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An Analytical Curvature B-Spline Algorithm for Effective Curve Modeling

  • Joi San TanEmail author
  • Ibrahim Venkat
  • Bahari Belaton
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9429)

Abstract

This paper presents a new algorithm based on an analytical approach for generating non-uniform cubic B-spline which has potential applications in curve modeling. For a given set of data points, knot vectors are computed using the centripetal approach. Next, number of data points is assimilated around the high curvature areas and the parametrization aspect is computed by the inverse chord length with the new set of data points. Second order derivatives are used to determine the high curvature areas of the curves. The method proposed here enables to construct the curves smoothly around high curvature areas by assigning adequate number of data points for the B-splines. Experimental validations justify the fact that the average curve fitting error yielded by the proposed approach is the lowest when compared to other standard curve models.

Keywords

Non-uniform cubic B-spline Centripetal method Second order derivative Inverse chord length 

Notes

Acknowledgment

This research is supported by the RU-PRGS Universiti Sains Malaysia (1001/PKOMP/846051) grant titled “Skull and Photo Superimposition with Conditional Anthropological Parameters using Computer Sciences.” and RUI grant (1001/PKOMP/811290). We would like to thank Prof. K.G Subramaniam for providing valuable comments to improve this paper.

References

  1. 1.
    Cohen, F.S., Wang, J.-Y.: Part I: modeling image curves using invariant 3-D object curve models-a path to 3-D recognition and shape estimation from image contours. IEEE Trans. Pattern Anal. Mach. Intell. 16, 1–12 (1994)CrossRefGoogle Scholar
  2. 2.
    Farin, G.E.: Curves and Surfaces for CAGD: A Practical Guide. Morgan Kaufmann, Burlington (2002)Google Scholar
  3. 3.
    Huang, Z., Cohen, F.S.: Affine-invariant B-spline moments for curve matching. IEEE Trans. Image Process. 5, 1473–1480 (1996)CrossRefGoogle Scholar
  4. 4.
    Sederberg, T.W.: Computer Aided Geometric Design. CAGD Course Notes. Brigham Young University, Provo, UT, 84602 (2012)Google Scholar
  5. 5.
    Wang, J.-Y., Cohen, F.S.: Part II: 3-D object recognition and shape estimation from image contours using B-splines, shape invariant matching, and neural network. IEEE Trans. Pattern Anal. Mach. Intell. 16, 13–23 (1994)CrossRefGoogle Scholar
  6. 6.
    Dai, X., Khorram, S.: A feature-based image registration algorithm using improved chain-code representation combined with invariant moments. IEEE Trans. Geosci. Remote Sens. 37, 2351–2362 (1999)CrossRefGoogle Scholar
  7. 7.
    Lin, Y.-L., Wang, M.-J.J.: Automated body feature extraction from 2D images. Expert Syst. Appl. 38, 2585–2591 (2011)CrossRefGoogle Scholar
  8. 8.
    Vaddi, R.S., Boggavarapu, L.N.P., Vankayalapati, H.D., Anne, K.R.: Contour detection using freeman chain code and approximation methods for the real time object detection. Asian J. Comput. Sci. Inf. Technol. 1 (2013)Google Scholar
  9. 9.
    Lee, C.P., Tan, A.W.C., Tan, S.C.: Gait recognition via optimally interpolated deformable contours. Pattern Recogn. Lett. 34, 663–669 (2013)CrossRefGoogle Scholar
  10. 10.
    Mebatsion, H.K., Paliwal, J., Jayas, D.S.: Evaluation of variations in the shape of grain types using principal components analysis of the elliptic Fourier descriptors. Comput. Electron. Agric. 80, 63–70 (2012)CrossRefGoogle Scholar
  11. 11.
    Kolesnikov, A.: ISE-bounded polygonal approximation of digital curves. Pattern Recogn. Lett. 33, 1329–1337 (2012)CrossRefGoogle Scholar
  12. 12.
    Marji, M., Siy, P.: A new algorithm for dominant points detection and polygonization of digital curves. Pattern Recogn. 36, 2239–2251 (2003)zbMATHCrossRefGoogle Scholar
  13. 13.
    Yin, P.-Y.: A discrete particle swarm algorithm for optimal polygonal approximation of digital curves. J. Vis. Commun. Image Represent. 15, 241–260 (2004)CrossRefGoogle Scholar
  14. 14.
    Anuar, F.M., Setchi, R., Lai, Y.K.: Trademark image retrieval using an integrated shape descriptor. Expert Syst. Appl. 40, 105–121 (2013)CrossRefGoogle Scholar
  15. 15.
    Chen, X.-D., Ma, W., Paul, J.-C.: Cubic B-spline curve approximation by curve unclamping. Comput. Aided Des. 42, 523–534 (2010)CrossRefGoogle Scholar
  16. 16.
    Hu, S.-M., Tai, C.-L., Zhang, S.-H.: An extension algorithm for B-splines by curve unclamping. Comput. Aided Des. 34, 415–419 (2002)CrossRefGoogle Scholar
  17. 17.
    Piegl, L., Tiller, W.: Curve and Surface Basics. Springer, Heidelberg (1995)CrossRefGoogle Scholar
  18. 18.
    Bein, M., Fellner, D.W., Stork, A.E.: Genetic B-spline approximation on combined B-reps. Vis. Comput. 27, 485–494 (2011)CrossRefGoogle Scholar
  19. 19.
    Liu, H., Latecki, L.J., Liu, W.: A unified curvature definition for regular, polygonal, and digital planar curves. Int. J. Comput. Vis. 80, 104–124 (2008)CrossRefGoogle Scholar
  20. 20.
    Hermann, S., Klette, R.: Multigrid analysis of curvature estimators. In: Proceedings of the Image Vision Computing, pp. 108–112. New Zealand (2003)Google Scholar
  21. 21.
    Marji, M., Klette, R., Siy, P.: Corner detection and curve partitioning using arc-chord distance. In: Klette, R., Žunić, J. (eds.) IWCIA 2004. LNCS, vol. 3322, pp. 512–521. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  22. 22.
    Kovalevsky, V.: Curvature in digital 2D images. Int. J. Pattern Recogn. Artif. Intell. 15, 1183–1200 (2001)CrossRefGoogle Scholar
  23. 23.
    Abbas, A., Nasri, A., Maekawa, T.: Generating B-spline curves with points, normals and curvature constraints: a constructive approach. Vis. Comput. 26, 823–829 (2010)CrossRefGoogle Scholar
  24. 24.
    Medioni, G., Yasumoto, Y.: Corner detection and curve representation using cubic B-splines. In: 1986 IEEE International Conference on Robotics and Automation. Proceedings, vol. 3, pp. 764–769. IEEE (1986)Google Scholar
  25. 25.
    Goldenthal, R., Bercovier, M.: Spline curve approximation and design by optimal control over the knots. In: Hahmann, S., Brunnett, G., Farin, G., Goldman, R. (eds.) Geometric Modelling, pp. 53–64. Springer, Vienna (2004)CrossRefGoogle Scholar
  26. 26.
    Zhao, X., Zhang, C., Yang, B., Li, P.: Adaptive knot placement using a GMM-based continuous optimization algorithm in B-spline curve approximation. Comput. Aided Des. 43, 598–604 (2011)CrossRefGoogle Scholar
  27. 27.
    Lim, C.-G.: A universal parametrization in B-spline curve and surface interpolation. Comput. Aided Geom. Des. 16, 407–422 (1999)zbMATHCrossRefGoogle Scholar
  28. 28.
    Lü, W.: Curves with chord length parameterization. Comput. Aided Geom. Des. 26, 342–350 (2009)zbMATHCrossRefGoogle Scholar
  29. 29.
    Hoschek, J., Lasser, D., Schumaker, L.L.: Fundamentals of Computer Aided Geometric Design. AK Peters, Ltd., Natick (1993)zbMATHGoogle Scholar
  30. 30.
    Foley, T.A., Nielson, G.M.: Knot Selection for Parametric Spline Interpolation. Academic Press Professional, Inc., Waltham (1989)CrossRefGoogle Scholar
  31. 31.
    Haron, H., Rehman, A., Adi, D.I.S., Lim, S.P., Saba, T.: Parameterization method on B-spline curve. Math. Probl. Eng. 2012, (2012)Google Scholar
  32. 32.
    Fang, J.-J., Hung, C.-L.: An improved parameterization method for B-spline curve and surface interpolation. Comput. Aided Des. 45, 1005–1028 (2013)MathSciNetCrossRefGoogle Scholar
  33. 33.
    Hermann, S., Klette, R.: A comparative study on 2d curvature estimators. pp. (2006)Google Scholar
  34. 34.
    Chui, H., Rangarajan, A.: A new point matching algorithm for non-rigid registration. Comput. Vis. Image Underst. 89, 114–141 (2003)zbMATHCrossRefGoogle Scholar
  35. 35.
    Sebastian, T.B., Klein, P.N., Kimia, B.B.: Recognition of shapes by editing their shock graphs. IEEE Trans. Pattern Anal. Mach. Intell. 26, 550–571 (2004)CrossRefGoogle Scholar
  36. 36.
    Harris, C., Stephens, M.: A combined corner and edge detector. In: Alvey Vision Conference, vol. 15, Manchester, UK (1988)Google Scholar
  37. 37.
    De Boor, C.: A practical guide to splines. In: Mathematics of Computation. Springer, New York (1978)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.School of Computer SciencesUniversiti Sains MalaysiaPulau PinangMalaysia

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