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Slope transform: a theoretical insight into morphological operations in surface measurement

Lou, Shan, Jiang, Xiang, Zeng, Wenhan and Scott, Paul J. (2014) Slope transform: a theoretical insight into morphological operations in surface measurement. In: 13th CIRP Conference on Computer Aided Tolerancing, 11-14 May 2014, Hangzhou, China.

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Linear convolution and morphological (nonlinear) operations are two kinds of operations that have wide applications in the field of surface measurement. Well-established computational and analytical methods are available for linear convolution, such as the Fourier Transform. A counterpart transform, called the slope transform, which resembles the Fourier transform in many aspects, can provide the analytical ability for morphological operations. The tangential dilation is the extension of the classical dilation, providing the basis for the slope transform. The slope transform sets out to decompose the input function into the eigenfunctions (planar functions), each of which is a point in the slope domain representing the slope and intercept of the tangent line of the input function. Under the slope transform, the tangential dilation becomes the addition, just as by the Fourier transform, the convolution becomes the multiplication. By investigating the slope and curvature change, the slope transform can offer a deeper understanding of morphological operations in surface measurement.

Item Type: Conference or Workshop Item (Paper)
Subjects: T Technology > TJ Mechanical engineering and machinery
Schools: School of Computing and Engineering > Centre for Precision Technologies > EPSRC Centre for Innovative Manufacturing in Advanced Metrology
School of Computing and Engineering
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References: [1] ISO 11562 Geometrical Product Specification (GPS)–Surface texture: Profile method– Metrological characteristics of phase correct filter, Switzerland; 1996. [2] ISO 16610-41 Geometrical Product Specification (GPS)-Filtration Part 41: Morphological profile filters: Disk and horizontal line-segment filters, Switzerland; 2010. [3] Bracewell R. The Fourier Transform and Its Applications, 3rd ed. New York: McGraw-Hill, 1999:108-112. [4] Serra J. Image Analysis and Mathematical Morphology, Academic Press New York; 1982. [5] Dorst L, van den Boomgaard R, Morphological signal processing and the slope transform. Signal Proces. 1994;38: 79-98. [6] Maragos P. Slope transforms: theory and application to nonlinear signal processing. IEEE T. Signal Proces. 1995;43: 864-77. [7] Lou S, Jiang X, Scott PJ. Applications of Morphological Operations for Geometrical Metrology. 14th International Conference on Metrology and Properties of Engineering Surfaces 2013;327-38. [8] Lou S, Jiang X, Scott PJ. Application of the morphological alpha shape method to the extraction of topographical features from engineering surfaces. Measurement 2013;42:1002-8. [9] Malburg CM. Surface Profile Analysis for Conformable Interfaces. J. Manuf. Sci. Eng. 2003;125:624-7. [10] Lou S, Jiang X, Bills PJ, Scott PJ. Defining true tribological contact through application of the morphological method to surface topography. Tribol. Lett. 2013;50: 185-93. [11] D. Keller Reconstruction of STM and AFM images distorted by finite-size tips. Surf. Sci. 1991;253: 353–64.
Depositing User: Shan Lou
Date Deposited: 22 Jul 2014 14:38
Last Modified: 28 Aug 2021 19:10


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