Normalized Averaging Using Adaptive Applicability Functions with Applications in Image Reconstruction from Sparsely and Randomly Sampled Data

  • Tuan Q. Pham
  • Lucas J. van Vliet
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2749)

Abstract

In this paper we describe a new strategy for using local structure adaptive filtering in normalized convolution. The shape of the filter, used as the applicability function in the context of normalized convolution, adapts to the local image structure and avoids filtering across borders. The size of the filter is also adaptable to the local sample density to avoid unnecessary smoothing over high certainty regions. We compared our adaptive interpolation technique with conventional normalized averaging methods. We found that our strategy yields a result that is much closer to the original signal both visually and in terms of MSE, meanwhile retaining sharpness and improving the SNR.

Keywords

Mean Square Error Uncertain Data Mean Square Error Normalize Gradient Magnitude Image Inpainting 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    A. Okabe, B. Boots, K. Sugihara, Spatial tessellations concepts and application of Voronoi diagrams, Wiley, 1992.Google Scholar
  2. 2.
    H. Knutsson, C-F Westin, Normalized and differential convolution: Methods for interpolation and filtering of incomplete and uncertain data, in CVPR’93, 1993. 515–523.Google Scholar
  3. 3.
    I.T. Young, L.J. van Vliet, Recursive implementation of the Gaussian filters, Signal Processing, 44(2), 1995. 139–151.CrossRefGoogle Scholar
  4. 4.
    K. Andersson, H. Knutsson, Continuous Normalized Convolution, ICME’02, 2002. 725–728.Google Scholar
  5. 5.
    P.E. Danielsson. Euclidean distance mapping. CGIP, 14, 1980. 227–248.Google Scholar
  6. 6.
    F. de Jong, L.J. van Vliet, P.P. Jonker, Gradient estimation in uncertain data, MVA’98 IAPR Workshop on Machine Vision Applications, Makuhari, Chiba, Japan, Nov. 1998. 144–147.Google Scholar
  7. 7.
    L.J. van Vliet, P.W. Verbeek, Estimators for orientation and anisotropy in digitized images, in J. van Katwijk et.al. (eds.), ASCI’95, Proc. First Annual Conf. of the Advanced School for Computing and Imaging, Heijen, the Netherlands, 1995. 442–450.Google Scholar
  8. 8.
    H. Knutsson, Representing local structure using tensors, SCIA’89, Oulu, Finland, 1989. 244–251.Google Scholar
  9. 9.
    M. van Ginkel, J. van de Weijer, L.J. van Vliet, P.W. Verbeek, Curvature estimation from orientation fields, SCIA’99, Greenland, 1999. 545–551.Google Scholar
  10. 10.
    M. Nitzberg, T. Shiota, Nonlinear Image Filtering with Edge and Corner Enhancement. IEEE Trans. on PAMI 14(8), 1992. 826–833.Google Scholar
  11. 11.
    A. Almansa and T. Lindeberg, Enhancement of Fingerprint Images using Shape-Adapted Scale-Space Operators, in J. Sporring, M. Nielsen, L. Florack and P. Johansen (eds.), Gaussian Scale-Space Theory, Kluwer Academic Publishers, 1997. 21–30.Google Scholar
  12. 12.
    J. Dijk, D. de Ridder, P.W. Verbeek, J. Walraven, I.T. Young, L.J. van Vliet, “A new measure for the effect of sharpening and smoothing filters on images”, in SCIA’99, Greenland, 1999. 213–220.Google Scholar
  13. 13.
    C. Ballester, M. Bertalmio, V. Caselles, G. Sapiro, J. Verdera, Filling-in by Joint Interpolation of Vector Fields and Gray Levels, IEEE Transactions on Image Processing, 10(8), 2001. 1200–1211.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Tuan Q. Pham
    • 1
  • Lucas J. van Vliet
    • 1
  1. 1.Pattern Recognition GroupDelft University of TechnologyDelftThe Netherlands

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