Skip to main content

Surface Quality Inspection of Deformable Parts with Variable B-Spline Surfaces

  • Conference paper
Pattern Recognition (DAGM/OAGM 2012)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 7476))

Abstract

High precision range sensors can be used for measuring 3D point clouds of object surfaces for quality inspection in industrial production. It is often difficult to formally describe acceptable tolerance ranges of real surfaces, especially for deformable objects. Instead of a formal definition, the surface and its tolerance range can rather be given by a set of training samples.

In this paper we describe how to apply the Karhunen-Loève-Transform (KLT) on B-spline surfaces. With this transform, a group of similar surfaces can be described with very few characteristic coefficients in the transformed domain, thus allowing the detection of marginal surface deviations on deformable parts.

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 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight 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.

References

  1. Besl, P.J., Mckay, H.D.: A method for registration of 3-D shapes. IEEE Transactions on Pattern Analysis and Machine Intelligence 14(2), 239–256 (1992)

    Article  Google Scholar 

  2. Bispo, E.M., Fisher, R.B.: Free-form surface matching for surface inspection. In: Proceedings of the 6th IMA Conference on the Mathematics of Surfaces, pp. 119–136. Clarendon Press (1994)

    Google Scholar 

  3. Björck, A.: Numerics of Gram-Schmidt orthogonalization. Linear Algebra and its Applications 197/198, 297–316 (1994)

    Article  Google Scholar 

  4. Broggiato, G.B., Campana, F., Gerbino, S.: Shape deviation analysis on sheet-metal parts through reverse engineering techniques. In: ADM International Conference, vol. 12 (2001)

    Google Scholar 

  5. Farin, G.: Curves and Surfaces for CAGD - A Practical Guide, 5th edn. Morgan Kaufmann (2002)

    Google Scholar 

  6. Gerbrands, J.J.: On the relationships between SVD, KLT and PCA. Pattern Recognition 14(1-6), 375–381 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  7. Koch, K.R.: Three-dimensional NURBS surface estimated by lofting method. Int. Journal of Advanced Manufacturing Technology 49, 1059–1068 (2010)

    Article  Google Scholar 

  8. Li, Y., Gu, P.: Free-form surface inspection techniques start of the art review. Computer-Aided Design 36(13), 1395–1417 (2004)

    Article  Google Scholar 

  9. Lilienblum, E., Michaelis, B.: Optical 3D surface reconstruction by a multi-period phase shift method. Journal of Computers 2(2) (2007)

    Google Scholar 

  10. Lilienblum, T., Albrecht, P., Calow, R., Michaelis, B.: Dent detection in car bodies. In: Proc. 15th Int. Pattern Recognition Conf., vol. 4, pp. 775–778 (2000)

    Google Scholar 

  11. Michaelis, B.: Zusammengesetzte Messgrößen und ihre Anwendung. Ph.D. thesis, TH Magdeburg (1980)

    Google Scholar 

  12. Özkul, M.: Qualitätsansprüche bezüglich des äußeren Erscheinungsbildes von Automobilen der Premiumklasse. Ph.D. thesis, TU Munich (2009)

    Google Scholar 

  13. Park, H., Jung, H., Kim, K.: A new approach for lofted B-spline surface interpolation to serial contours. The International Journal of Advanced Manufacturing Technology 23, 889–895 (2004)

    Google Scholar 

  14. Peng, J., Strela, V., Zorin, D.: A simple algorithm for surface denoising. In: VIS 2001: Proceedings of the Conference on Visualization 2001, pp. 107–112. IEEE Computer Society, Washington, DC (2001)

    Chapter  Google Scholar 

  15. Piegl, L., Tiller, W.: The Nurbs Book. Monographs in Visual Communication. Springer (1997)

    Google Scholar 

  16. Qin, K.: General matrix representations for B-splines. The Visual Computer 16, 177–186 (2000)

    Article  Google Scholar 

  17. Recknagel, R.J.: Defekterkennung an Oberflächen mittels Waveletmethoden. Ph.D. thesis, Universität Jena (2000)

    Google Scholar 

  18. Redd, A.: A comment on the orthogonalization of B-spline basis functions and their derivatives. In: Statistics and Computing, pp. 1–7 (2011)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

von Enzberg, S., Michaelis, B. (2012). Surface Quality Inspection of Deformable Parts with Variable B-Spline Surfaces. In: Pinz, A., Pock, T., Bischof, H., Leberl, F. (eds) Pattern Recognition. DAGM/OAGM 2012. Lecture Notes in Computer Science, vol 7476. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32717-9_18

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-32717-9_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-32716-2

  • Online ISBN: 978-3-642-32717-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics