Richard Leach - Fundamental prinsiples of engineering nanometrology (778895), страница 54
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Much of the early researchwork on feature parameters stemmed from work in such areas as machinevision and cartography.Feature characterization does not have specific feature parameters definedbut has instead a toolbox of pattern-recognition techniques that can be usedto characterize specified features on a scale-limited surface. The featurecharacterization process defined in ISO 25178 part 2 [25] has five stageswhich are presented below.8.3.7.1 Step 1 – Texture feature selectionThe three main types of surface texture features are areal features, linefeatures and point features (see Table 8.3). It is important to select theappropriate type of surface texture feature to describe the function of thesurface that is being characterized.
The various types of feature will beexplained by example in the following sections.8.3.7.2 Step 2 – SegmentationSegmentation is used to determine regions of the scale-limited surface thatdefine the scale-limited features. The segmentation process consists of firstfinding the hills and dales on the scale-limited surface. This usually results in243244C H A P T ER 8 : Surface topography characterizationTable 8.3Types of scale-limited featuresClass of scale-limited featureType of scale-limited featureSymbolArealHillDaleCourse lineRidgePeakPitSaddle pointHDCRPVSLinePointover-estimation of the surface and so the smaller, or less significant,segments are pruned out to leave a suitable segmentation of the surface.Some criteria of size that can be used to define a threshold for small segmentsto prune out are given in Table 8.4.A surface can be divided into regions consisting of hills and regionsconsisting of dales.
Here a hill is defined as an area from which maximumuphill paths lead in to one particular peak, and a dale is defined as an areafrom which maximum downhill paths lead to one particular pit. By definitionthe boundaries between hills are course lines and the boundaries betweendales are ridge lines. Ridge and course lines are maximum uphill anddownhill paths respectively emanating from saddle points and terminating atpeaks and pits.ISO 25178 part 2 [25] defines a dale as consisting of a single dominant pitsurrounded by a ring of ridge lines connecting peaks and saddle points, anda hill as consisting of a single dominant peak surrounded by a ring of courselines connecting pits and saddle points.
Within a dale or hill there may beother pits or peaks, but they will be insignificant compared to the dominantpit or peak. Figure 8.18 shows a simulated surface and Figure 8.19 shows thecorresponding contour representation displaying all the features describedabove (a simulated surface has been used for reasons described in section8.3.7.2.1).Table 8.4Criteria of size for segmentationCriteria of sizeSymbolThresholdLocal peak/pit height (Wolf pruning – see sectionVolume of hill/dale (at height of connected saddle on change tree)Area of hill/daleCircumference of hill/daleWolfpruneVolSAreaCirc% of SzSpecified volume% of definition areaSpecified lengthAreal surface texture characterizationFIGURE 8.18 Example simulated surface.FIGURE 8.19 Contour map of Figure 8.18 showing critical lines and points.8.3.7.2.1 Change treeA useful way to organise the relationships between critical points in hills anddales, and still retain relevant information, is that of the change tree [36].The change tree represents the relationships between contour lines froma surface.
The vertical direction on the change tree represents the height. Ata given height all individual contour lines are represented by a point that is245246C H A P T ER 8 : Surface topography characterizationpart of a line representing that contour line continuously varying with height.Saddle points are represented by the merging of two or more of these linesinto one. Peaks and pits are represented by the termination of a line.Consider filling a dale gradually with water. The point where the waterfirst flows out of the dale is a saddle point. The pit in the dale is connected tothis saddle point in the change tree. Continuing to fill the new lake, the nextpoint where the water flows out of the lake is also a saddle point.
Again theline on the change tree, representing the contour of the lake shoreline, will beconnected to the saddle point in the change tree. This process can becontinued and establishes the connection between the pits, saddle points andthe change tree. By inverting the surface so that peaks become pits, a similarprocess will establish the connection between peaks, saddle points and thechange tree.There are three types of change tree:-the full change tree (see Figure 8.20), which represents therelationships between critical points in the hills and dales;-the dale change tree (see Figure 8.21), which represents therelationships between pits and saddle points;-the hill change tree (see Figure 8.22), which represents the relationshipbetween peaks and saddle points.The dale and hill change trees can be calculated from the full change tree.FIGURE 8.20 Full change tree for Figure 8.19.Areal surface texture characterizationFIGURE 8.21 Dale change tree for Figure 8.19.FIGURE 8.22 Hill change tree for Figure 8.19.247248C H A P T ER 8 : Surface topography characterizationIn practice change trees can be dominated by very short contour lines dueto noise and insignificant features on a surface (this is the reason thata simulated surface was used at the beginning of this section).
A mechanism isrequired to prune the change tree, reducing the noise but retaining significantfeatures. There are many methods for achieving this pruning operation thatare too complex to be presented here (see [43] for a thorough mathematicaltreatment). It is expected that the software packages for feature characterization will include pruning techniques.
One method stipulated in ISO 25178part 2 [25] is Wolf pruning and details of this methods can be found in [44].8.3.7.3 Step 3 – Significant featuresIt is important to determine the features on a surface that are functionallysignificant and those that are not. For each particular surface function thereneeds to be defined a segmentation function that identifies the significantand insignificant features defined by the segmentation. The set of significantfeatures is then used for characterization.
Methods (segmentation functions)for determining significant features are given in Table 8.5. Once again, it isexpected that all these functions will be carried out by the software packagesused for feature characterization. Various research groups are currentlydeveloping further methods for determining significant features.8.3.7.4 Step 4 – Selection of feature attributesOnce the set of significant features have been determined it is necessary todetermine suitable feature attributes for characterization.
Most attributes area measure of the size of features, for example the length or volume ofa feature. Some feature attributes are given in Table 8.6. Various researchgroups are currently developing further methods for selecting feature attributes and different forms of attribute.Table 8.5Methods for determining significant featuresClass of featureSegmentation functionsSymbolParameter unitsArealFeature is significant if not connected to the edgeat a given heightFeature is significant if not connected to the edgeat a given heightA peak is significant if it has one of the top N Wolfpeak heightsA pit is significant if it has one of the top N Wolf pitheightsClosedTopHeight is given as materialratioHeight is given as materialratioN is an integerBotN is an integerAll–PointAreal, line, pointOpenAreal surface texture characterizationTable 8.6Feature attributesFeature classFeature attributeSymbolArealLocal peak/pit heightVolume of areal featureArea of areal featureCircumference of areal featureLength of lineLocal peak/pit heightLocal curvature at critical pointAttribute takes value of oneLpvhVolSVolEAreaLenglpvhCurvatureCountLinePointAreal, line, point8.3.7.5 Step 5 – Quantification of feature attribute statisticsThe calculation of a suitable statistic of the attributes of the significantfeatures, a feature parameter, or alternatively a histogram of attribute values,is the final part of feature characterization.
Some attribute statistics are givenin Table 8.7. Various research groups are currently developing furthermethods for quantifying feature attribute statistics.8.3.7.6 Feature parametersTo record the results of feature characterization it is necessary to indicate theparticular tools that were used in each of the five steps. An example of how todo this that shows the convention isFC; D; Wolfprune : 5 %; Edge : 60 %; VolE; HistTable 8.7Attribute statisticsAttribute statisticSymbolThresholdArithmetic mean of attribute valueMaximum attribute valueMinimum attribute valueRMS attribute valuePercentage above a specified valueMeanMaxMinRMSPercHistogramSum of attribute valuesSum of all the attribute valuesdivided by the definition areaHistSumDensity––––Value of threshold in units ofattribute–––249250C H A P T ER 8 : Surface topography characterizationwhere FC denotes feature characterization and the next five symbols,delimited by semicolons, are the symbols from the five tables correspondingto the five steps.In sections 8.3.7.6.1 to 8.3.7.6.9 the default value for X is 5 % [26].8.3.7.6.1 Density of peaks, SpdThe density of peaks, Spd, is the number of peaks per unit area,Spd ¼ FC; H; Wolfprune : X %; All; Count; Density:(8.29)8.3.7.6.2 Arithmetic mean peak curvature, SpcThe Spc parameter is the arithmetic mean of the principle curvatures ofpeaks with a definition area,Spc ¼ FC; P; Wolfprune : X %; All; Curvature; Mean:(8.30)8.3.7.6.3 Ten point height of surface, S10zThe S10z parameter is the average of the heights of the five peaks with largestglobal peak height added to the average value of the heights of the five pitswith largest global pit height, within a definition area,S10z ¼ S5p þ S5v:(8.31)8.3.7.6.4 Five point peak height, S5pThe S5p parameter is the average of the heights of the five peaks with largestglobal peak height, within a definition area,S5p ¼ FC; H; Wolfprune : X %; Top : 5; lpvh; Mean:(8.32)8.3.7.6.5 Five point pit height, S5vThe S5v parameter is the average of the heights of the five pits with largestglobal pit height, within a definition area,S5v ¼ FC; D; Wolfprune : X %; Bot : 5; lpvh; Mean:(8.33)8.3.7.6.6 Closed dale area, Sda(c)The Sda(c) parameter is the average area of dales connected to the edge atheight c,SdcðcÞ ¼ FC; D; Wolfprune : X %; Open : c : Area; Mean:(8.34)Fractal methods8.3.7.6.7 Closed hill area, Sha(c)The Sha(c) parameter is the average area of hills connected to the edge atheight c,ShaðcÞ ¼ FC; D; Wolfprune : X %; Open : c; Area; Mean:(8.35)8.3.7.6.8 Closed dale volume, Sdc(c)The Sdc(c) parameter is the average volume of dales connected to the edge atheight c,SdcðcÞ ¼ FC; D; Wolfprune : X %; Open : c; VolE; Mean:(8.36)8.3.7.6.9 Closed hill volume, Shv(c)The Shv(c) parameter is the average of hills connected to the edge at height c,ShvðcÞ ¼ FC; H; Wolfprune : X %; Open : c; VolE; Mean:(8.37)8.4 Fractal methodsFractal methods have been shown to have a strong ability to discriminateprofiles measured from different surfaces and can be related to functionalmodels of interactions with surfaces.
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