Computing and Library Services - delivering an inspiring information environment

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

Jiang, Xiang, Lou, Shan and Scott, Paul J. (2011) Morphological method for surface metrology and dimensional metrology based on the alpha shape. Measurement Science and Technology, 23 (1). 015003. ISSN 0957-0233

PDF - Accepted Version
Download (973kB) | Preview


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.

▼ Jump to Download Statistics
Item Type: Article
Additional Information: IOPSelect paper (Articles from the last 12 months that have been chosen by our editors for their novelty, significance and potential impact on future research. All select articles are first published in the source journals.).
Subjects: T Technology > TJ Mechanical engineering and machinery
Schools: School of Computing and Engineering
School of Computing and Engineering > Centre for Precision Technologies > Surface Metrology Group
School of Computing and Engineering > Centre for Precision Technologies > EPSRC Centre for Innovative Manufacturing in Advanced Metrology
Related URLs:

Decenciere E and Jeulin D 2001 Morphological decomposition of the surface topography of an internal combustion engine cylinder to characterize wear Wear 249 482–8
Edelsbrunner H and Mucke E P 1994 Three-dimensional alpha shapes ACM Trans. Graph. 13 43–72
Fischer K 2000 Introduction to alpha shapes
Heijmans H J A M 1995 Mathematical morphology: a modern approach in image processing based on algebra and geometry SIAM Rev. 37 1–36
ISO 11562 1996 Geometrical Product Specification (GPS)—surface texture. Profile method—metrological characteristics of phase
correct filter
ISO 16610 2010 Geometrical Product Specification (GPS)—filtration
Jiang X, Copper P and Scott P J 2011 Freeform surface filtering using the diffusion equation Proc. R. Soc. A 467 841–59
Jiang X, Scott P J, Whitehouse D J and Blunt L 2007 Paradigm shifts in surface metrology: part II. The current shift Proc. R. Soc. A 463 2071–99
Malburg C M 2003 Surface profile analysis for conformable interfaces Trans. ASME 125 624–7
Minkowski H 1903 Volumen and Oberflache Math. Ann. 57 447–95
O’Rourke J 1994 Computational Geometry in C (New York: Cambridge University Press)
Scott P J 1992 The mathematics of motif combination and their use for functional simulation Int. J. Mach. Tools Manuf. 32 69–73
Scott P J 2000 Scale-space techniques Proc. 10th Int. Colloquium on Surfaces pp 153–61
Serra J 1982 Image Analysis and Mathematical Morphology (New York: Academic)
Shunmugam M S and Radhakrishnan V 1974 Two-and three dimensional analyses of surfaces according to the E-system Proc. Inst. Mech. Eng. 188 691–9
Srinivasan V 1998 Discrete morphological filters for metrology Proc. 6th ISMQC Symp. on Metrology for Quality Control in Production pp 623–8
Von Weingraber H 1956 U¨ ber die Eignung des Hu¨llprofils als Bezugslinie f¨ur die Messung der Rauheit Ann. CIRP 5 116–28
Whitehouse D J 1994 Surface Metrology (Bristol: Institute of Physics Publishing)
Worring M and Smelders W M 1994 Shape of arbitrary finite point set in R2 J. Math. Image Vis. 4 151–70

Depositing User: Shan Lou
Date Deposited: 05 Jan 2012 16:15
Last Modified: 21 Jan 2013 16:20


Downloads per month over past year

Repository Staff Only: item control page

View Item View Item

University of Huddersfield, Queensgate, Huddersfield, HD1 3DH Copyright and Disclaimer All rights reserved ©