales that represent different frequency bands, and at each scale, the position of the signal's instantaneous structures can be determined approximately. Such a property can be used for the denoising process [58]. According to the versatility of the wavelet applications, the wavelet denoising filter (DWF), based on the orthogonal Daubechies wavelet [59], was proposed. All of the above filters, except the wavelet approaches, are available in the commercial software that the main purpose of their application was to determine its usage for the process of reduction in the high-frequency errors from the results of surface texture measurements.

The Effect of Feature Occurrence on the Areal form Removal by Regular Procedures
The effect of feature (dimples, valleys, scratches) size, density, and distribution on the results of areal form removal commonly used (available in commercial, TalyMap Gold software) procedures were taken into consideration. In Figure 3, contour map plots and surface texture parameters, correspondingly, of three plateau-honed cylinder liner topographies with different densities and distribution of the dimples (oil pockets) are presented. It was found that the value of the Sq and Sa parameters increased, but the values of the Sz parameter changed slightly when the density of oil pockets was larger. No significant changes in the maximum height parameter value are caused by the constant depth of the ST features, oil pockets in particular. Noteworthy is that the 'dominant' texture direction is related to the number (and density) of the features, such as dimples (oil pockets) and (relatively) deep scratches. When the number of dimples was greater than the number of deep scratches, the Std value was affected by the direction of the scratches. Otherwise, the texture direction parameter value was dependent on the direction of the oil pockets (dimples). Therefore, the density of the valleys can affects the value of the Std parameter more than the direction of the scratches created by the honing process.  Selection of the procedure for an areal form removal of plateau-honed cylinder liner surfaces, especially those containing additionally burnished dimples, was proposed with minimizing (maximizing) of the values of Sk and Spk (Svk) parameters [9]. It was indicated that the core roughness of the surface should be minimized when the depth of the valleys was maximized simultaneously, the dimples could not be distorted, it was found that the oil pockets are often flattened when an improper algorithm was applied. In line with the previous research results, the 2nd degree of polynomial seemed to be the most encourages when plateau-honed cylinder liner contained oil reservoirs, the 4th degree (Poly 4th) was proposed for honed cylinder liners with no additionally created dimples. Nevertheless, the 2nd-degree least-square fitted polynomial plane (Poly 2nd) may not be appropriate when dimples were distributed unevenly (Figure 3c). The values of the Sk parameter were minimized when oil pockets were located equally over the entire analyzed detail. In general, the polynomial plane of the 2nd or 4th degree was more sensitive to the location (distribution) of the features (oil pockets) than their densities. Similar observations can be presented for areal form filtering by the Gaussian regression (Gauss) or robust (Robust) methods. When the distribution of valleys was equal on the entire surface, both procedures made it possible to obtain acceptable results. Nonetheless, a robust filter minimized the sum of the Sk and Spk parameters when, concurrently, the value of the Svk parameter increased according to the regular Gaussian regression filter application. The description of all studied parameters was presented in Table 1. Apart from the influence of the density of surface features, the size and distribution of dimples, scratches, and valleys, in general, affect both the results of processing of the raw measured data and the values of the calculated surface topography parameters. In Figure 4, turned or isotropic cylindrical surfaces are presented, containing dimples with a different location, as follows: edge-located (a,b) with different densities where detail (b) contain the dimples located on (near to) the edge of an analyzed surface, and center-distributed (c) where valleys were quite far (more than 0.4 mm) from the edge of a considered surface.
From the analysis of the isometric views of the details, it was found that the polynomial form removal (for various degrees) was influenced if the feature (valley) was evenly situated more than the dimple size or density. For both filters, regular Gaussian regression and robust Gaussian regression, that when the distance of the dimple(s) to the edge of analyzed detail was smaller than the cut-off value of the applied filter, e.g., 0.8 mm, then the distortion (usually flatness) of the valleys increased. Moreover, when the distance between dimples was smaller than the cut-off value irrespective of the dimple-to-edge distance, the feature exaggerations also tends to increase. situated more than the dimple size or density. For both filters, regular Gaussian regression and robust Gaussian regression, that when the distance of the dimple(s) to the edge of analyzed detail was smaller than the cut-off value of the applied filter, e.g., 0.8 mm, then the distortion (usually flatness) of the valleys increased. Moreover, when the distance between dimples was smaller than the cut-off value irrespective of the dimple-to-edge distance, the feature exaggerations also tends to increase.
It was also found in previous studies [12] that the feature depth, especially when deep dimples were considered, influenced the selection of procedure for an areal form removal. Usually, when the valley depth increased, the distortion of the F-surface also increased for least-squares fitting methods, in general.  It was found ( Table 2) that the values of Sk and Spk (Svk) parameters were minimized (simultaneously maximized) when the least-square fitted of the 2nd-degree polynomial plane was established, the sum of values of the Sk and Spk parameters was minimized. The robust filter can be applied alternatively that the value of core roughness (Sk) was It was also found in previous studies [12] that the feature depth, especially when deep dimples were considered, influenced the selection of procedure for an areal form removal. Usually, when the valley depth increased, the distortion of the F-surface also increased for least-squares fitting methods, in general.
It was found ( Table 2) that the values of Sk and Spk (Svk) parameters were minimized (simultaneously maximized) when the least-square fitted of the 2nd-degree polynomial plane was established, the sum of values of the Sk and Spk parameters was minimized. The robust filter can be applied alternatively that the value of core roughness (Sk) was minimized when a robust approach was used, the regular Gaussian filter for the calculation of the parameters after form removal is not suggested that the valleys were disaggregated seriously, usually flattened, that the value of reduced valley depth (Svk) also decreased significantly.
When the analyzed detail did not contain edge-distributed features, dimples in this particular example, the 'minimizing technique', widely commented in reference [9], indicated the robust filtering as this most useful for the separation of the form from the topographies containing deep/wide features such as burnished oil reservoirs. However, the form-separation algorithm should be selected carefully that the value of the Sv parameter was maximized, but, unfavorably, the values of the Sp parameter also increased. For all of the considered feature densities, the F-surface defined by the polynomial of 2nd degree provided the most encouraging results that the sum of the heights of the core and plateau components of the surface (Sk and Spk) was minimized. The other, higher (4th) degree of the polynomial plane might be valuable when the Sp-Spk sum was calculated, but the valley depth (Svk, Sv) was reduced, which might indicate the flatness (distortion) of the oil pockets. This disaggregation of the valley capacity may result in the erroneous estimation of the surface sliding properties and caused a false classification of the manufactured parts.
From all of the above, it is suggested to select the form-separation scheme with both visual and parametric assessments that the minimization (maximization) of the Sk-group parameters may not be convincing when the distortion of the surface features occurs.

Reducing the Influence of an End-Effect in the Analysis of Surface Topography
A very complicated and pressing problem is the effect of the boundary results in digital filtering. The weight modification, simply called the regression scheme, has been improved for machined surfaces [60], that the effect of boundary conditions in the digital metrology filtering was reduced. The regression modification was often proposed, considering surface texture analysis, for the Gaussian filters, especially when robust properties [61] were reasonably required. Robust and regression qualities of the filter improved the functionality of the algorithms applied; nevertheless, distortions of some of the surface texture features still occurred when they were located in (near) the edge areas of the analyzed detail.
Contrary to the robust and regression algorithms, the procedures based on the feature extraction, filling, and omitting, in particular, may provide reasonable results for areal shape and waviness separations. This technique was suggested for cylindrical surfaces containing deep or wide features [41] when their width is greater than half of the F-filter cut-off value. The method of selection of the thresholding value (b) was presented in Figure 5 with Abbott-Firestone (a) and profile characterizations (c,d) by indicating the T point (value). Excluded in the proposed technique, valleys did not influence the accuracy of the areal form removal process provided by regular algorithms (filter or a least-square fitted polynomial planes). The distortion of both features (valleys) and edges of an analyzed surface topography detail was reduced. For validation of the proposed procedure analysis based on the characterization of the surface topography parameters, profiles (2D) and specified areas (3D) of studied details were taken into consideration.
In Figure 6, examples of profiles received from a surface after reducing the end-effect in the process of an areal form removal are presented. In the left column, the details after the application of regular methods (F-surfaces created by the polynomials or Gaussian filters) are presented. When dimples were located near (on) the edge of an analyzed surface, the distortion of both oil reservoirs and edge areas increased enormously. Oil pockets were distorted (flattened), especially when a widely used regular Gaussian filter (cut-off = 0.8 mm) was applied. Application of the thresholding method (right column) allowed to reduce the effect of an edge form removal and minimization of possibility of a false classification of properly manufactured parts as a lack. Some of the exaggerated profile features were indicated by the arrows. eal shape and waviness separations. This technique was suggested for cylindrical surfaces containing deep or wide features [41] when their width is greater than half of the F-filter cut-off value. The method of selection of the thresholding value (b) was presented in Figure 5 with Abbott-Firestone (a) and profile characterizations (c,d) by indicating the T point (value). Excluded in the proposed technique, valleys did not influence the accuracy of the areal form removal process provided by regular algorithms (filter or a least-square fitted polynomial planes). The distortion of both features (valleys) and edges of an analyzed surface topography detail was reduced. For validation of the proposed procedure analysis based on the characterization of the surface topography parameters, profiles (2D) and specified areas (3D) of studied details were taken into consideration. In Figure 6, examples of profiles received from a surface after reducing the e in the process of an areal form removal are presented. In the left column, the det the application of regular methods (F-surfaces created by the polynomials or G filters) are presented. When dimples were located near (on) the edge of an analy face, the distortion of both oil reservoirs and edge areas increased enormously. Oi were distorted (flattened), especially when a widely used regular Gaussian filte = 0.8 mm) was applied. Application of the thresholding method (right column) al reduce the effect of an edge form removal and minimization of possibility of a fa sification of properly manufactured parts as a lack. Some of the exaggerated pr tures were indicated by the arrows.
In Figure 7, examples of dimple details distributed in the edge-area of the a surface with parameters are presented. From the analysis of contour map plo edge-located dimples, it was found that the application of a thresholding method to reduce the distortion of the oil pockets. Usually, the values of Sk and Spk (Svk eters were reduced (increased) when the polynomial (of 2nd or 4th degree) or Gaussian plane was calculated. When the robust Gaussian filter was used, the ap of a thresholding procedure caused an increase in the Sk and Spk, but the useful proposed method was preserved that the regular algorithms may cause the flatne deep and wide features, oil pockets, valleys, and scratches, in particular. In Figure 7, examples of dimple details distributed in the edge-area of the analyzed surface with parameters are presented. From the analysis of contour map plots of the edge-located dimples, it was found that the application of a thresholding method allowed to reduce the distortion of the oil pockets. Usually, the values of Sk and Spk (Svk) parameters were reduced (increased) when the polynomial (of 2nd or 4th degree) or regular Gaussian plane was calculated. When the robust Gaussian filter was used, the application of a thresholding procedure caused an increase in the Sk and Spk, but the usefulness of a proposed method was preserved that the regular algorithms may cause the flatness of the deep and wide features, oil pockets, valleys, and scratches, in particular.

The Influence of Feature Size, Density, and Distribution on the Processes of Detection of High-Frequency Errors
It was found in previous studies that the profile (2D) analysis might have been more valuable in the detection of the high-frequency components of textured surfaces than the areal (3D) assessments [46]. Thus, the detection of the high-frequency errors with an analysis of the PSD and ACF graphs was applied. It was assumed that the feature occurrence and simultaneously density affect the PSD and ACF profile noise detection.
In Figure 8, profiles received from the plateau-honed cylinder liner surface, with their PSDs and ACFs, respectively, and with a various number (density) of the features (dimples, valleys, scratches) are presented, as follows: three dimples (a), two dimples and one scratch (b), two dimples (c), one dimple and two scratches (d), one dimple and one scratch (e), one dimple and no scratches (f), two scratches but no dimples (g) and no dimples and no scratches (h) profile. When profiles contained the dimples (oil reservoirs), the highfrequency components were not visible on the PSD graph (a-e in Figure 8). In this case, the number (density) of the dimples was negligible, that they did not affect the accuracy of noise detection. Even one dimple considerably reduced the possibility of high-frequency noise identification.
Moreover, the occurrence of the other features, e.g., valleys, scratches, has a negligible impact on the accuracy of the detection process. Notwithstanding, the number (density) of the scratches had a considerable influence on the disclosure of the high-frequency components when oil reservoirs did not occur (g, h). The smallest density (number) of features (oil pockets, valleys, scratches) was found the biggest applicability of the PSD method was observed. Consequently, it is thoroughly recommended to detect the high-frequency errors from the results of profile measurements of plateau-honed surface topography, considering the PSDs and ACFs applications, with no (deep, wide) feature occurrence.
For surfaces with traces of the laser treatments (Figure 9), it was observed that the flat (with no laser-manufacturing areas) profiles can be quite valuable in the high-frequency errors detection (e) that both valleys (c) and hills (d) negatively affected the accuracy of the PSDs and ACFs noise detection with profile explorations. The shape of the center part of the ACF, in the areas of the maximum value of this function, has also been modified when the noise was observed with no-trace profiles. It was noticed that the noise profile contain the ACF with a higher degree of increase when the maximum (near the '1') value was considered. This dependence was followed for each type of surface.
The 'no-trace' technique may be partially modified for milled surfaces ( Figure 10). It was observed that horizontal (b) or vertical (c) extraction of profiles did not provide valuable information about the high-frequency noise concurrence with PSDs or ACFs graphs assessment. For this type of texture, where one direction of traces received with the manufacturing process can be defined, the direction of profile extraction for noise detection should be purposed with a direction of the traces of the surface finishing. This method can be designated (named) as a 'treatment-(traces) direction method' (TDM). However, in the case of the milled or turned surfaces, the TDM can be applied for the top (d) or bottom (e) area of the studied detail. It was noticed that the analysis of a 'bottom' profile (B4) could be much more useful in a high-frequency noise detection than the 'top' profile (B3) regardless of the distance of the profiles was relatively small.   Generally, it was observed that the PSD and ACF high-frequency noise profile detection is even more beneficial when the amplitude of the analyzed profile is small, does not contain the dimples, valleys, scratches, or, simultaneously, are defined with the direction of the manufacturing (finishing) process. Both techniques can be used concurrently or alternately when the PSD or ACF profile detection of the high-frequency noise is not conclusive.

Reduction in the High-Frequency Errors with a Modeled Data Analysis
For validation of the commonly used, i.a. available in the commercial software, procedures, characterization based on the modeled data (noise) was proposed. For the data of various surface textures (start data), the high-frequency noise data were added (noise data, data with noise, or simply noise) and then removed by different filters, described in one of the previous sections. The selection of the cut-off value for noise suppressions was studied previously [47] and is also presented in the next chapter, which is dedicated to the analysis of a measured surface. It is obvious that results received after different filtering, regardless they all are dedicated to the reduction in the high-frequency components from the data, is also different [62]. Nevertheless, applying filters dedicated to the suppression of the high-frequency components of the data seems to be a logical solution.
Generally, results obtained after noise removal should be similar to those before adding noise data and, simultaneously, differences in values of the surface texture parameters should be minimized as well. Moreover, it was also concluded that the noise added to the surface should also be close to the data removed after the application of the noise-removal algorithm. Therefore both comparisons might be taken into consideration while selecting the procedures for suppressions of the high-frequency noise from measured data such as commonly used and available in regular commercial software.
For surfaces of cylinder liners after the plateau-honing process, distortion of height (amplitude) parameters was minimized when Gaussian or moving average filters were applied. Usually, differences for special parameters (Sal, Str, Std) were under 5% or were negligible, and when hybrid parameters were considered, the differences for root mean square gradient (Sdq) were slight. Nonetheless, all of those four parameters were defined previously as robust for the presence of the (high-frequency) noise [18]. Parameters related to the characterization of the peaks (Spd, Spc) underwent the greatest changes. Results after the application of various filters were also significant. Results also varied after various filtering methods for the Sk-group and functional indices.
When plateau-honed cylinder liner surfaces contained additionally burnished dimples, oil pockets, or other deep/wide valleys, the less distorted parameters were received when wavelet (WDF) was applied. The WDF caused the minimization of exaggerations of amplitude parameters, excluding the root mean square high (Sq) of the surface. For this type of surface, it was found that different filters minimized distortion of parameters from a different group, that median approach (DMF) minimized changes of Sk and Spk parameters, Gaussian denoising filter (DGS-F) reduced the most errors in computing the functional indices (Sbi, Sci, Svi), moving average scheme (MADF) minimized variation of the peakdependent indicators (Spd and Spc). Distortion of most parameters was minimized by the application of the WDF algorithm; nevertheless, secondary in terms of numbers and peak density subjections, the MADF may be suggested alternatively. All of the analyses of cylinder liner surface texture parameters are presented in Table 3.
Moving average and median filters seems to be suitable for high-frequency errors reduction when turned or ground surfaces are studied. From all four compared filters, for minimization of the high-frequency errors in the measurement of milled surfaces, it is extremely difficult to select an appropriate method; nonetheless, errors in the calculation of parameters of the laser-textured surfaces are considerable reduced with an application of a DGF-S method. A method based on the Gaussian function can also be valuable when ceramic, composite, isotropic in general, surfaces are studied. All of the values of the mentioned parameters are presented in Tables 4 and 5.

Proposals of High-Frequency Noise Suppressions with Measured Data Studies
Appertaining to the results obtained in previous studies and based on the modeled data, it was found that the presence of the high-frequency noise affects the values of selected surface topography parameters, defined as 'noise-sensitive parameters' (NSP) [18], to a much greater extent than other parameters. The following parameters have been highlighted as an NSP: Sz, Sdq, Sdr, Spd, Spc, and Sk. It was also suggested to reduce the high-frequency noise with the biggest variations of values of the NSP and, simultaneously, with minimizing the differences in other (non-noise-sensitive) parameters.
Moreover, the results of noise removal, specified as an S-surface, can be studied to find the best solution from the considered commonly used algorithms. In general, the S-surface should both contain only those frequencies (visible in the PSD and ACF graphs) that are required to be removed from the raw measured data and maximizing the value of the peak density (Spd) parameter. In particular, the S-surface should contain the high-frequency components as its dominant frequency [63] or only frequencies in the high domain in the nominal, ideal case. Moreover, the S-surface should be isotropic in general, regardless of the type (direction) of the analyzed surface. Characterization of the process of noise removal can be provided with profiles (2D) and areal (3D) analysis.
In Figure 11, results of removal of the high-frequency errors from plateau-honed cylinder liner, milled and laser-textured surfaces, by application of a regular Gaussian denoising filter, are presented. For improving the view validation of the algorithm, the thresholding method for S-surface processing was proposed. This technique was beneficial in recognition of the features located on the S-surface that are not in the high-frequency domain and, respectively, should not have been removed from the analyzed data (S-F surface). For plateau-honed surface, the S-surface contained the scratches, and when laser-textured topographies were studied, some laser treatment traces were located on the received noise surface as well. Gaussian denoising may be valuable for milled textures; nonetheless, the S-surface was not entirely in an isotropic manner. Reduction in sizes of the surface features, caused by an occurrence of features on the S-surface, is clearly undesirable in the processing of raw measured data.
In Figure 12 example of properly accomplished a denoising process was presented with a characterization (usage) of a regular median denoising filter. In this case, the thresholding technique was performed for both S-surface (g) and its ACF (h). In both instances, the S-surface did not contain surface finishing traces. The cut-off value also needs to be defined with analysis of an S-surface and its lack of manufacturing marks. When traces occur, then filter bandwidth should be reduced to receive non-feature S-surface. While DMF was applied, the cut-off was proposed with a 0.025 mm value. Moreover, the S-surface is also isotropic (i). cial in recognition of the features located on the S-surface that are not in the high-frequency domain and, respectively, should not have been removed from the analyzed data (S-F surface). For plateau-honed surface, the S-surface contained the scratches, and when laser-textured topographies were studied, some laser treatment traces were located on the received noise surface as well. Gaussian denoising may be valuable for milled textures; nonetheless, the S-surface was not entirely in an isotropic manner. Reduction in sizes of the surface features, caused by an occurrence of features on the S-surface, is clearly undesirable in the processing of raw measured data. (e) (f) Figure 11. Defined for plateau-honed cylinder liner (left column), milled (center), and laser-textured (right column) surfaces: contour map plots of detail after DGS-F (cut-off = 0.025 mm) noise reduction (a) with selected surface topography parameters (b), correspondingly, received S-surface (c) with their PSDs (d), respectively, and S-surfaces after thresholding (0.13-99.87%) method (e) with their texture direction graphs (f) appropriately.
In Figure 12 example of properly accomplished a denoising process was presented with a characterization (usage) of a regular median denoising filter. In this case, the thresholding technique was performed for both S-surface (g) and its ACF (h). In both instances, the S-surface did not contain surface finishing traces. The cut-off value also needs Figure 11. Defined for plateau-honed cylinder liner (left column), milled (center), and laser-textured (right column) surfaces: contour map plots of detail after DGS-F (cut-off = 0.025 mm) noise reduction (a) with selected surface topography parameters (b), correspondingly, received S-surface (c) with their PSDs (d), respectively, and S-surfaces after thresholding (0.13-99.87%) method (e) with their texture direction graphs (f) appropriately. thresholding technique was performed for both S-surface (g) and its ACF (h). In both instances, the S-surface did not contain surface finishing traces. The cut-off value also needs to be defined with analysis of an S-surface and its lack of manufacturing marks. When traces occur, then filter bandwidth should be reduced to receive non-feature S-surface. While DMF was applied, the cut-off was proposed with a 0.025 mm value. Moreover, the S-surface is also isotropic (i). (h) (i) Figure 12. Contour map plot of the milled surface after a high-frequency errors reduction by a DMF method (a) with material ratio curve (b) and selected surface topography parameters (c) correspondingly, the S-surface received by application of DMF approach with cut-off = 0.025 mm (d), its PSD (e) and ACF (f), results of thresholding (0.13-99.87%) of Ssurface (g) and ACF (h), the texture direction graph (i) defined for thresholded S-surface presented in (g) subsection of the figure. Figure 12. Contour map plot of the milled surface after a high-frequency errors reduction by a DMF method (a) with material ratio curve (b) and selected surface topography parameters (c) correspondingly, the S-surface received by application of DMF approach with cut-off = 0.025 mm (d), its PSD (e) and ACF (f), results of thresholding (0.13-99.87%) of S-surface (g) and ACF (h), the texture direction graph (i) defined for thresholded S-surface presented in (g) subsection of the figure.