Skip to main content

Statistical Shape Analysis of Manufacturing Data

  • Chapter
Geometric Tolerances

Abstract

We show how statistical shape analysis, a set of techniques used to model the shapes of biological and other kinds of objects in the natural sciences, can also be used to model the geometric shape of a manufactured part. We review Procrustes-based methods, and emphasize possible solutions to the basic problem of having corresponding, or matching, labels in the measured “landmarks”, the locations of the measured points on each part acquired with a coordinate measuring machine or similar instrument.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 189.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 249.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 249.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  • Adams DC, Rohlf FJ, Slice DE (2004) Geometric morphometrics: ten years of progress following the “revolution”. Ital J Zool 71:5–16

    Article  Google Scholar 

  • ASME Y14.5M (1994) Dimensioning and tolerancing. American Society of Mechanical Engineers, New York

    Google Scholar 

  • Belongie S, Malik J, Puzicha J (2002) Shape matching and object recognition using shape contexts. IEEE Trans Pattern Anal Mach Intell 24:509–522

    Article  Google Scholar 

  • Besl PJ, McKay ND (1992) A method for registration of 3-D shapes. IEEE Trans Pattern Anal Mach Intell 14:239–256

    Article  Google Scholar 

  • Chui H, Rangarajan A (2000) A new algorithm for non-rigid point matching Proc IEEE Conf Comput Vis Pattern Recognit 44–51

    Google Scholar 

  • Colosimo BM, Pacella M, Semeraro Q (2008) Statistical process control for geometric specifications: on the monitoring of roundness profiles. J Qual Technol 40:1–18

    Google Scholar 

  • Davies R, Twining C, Taylor C (2008), Statistical models of shape, optimisation and evaluation. Springer, London

    MATH  Google Scholar 

  • Del Castillo E, Colosimo BM (2010) Statistical shape analysis of experiments for manufacturing processes. Technometrics (in press)

    Google Scholar 

  • Dryden IL, Mardia KV (1998) Statistical shape analysis. Wiley, Chichester

    MATH  Google Scholar 

  • Frome A, Huber D, Kolluri R, Bulow T, Malik J (2004) Recognizing objects in range data using regional point descriptors. In: Proceedings of the 8th European conference on computer vision, vol 3, pp 224–237

    Google Scholar 

  • Gold S, Rangarajan A, Lu C-P, Pappu S, Mjolsness E (1998) New algorithms for 2D and 3D point matching: pose estimation and correspondence. Pattern Recognit 31:1019–1031

    Article  Google Scholar 

  • Goodall C (1991) Procrustes methods in the statistical analysis of shape. J R Stat Soc B,53:285–339

    MATH  MathSciNet  Google Scholar 

  • Gower JC (1975) Generalized Procrustes analysis. Psychometrika 40:33–51

    Article  MATH  MathSciNet  Google Scholar 

  • Green PJ, Mardia KV (2006) Bayesian alignment using hierarchical models, with applications in protein bioinformatics. Biometrika 93:235–254

    Article  MATH  MathSciNet  Google Scholar 

  • Horn BKP, Hilden HM, Negahdaripour S (1988) Closed-form solution of absolute orientation using orthonormal matrices. J Opt Soc Am A 5:1127–1135

    Article  MathSciNet  Google Scholar 

  • Jackson JE (2003) A user’s guide to principal components. Wiley, New York

    Google Scholar 

  • Kang L, Albin SL (2000) On-line monitoring when the process yields a linear profile. J Qual Technol 32:418–426

    Google Scholar 

  • Kendall DG (1984) Shape manifolds, Procrustean metrics, and complex projective spaces. Bull Lond Math Soc 16:81–121

    Article  MATH  MathSciNet  Google Scholar 

  • Kendall DG (1989) A survey of the statistical theory of shape Stat Sci 4:87–89

    Article  MATH  MathSciNet  Google Scholar 

  • Kent JT, Mardia KV (2001) Shape, Procrustes tangent projections and bilateral symmetry. Biometrika 88:469–485

    Article  MATH  MathSciNet  Google Scholar 

  • Klingenberg CP, McIntyre GS (1998) Geometric morphometrics of developmental instability: analyzing patterns of fluctuating asymmetry with Procrustes methods. Evolution 52:1363–1375

    Article  Google Scholar 

  • Lele SR, Richtsmeier JT (2001) An invariant approach to statistical analysis for shapes. Chapman & Hall/CRC, Boca Raton

    Book  Google Scholar 

  • Papadimitrou CH, Steiglitz K (1982) Combinatorial optimization, algorithms and complexity. Prentice Hall, Englewood Cliffs

    Google Scholar 

  • Rosenbaum PR (2005) An exact distribution-free test comparing two multivariate distributions based on adjacency. J R Stat Soc B 67:515–530

    Article  MATH  MathSciNet  Google Scholar 

  • Ten Berge JMF (1977) Orthogonal Procrustes rotation for two or more matrices. Psychometrika 42(2):267–276

    Article  MATH  MathSciNet  Google Scholar 

  • Woodall WH, Spitzner DJ, Montgomery DC, Gupta S (2004) Using control charts to monitor process and product quality profiles. J Qual Technol 36:309–320

    Google Scholar 

  • Zelditch ML, Swiderski DL, Sheets HD, Fink WL (2004) Geometric morphometrics for biologists, a primer. Elsevier, San Diego

    Google Scholar 

  • Zhang Z (1998) Iterative point matching for registration of free-form curves. Reports de recherche no. 1658. IRIA, Sophia Antipolis

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag London Limited

About this chapter

Cite this chapter

del Castillo, E. (2011). Statistical Shape Analysis of Manufacturing Data. In: Colosimo, B., Senin, N. (eds) Geometric Tolerances. Springer, London. https://doi.org/10.1007/978-1-84996-311-4_7

Download citation

  • DOI: https://doi.org/10.1007/978-1-84996-311-4_7

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-84996-310-7

  • Online ISBN: 978-1-84996-311-4

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics