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CLC number: TB9; TG8

On-line Access: 2015-05-04

Received: 2014-07-26

Revision Accepted: 2014-10-16

Crosschecked: 2015-04-15

Cited: 0

Clicked: 2643

Citations:  Bibtex RefMan EndNote GB/T7714

 ORCID:

Shan Lou

http://orcid.org/0000-0002-8426-5596

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Journal of Zhejiang University SCIENCE A 2015 Vol.16 No.5 P.395-403

http://doi.org/10.1631/jzus.A1400223


A theoretical insight into morphological operations in surface measurement by introducing the slope transform


Author(s):  Shan Lou, Xiang-qian Jiang, Wen-han Zeng, Paul J. Scott

Affiliation(s):  EPSRC Innovative Manufacure Research Centre in Advanced Metrology, School of Computing and Engineering, University of Huddersfield, Queensgate, Huddersfield, HD1 3DH, UK

Corresponding email(s):   s.lou@hud.ac.uk

Key Words:  Morphological operations, Slope transform, Tangential dilation, Linear convolution, Surface metrology


Shan Lou, Xiang-qian Jiang, Wen-han Zeng, Paul J. Scott. A theoretical insight into morphological operations in surface measurement by introducing the slope transform[J]. Journal of Zhejiang University Science A, 2015, 16(5): 395-403.

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Abstract: 
As one of the tools for surface analysis, morphological operations, although not as popular as linear convolution operations (e.g., the Gaussian filter), are really useful in mechanical surface reconstruction, surface filtration, functional simulation, etc. By introducing the slope transform originally developed for signal processing into the field of surface metrology, an analytic capability is gained for morphological operations, paralleling that of the Fourier transform in the context of linear convolution. Using the slope transform, the tangential dilation is converted into the addition in the slope domain, just as by the Fourier transform, the convolution switches into the multiplication in the frequency domain. Under the theory of the slope transform, the slope and curvature changes of the structuring element to the operated surface can be obtained, offering a deeper understanding of morphological operations in surface measurement. The analytical solutions to the tangential dilation of a sine wave and a disk by a disk are derived respectively. An example of the discretized tangential dilation of a sine wave by the disks with two different radii is illustrated to show the consistency and distinction between the tangential dilation and the classical dilation.

The paper presents an interesting transform approach for morphological filters, which have been slowly gaining currency in characterizing engineered surfaces. so, this paper is a good addition to the knowledge base for this field. This is a good first step in to this domain and opens up the possibility for further work in 3D engineered surface analysis.

基于坡变换的表面测量中的形态学操作理论探究

目的:通过引入坡变换,揭示表面测量中形态学操作的本质。
创新点:引入坡变换,将空间域的形态学膨胀操作转换为坡域的加法操作,揭示结构元素对表面轮廓坡度和曲率的改变。
方法:1.基于坡变换理论,空间域的切膨胀操作对应于坡域的加法操作(图9);2.分析圆结构元素作用于正弦波和圆的理论解;3.用不同半径的圆结构元素作用于正弦波,分析切膨胀和经典膨胀的相同和不同之处。
结论:1.坡变换将形态学操作从空间域转换到坡域,可获取类似于傅立叶变换将卷积操作从空间域转换到频域的分析能力;2.切膨胀操作为经典膨胀操作的上确界,但会产生重叠区域。

关键词:形态学操作;坡变换;切膨胀;卷积;表面测量

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

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[8]Lou, S., Jiang, X., Bills, P.J., et al., 2013a. Defining true tribological contact through application of the morpholo-gical method to surface topography. Tribology Letters, 50(2):185-193.

[9]Lou, S., Jiang, X., Scott, P.J., 2013b. Applications of morphological operations for geometrical metrology. Journal of Physics: Conference Serial, 483:012020.

[10]Lou, S., Jiang, X., Scott, P.J., 2013c. Application of the morphological alpha shape method to the extraction of topographical features from engineering surfaces. Measurement, 46(2):1002-1008.

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[14]Soille, P., 1999. Morphological Image Analysis Principles and Applications. Springer-Verlag Berlin Heidelberg.

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