Skip to main content
SpringerLink
Log in

Edge-driven Image Interpolation using Adaptive Anisotropic Radial Basis Functions

  • Published:
Journal of Mathematical Imaging and Vision Aims and scope Submit manuscript

Abstract

This paper investigates the image interpolation problem, where the objective is to improve the resolution of an image by dilating it according to a given enlargement factor. We present a novel interpolation method based on Radial Basis Functions (RBF) which recovers a continuous intensity function from discrete image data samples. The proposed anisotropic RBF interpolant is designed to easily deal with the local anisotropy in the data, such as edge-structures in the image. Considering the underlying geometry of the image, this algorithm allows us to remove the artifacts that may arise when performing interpolation, such as blocking and blurring. Computed examples demonstrate the effectiveness of the method proposed by visual comparisons and quantitative measures.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Allebach, J., Wong, P.W.: Edge-directed interpolation. Proc. IEEE Int. Conf. Image Process. 3, 707–710 (1996)

    Article  Google Scholar 

  2. Carey, W.K., Chang, D.B., Hermami, S.S.: Regularity-preserving image interpolation. IEEE Trans. Image Process. 8, 1293–1297 (1999)

    Article  Google Scholar 

  3. Casciola, G., Lazzaro, D., Montefusco, L.B., Morigi, S.: Fast surface reconstruction and hole filling using radial basis functions. Numer. Algorithms 39, 289–305 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  4. Casciola, G., Lazzaro, D., Montefusco, L.B., Morigi, S.: Shape preserving surface reconstruction using locally anisotropic RBF Interpolants. Comput. Math. Appl. 51, 1185–1198 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  5. Casciola, G., Montefusco, L.B., Morigi, S.: The regularizing properties of anisotropic radial basis functions. Appl. Math. Comput. 190(2), 1050–1062 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  6. Cha, Y., Kim, S.: Edge-forming methods for image zooming. J. Math. Imaging Vis. 25(3), 353–364 (2006). ISSN: 0924-9907

    Article  MathSciNet  Google Scholar 

  7. Chen, M.J., Huang, C.H., Lee, W.L.: A fast edge-oriented algorithm for image interpolation. Image Vis. Comput. 23(9), 791–798 (2005)

    Article  Google Scholar 

  8. Guichard, F., Malgouyres, F.: Total variation based interpolation. Proc. Eur. Signal Process. Conf. 3, 1741–1744 (1998)

    Google Scholar 

  9. Hwang, J.W., Lee, H.S.: Adaptive image interpolation based on local gradient features. IEEE Signal Process. Lett. 11(3), 359–362 (2004)

    Article  Google Scholar 

  10. Jensen, K., Anastassiou, D.: Subpixel edge localization and the interpolation of still images. IEEE Trans. Image Process. 4, 285–295 (1995)

    Article  Google Scholar 

  11. Jiang, H., Moloney, C.: A new direction adaptive scheme for image interpolation. Proc. IEEE Int. Conf. Image Process., 369–372 (2002)

  12. Lazzaro, D., Montefusco, L.B.: Radial basis functions for the multivariate interpolation of large scattered data sets. J. Comput. Appl. Math. 140, 521–536 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  13. Lehmann, T.M., Gonner, C., Spitzer, K.: Survey: interpolation methods in medical image processing. IEEE Trans. Med. Imag. 18, 1049–1075 (1999)

    Article  Google Scholar 

  14. Li, X., Orchard, M.T.: New Edge-Directed Interpolation. IEEE Trans. Image Process. 10(10), 1521–1527 (2001)

    Article  Google Scholar 

  15. Malgouyres, F., Guichard, F.: Edge direction preserving image zooming: a mathematical and numerical analysis. SIAM J. Numer. Anal. 39, 1–37 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  16. Schaback, R.: Error estimates and condition numbers for radial basis function interpolation. Adv. Comput. Math. 3, 251–264 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  17. Schaback, R.: Optimal recovery in translation-invariant spaces of functions. Ann. Numer. Math. 4, 547–555 (1997)

    MATH  MathSciNet  Google Scholar 

  18. Su, D., Willis, P.: Image interpolation by pixel level data-dependent triangulation. Comput. Graph. Forum 23, 189–201 (2004)

    Article  Google Scholar 

  19. Thurnhofer, S., Mitra, S.K.: Edge-enhanced image zooming. Opt. Eng. 35(7), 1862–1870 (1996)

    Article  Google Scholar 

  20. Weickert, J.: Coherence-enhancing diffusion of colour images. Image Vis. Comput. 17, 201–212 (1999)

    Article  Google Scholar 

  21. Weickert, J., Scharr, H.: A scheme for coherence enhancing diffusion filtering with optimized rotation invariance. J. Vis. Commun. Image Represent. 13(1/2), 103–118 (2002)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Bologna, P.zza di Porta San Donato 5, 40127, Bologna, Italy

    G. Casciola, L. B. Montefusco & S. Morigi

Authors
  1. G. Casciola
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. B. Montefusco
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. Morigi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. Morigi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Casciola, G., Montefusco, L.B. & Morigi, S. Edge-driven Image Interpolation using Adaptive Anisotropic Radial Basis Functions. J Math Imaging Vis 36, 125–139 (2010). https://doi.org/10.1007/s10851-009-0176-8

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10851-009-0176-8

Keywords

Search

Navigation