Morphological method for surface metrology and dimensional metrology based on the alpha shape

Abstract

Abstract. Morphological filters are useful tools as they are commonly employed in surface metrology and dimensional metrology, serving for surface texture analysis and data smoothing respectively. Compared to the mean-line filtering techniques, such as the Gaussian filter, morphological filters have the merits of compact support, no need to remove form, and being relevant to geometrical properties of surfaces. This paper proposes a novel morphological method based on the alpha shape. The proposed method has the advantages over the traditional methods that it runs relative fast, enables arbitrary large ball radii, and applies to freeform surfaces and nonuniform sampled surfaces. The theory of basic morphological operations and the alpha shape are introduced and the theoretical link between the alpha hull and the morphological closing and opening operation is presented. A practical algorithm is developed that corrects possible singularities caused by data spikes and reduces the amount of calculation for open profiles/surfaces. Computer simulation is used to compare the results from the traditional algorithm and the proposed one. Experimental studies are conducted to demonstrate the feasibility and applicability of using the proposed method. IntroductionSurface metrology and dimensional metrology have profound influences on product manufacturing. Surface metrology inspects small scale geometrical features on product surfaces while dimensional metrology measures form and size in relative large scale. They work in a complementary manner to ensure the good quality and a satisfactory performance.Filtration is a technique that separates the desirable features from other features in the data set. It is commonly used in surface metrology and dimensional metrology. In dimensional metrology, filtration plays a role of data smoothing while in surface metrology it usually serves as part of the analysis of the surface topography. Conventionally, there are two filtering systems: M-system (Mean-line filtering system) and E-system (Envelope filtering system). The mean-line filtering techniques decompose the surface signal into differing components according to their bandwidth in the frequency domain and thus extract the components of interest within the given wavelength bandwidth. The envelope filtering system is an alternative method depending on the geometrical structures of surfaces. The envelope filtration is achieved by rolling a ball of the selected radius over the surface (Von Weingraber 1956).The Gaussian filter, the most typical representative of the M-system techniques, is the standardized filter both for surface metrology and dimensional metrology (ISO 11562 1994). It is based on the time-frequency analysis technique, which convolves the signal with the weighting function (Gaussian function) to obtain the weighted average value. In surface metrology, the Gaussian filter is employed

Application of the morphological alpha shape method to the extraction of topographical features from engineering surfaces

“…Recently we [17,18] proposed a novel method for morphological filters based on the link between the alpha hull and morphological operations. The alpha shape was introduced by Edelsbrunner [19] aiming to describe the specific "shape" of a finite point set with a real parameter α controlling the desired level of details.…”

Robust Filtration Techniques in Geometrical Metrology and Their Comparison

“…Combining dilation and erosion operations in sequence will yield closing and opening envelopes. Nevertheless there are more capable and efficient computational methods available for the filtration of complex surfaces [26,27] . For instance, the geometrical method based on the convex hull differs from the traditional approach in that the algorithm sets out to compute the contact points as the disk is rolling over the profile.…”

“…With respect to nonuniform sampling data, there is no evidence showing the Gaussian filter and the robust Gaussian version are able to deal with this kind of data. On the contrary, the spline filter and morphological filters are capable if the appropriate algorithms are taken [24,26] . The standard and robust Gaussian filter could be modified to handle the roundness data [30] .…”

“…However, traditional methods are restricted to planar surfaces. Recently, a novel implementation of morphological filters based on the alpha shape algorithm offers the possibility of dealing with roundness data [26] .…”

Using Wavelet Packet Transform for Surface Roughness Evaluation and Texture Extraction

“…Morphological filtration is carried out by performing morphological operations on the input signal. It has a drawback of being time-consuming for a large data set [ 5 , 6 ]. Wavelet, an attractive mathematical tool, can describe the surface with variable resolution.…”