Skip to main content
Log in

Verification of 3D freeform parts by registration of multiscale shape descriptors

  • ORIGINAL ARTICLE
  • Published:
The International Journal of Advanced Manufacturing Technology Aims and scope Submit manuscript

Abstract

Precision inspection of freeform parts takes an important role in manufacturing quality control. The aim of this inspection is to verify that the geometric dimensions and produced part tolerances meet quality requirements. This is achieved by fitting the scanned data to the computer-aided design (CAD) model. This verification is complicated since the produced part includes defects and distortions. Currently, industry uses semimanual verification, which is expensive, often inaccurate, and very time-consuming. This paper describes a new method for automatic registration and alignment of two 3D freeform shapes, one from the scanned data and the other from the CAD model. The method makes no assumptions about their initial positions. Instead, the proposed algorithm uses a multiscale shape descriptor to select features on the scanned data and identify their corresponding features on the CAD model. The proposed shape descriptor is invariant with respect to local shapes and is robust to noise. A coarse alignment is computed by finding and registering the best matching triplet of features. The iterative closest point algorithm uses resulting coarse alignment to achieve a tuned alignment. The proposed method is automatic, efficient, and straightforward to implement. The algorithm can also be effective in the case of partial scanned inspected shapes. The feasibility of the proposed method is demonstrated on a blade model.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Spyridi AJ, Requicha AG (1990) Accessibility analysis for the automatic inspection of mechanical parts by coordinate measuring machines. IEEE international conference on robotics and automation, Cincinnati

    Google Scholar 

  2. Farin G (1988) Curves and surfaces for CAGD. A practical guide. Academic, San Diego

    Google Scholar 

  3. Hameiri Y, Shimshoni I (2002) Estimating the principal curvatures and the Darboux frame from real 3D range data. At 1st International Symposium on 3D Data Processing Visualization and Transmission (3DPVT 2002)

  4. Stokely EM, Wu SY (1992) Surface parameterization and curvature measurement of arbitrary 3-D objects: five practical methods. IEEE Trans Pattern Anal Mach Intell 14(8):833–840

    Article  Google Scholar 

  5. Lipshitz B, Fischer A (2005) Verification of scanned engineering parts with CAD models based on discrete curvature estimation. Journal of Computing and Information Science in Science and Engineering 5(2):116–117

    Article  Google Scholar 

  6. Meek DS, Walton DJ (2000) On surface normal and Gaussian curvature approximations given data sampled from a smooth surface. Comput Aided Geom Des 17:521–543

    Article  MATH  MathSciNet  Google Scholar 

  7. Wolfson H, Rigoutsos I (1997) Geometric hashing: an overview. IEEE Computer Science and Engineering 10–21

  8. Hamann B (1993) Curvature approximation for triangulated surfaces. Computing Suppl 8:139–153

    MathSciNet  Google Scholar 

  9. Taubin G (1995) Estimating the tensor of curvature of a surface from polyhedral approximation. Proceedings Intl Conf on Computer Vision 902–907

  10. Do Carmo MP (1976) Differential geometry of curves and surfaces. Prentice-Hall, Englewood Cliffs

    MATH  Google Scholar 

  11. Meyer M, Desbrun M, Schröder P, Barr AH (2002) Discrete differential geometry operators for triangulated 2-manifolds. Proceedings of VisMath '02 Berlin, Germany

  12. Gelfand N, Mitra N, Guibas L, Pottmann H (2005) Robust global registration. Proc Eurographics Symp Geom Processing 197–206

  13. Stockman G (1987) Object recognition and localization via pose clustering. CVGI 361–387

  14. Eggert DW, Lorusso A, Fisher RB (1997) Estimating 3D rigid body transformations: a comparison of four major algorithms. Mach Vis Appl 272–290

  15. Besl PJ, McKay ND (1992) A method for registration of 3-D shapes. IEEE Trans Pattern Anal Mach Intell 14(2):239–256

    Article  Google Scholar 

  16. Sharp GC, Lee SW, Wehe DK (2002) ICP registration using invariant features. PAMI 24(1):90–102

    Google Scholar 

  17. Barequet G, Sharir M (1997) Partial surface and volume matching in three dimensions. PAMI 929–948

  18. Manay S, Hong B,Yezzi A, Soatto S(2004) Integral invariant signatures. In ECCV 87–99

  19. Fishkel F, Fischer A, Ar S (2006) Verification of engineering models based on bipartite graph matching for inspection applications, Lecture Notes in Computer Science, Geometric Modeling and Processing—GMP. Springer, pp 485–499

  20. Kase K, Makinouchi A, Nakagawa T, Suzuki H, Kimura F (1999) Shape error evaluation method of free-form surfaces. Comput Aided Des 31(8):495–505

    Article  MATH  Google Scholar 

  21. Kimmel R, Sethian JA (1998) Computing geodesic paths on manifolds. In Proceedings of the National Academy of Sciences No. 95, 8431–8435

  22. Pottmann H, Huang Q-X, Yang YL, Kolpl S (2005) Integral invariants for robust geometry processing. Technical Report 146. Vienna University of Technology

  23. Fischer A (2000) Multi-level models for reverse engineering and rapid prototyping in remote CAD systems. Comput Aided Des 32(1):27–38

    Article  Google Scholar 

  24. Scott D (1979) On optimal and data-based histograms. Biometrika 66:605–610

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Anath Fischer.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shmukler, A., Fischer, A. Verification of 3D freeform parts by registration of multiscale shape descriptors. Int J Adv Manuf Technol 49, 1093–1106 (2010). https://doi.org/10.1007/s00170-009-2447-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-009-2447-3

Keywords

Navigation