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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
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)
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)
Björck, A.: Numerics of Gram-Schmidt orthogonalization. Linear Algebra and its Applications 197/198, 297–316 (1994)
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)
Farin, G.: Curves and Surfaces for CAGD - A Practical Guide, 5th edn. Morgan Kaufmann (2002)
Gerbrands, J.J.: On the relationships between SVD, KLT and PCA. Pattern Recognition 14(1-6), 375–381 (1981)
Koch, K.R.: Three-dimensional NURBS surface estimated by lofting method. Int. Journal of Advanced Manufacturing Technology 49, 1059–1068 (2010)
Li, Y., Gu, P.: Free-form surface inspection techniques start of the art review. Computer-Aided Design 36(13), 1395–1417 (2004)
Lilienblum, E., Michaelis, B.: Optical 3D surface reconstruction by a multi-period phase shift method. Journal of Computers 2(2) (2007)
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)
Michaelis, B.: Zusammengesetzte Messgrößen und ihre Anwendung. Ph.D. thesis, TH Magdeburg (1980)
Özkul, M.: Qualitätsansprüche bezüglich des äußeren Erscheinungsbildes von Automobilen der Premiumklasse. Ph.D. thesis, TU Munich (2009)
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)
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)
Piegl, L., Tiller, W.: The Nurbs Book. Monographs in Visual Communication. Springer (1997)
Qin, K.: General matrix representations for B-splines. The Visual Computer 16, 177–186 (2000)
Recknagel, R.J.: Defekterkennung an Oberflächen mittels Waveletmethoden. Ph.D. thesis, Universität Jena (2000)
Redd, A.: A comment on the orthogonalization of B-spline basis functions and their derivatives. In: Statistics and Computing, pp. 1–7 (2011)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights 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)