Exact, Scaled Image Rotation Using the Finite Radon Transform

  • Imants Svalbe
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5810)


In traditional tomography, a close approximation of an object can be reconstructed from its sinogram. The orientation (or zero angle) of the reconstructed image can be chosen to be any one of the many projected view angles. The Finite Radon Transform (FRT) is a discrete analogue of classical tomography. It permits exact reconstruction of an object from its discrete projections. Reordering the discrete FRT projections is equivalent to an exact digital image rotation. Each FRT-based rotation preserves the intensity of all original image pixels and allocates new pixel values through use of an area-preserving, angle-specific interpolation filter. This approach may find application in image rotation for feature matching, and to improve the display of zoomed and rotated images.


Image Space Projection Angle Image Rotation Original Pixel Sequential Rotation 
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.


  1. 1.
    Danielsson, P.E., Hammerin, M.: High-accuracy rotation of images. Graphical Models and Image Processing (CVGIP) 54(4), 340–344 (1991)CrossRefGoogle Scholar
  2. 2.
    Matúš, F., Flusser, J.: Image representation via a finite Radon transform. IEEE Transactions on Pattern Analysis and Machine Intelligence 15(10), 996–1006 (1993)CrossRefGoogle Scholar
  3. 3.
    Svalbe, I., van der Spek, D.: Reconstruction of tomographic images using analog projections and the digital Radon transform. Linear Algebra and Its Applications 339, 125–145 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Svalbe, I.: Sampling properties of the discrete Radon transform. Discrete Applied Mathematics 139(1-3), 265–281 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Svalbe, I.: Image operations in discrete Radon space. In: Proc. of the Sixth Digital Image Computing Techniques and Applications, Dicta 2002, pp. 285–290 (2002)Google Scholar
  6. 6.
    Svalbe, I.: Natural representations for straight lines and the hough transform on discrete arrays. IEEE Transactions on Pattern Analysis and Machine Intelligence 11(9), 941–950 (1989)CrossRefGoogle Scholar
  7. 7.
    Kingston, A., Svalbe, I.: Projective transforms on periodic discrete image arrays. Advances in Imaging and Electron Physics 139, 75–177 (2006)CrossRefGoogle Scholar
  8. 8.
    Chandra, S., Svalbe, I.: A method for removing cyclic artefacts in discrete tomography using Latin squares. In: 19th International Conference on Pattern Recognition, December 2008, pp. 1–4 (2008)Google Scholar
  9. 9.
    Chandra, S., Svalbe, I., Guédon, J.P.: An exact, non-iterative Mojette inversion technique utilising ghosts. In: Coeurjolly, D., Sivignon, I., Tougne, L., Dupont, F. (eds.) DGCI 2008. LNCS, vol. 4992, pp. 401–412. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  10. 10.
    Servières, M., Normand, N., Guédon, J.P., Bizais, Y.: The Mojette transform: Discrete angles for tomography. In: Herman, G., Kuba, A. (eds.) Proceedings of the Workshop on Discrete Tomography and its Applications. Electronic Notes in Discrete Mathematics, vol. 20, pp. 587–606 (2005)Google Scholar
  11. 11.
    Guédon, J., Normand, N., Kingston, A., Parrein, B., Serviéres, M., Evenou, P., Svalbe, I., Autrusseau, F., Hamon, T., Bizais, Y., Coeurjolly, D., Boulos, F., Grail, E.: The Mojette Transform: Theory and Applications. ISTE-Wiley (2009)Google Scholar
  12. 12.
    Chen, X., Lu, S., Yuan, X.: Midpoint line algorithm for high-speed high-accuracy rotation of images. In: IEEE Conf. on Systems, Man and Cybernetics, Beijing, China, pp. 2739–2744 (1996)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Imants Svalbe
    • 1
  1. 1.School of PhysicsMonash UniversityAustralia

Personalised recommendations