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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Allebach, J., Wong, P.W.: Edge-directed interpolation. Proc. IEEE Int. Conf. Image Process. 3, 707–710 (1996)
Carey, W.K., Chang, D.B., Hermami, S.S.: Regularity-preserving image interpolation. IEEE Trans. Image Process. 8, 1293–1297 (1999)
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)
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)
Casciola, G., Montefusco, L.B., Morigi, S.: The regularizing properties of anisotropic radial basis functions. Appl. Math. Comput. 190(2), 1050–1062 (2007)
Cha, Y., Kim, S.: Edge-forming methods for image zooming. J. Math. Imaging Vis. 25(3), 353–364 (2006). ISSN: 0924-9907
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)
Guichard, F., Malgouyres, F.: Total variation based interpolation. Proc. Eur. Signal Process. Conf. 3, 1741–1744 (1998)
Hwang, J.W., Lee, H.S.: Adaptive image interpolation based on local gradient features. IEEE Signal Process. Lett. 11(3), 359–362 (2004)
Jensen, K., Anastassiou, D.: Subpixel edge localization and the interpolation of still images. IEEE Trans. Image Process. 4, 285–295 (1995)
Jiang, H., Moloney, C.: A new direction adaptive scheme for image interpolation. Proc. IEEE Int. Conf. Image Process., 369–372 (2002)
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)
Lehmann, T.M., Gonner, C., Spitzer, K.: Survey: interpolation methods in medical image processing. IEEE Trans. Med. Imag. 18, 1049–1075 (1999)
Li, X., Orchard, M.T.: New Edge-Directed Interpolation. IEEE Trans. Image Process. 10(10), 1521–1527 (2001)
Malgouyres, F., Guichard, F.: Edge direction preserving image zooming: a mathematical and numerical analysis. SIAM J. Numer. Anal. 39, 1–37 (2001)
Schaback, R.: Error estimates and condition numbers for radial basis function interpolation. Adv. Comput. Math. 3, 251–264 (1995)
Schaback, R.: Optimal recovery in translation-invariant spaces of functions. Ann. Numer. Math. 4, 547–555 (1997)
Su, D., Willis, P.: Image interpolation by pixel level data-dependent triangulation. Comput. Graph. Forum 23, 189–201 (2004)
Thurnhofer, S., Mitra, S.K.: Edge-enhanced image zooming. Opt. Eng. 35(7), 1862–1870 (1996)
Weickert, J.: Coherence-enhancing diffusion of colour images. Image Vis. Comput. 17, 201–212 (1999)
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)
Author information
Authors and Affiliations
Corresponding author
Rights 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
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10851-009-0176-8