Subpixel Registration Directly from the Phase Difference

  • Murat Balci
  • Hassan Foroosh
Open Access
Research Article
Part of the following topical collections:
  1. Super-Resolution Imaging: Analysis, Algorithms, and Applications


This paper proposes a new approach to subpixel registration, under local/global shifts or rotation, using the phase-difference matrix. We establish the exact relationship between the continuous and the discrete phase difference of two shifted images and show that their discrete phase difference is a 2-dimensional sawtooth signal. As a result, the exact shifts or rotations can be determined to subpixel or subangle accuracy by counting the number of cycles of the phase-difference matrix along the frequency axes. The subpixel portion is represented by a fraction of a cycle corresponding to the noninteger part of the shift or rotation. The rotation angle is estimated by applying our method using a polar coordinate system. The problem is formulated as an overdetermined system of equations and is solved by imposing a regularity constraint. The tradeoff for imposing the constraint is determined by exploiting the rank constraint leading to a closed-form expression for the optimal regularization parameter.


Coordinate System Information Technology Rotation Angle Phase Difference Quantum Information 


  1. 1.
    Brown LG: A survey of image registration techniques. ACM Computing Surveys 1992, 24(4):325–376. 10.1145/146370.146374CrossRefGoogle Scholar
  2. 2.
    Maintz JBA, Viergever MA: A survey of medical image registration. Medical Image Analysis 1998, 2(1):1–36.CrossRefGoogle Scholar
  3. 3.
    Zitová BA, Flusser J: Image registration methods: a survey. Image and Vision Computing 2003, 21(11):977–1000. 10.1016/S0262-8856(03)00137-9CrossRefGoogle Scholar
  4. 4.
    Abbiss JB, Brames BJ, Fiddy MA: Super-resolution algorithms for a modified Hopfield neural network. IEEE Transactions on Signal Processing 1991, 39(7):1516–1523. 10.1109/78.134391CrossRefGoogle Scholar
  5. 5.
    Aizawa K, Komatsu T, Saito T: A scheme for acquiring very high resolution images using multiple cameras. Proceeding of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '92), March 1992, San Francisco, Calif, USA 3: 289–292.Google Scholar
  6. 6.
    Boult TE, Wolberg G: Local image reconstruction and subpixel restoration algorithms. CVGIP: Graphical Models and Image Processing 1993, 55(1):63–77. 10.1006/cgip.1993.1005Google Scholar
  7. 7.
    Elad M, Feuer A: Restoration of a single super-resolution image from several blurred, noisy, and undersampled measured images. IEEE Transactions on Image Processing 1997, 6(12):1646–1658. 10.1109/83.650118CrossRefGoogle Scholar
  8. 8.
    Farsiu S, Robinson MD, Elad M, Milanfar P: Fast and robust multiframe super-resolution. IEEE Transactions on Image Processing 2004, 13(10):1327–1344. 10.1109/TIP.2004.834669CrossRefGoogle Scholar
  9. 9.
    (Shekarforoush) Foroosh H, Berthod M, Zerubia J, Werman M: Sub-pixel Bayesian estimation of albedo and height. International Journal of Computer Vision 1996, 19(3):289–300. 10.1007/BF00055148CrossRefGoogle Scholar
  10. 10.
    Irani M, Peleg S: Improving resolution by image registration. CVGIP: Graphical Models and Image Processing 1991, 53(3):231–239. 10.1016/1049-9652(91)90045-LGoogle Scholar
  11. 11.
    Keren D, Peleg S, Brada R: Image sequence enhancement using sub-pixel displacements. Proceeding of IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR '88), June 1988, Ann Arbor, Mich, USA 742–746.CrossRefGoogle Scholar
  12. 12.
    Kim SP, Bose NK, Valenzuela HM: Recursive reconstruction of high resolution image from noisy undersampled multiframes. IEEE Transactions on Signal Processing 1990, 38(6):1013–1027. 10.1109/29.56062CrossRefGoogle Scholar
  13. 13.
    Lim WB, Park MK, Kang MG: Spatially adaptive regularized iterative high-resolution image reconstruction algorithm. Visual Communications and Image Processing (VCIP '01), January 2001, San Jose, Calif, USA, Proceedings of SPIE 4310: 10–20.Google Scholar
  14. 14.
    Ng MK, Yip AM: A fast MAP algorithm for high-resolution image reconstruction with multisensors. Multidimensional Systems and Signal Processing 2001, 12(2):143–164. 10.1023/A:1011136812633MathSciNetCrossRefGoogle Scholar
  15. 15.
    Nguyen N, Milanfar P, Golub GH: A computationally efficient super-resolution image reconstruction algorithm. IEEE Transactions on Image Processing 2001, 10(4):573–583. 10.1109/83.913592CrossRefGoogle Scholar
  16. 16.
    Patti AJ, Sezan MI, Murat Tekalp A: Super-resolution video reconstruction with arbitrary sampling lattices and nonzero aperture time. IEEE Transactions on Image Processing 1997, 6(8):1064–1076. 10.1109/83.605404CrossRefGoogle Scholar
  17. 17.
    Peleg S, Keren D, Schweitzer L: Improving image resolution using subpixel motion. Pattern Recognition Letters 1987, 5(3):223–226. 10.1016/0167-8655(87)90067-5CrossRefGoogle Scholar
  18. 18.
    Schultz RR, Stevenson RL: Improved definition video frame enhancement. Proceeding of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '95), May 1995, Detroit, Mich, USA 4: 2169–2172.Google Scholar
  19. 19.
    (Shekarforoush) Foroosh , Chellappa R: Data-driven multichannel super-resolution with application to video sequences. Journal of Optical Society of America A 1999, 16(3):481–492. 10.1364/JOSAA.16.000481CrossRefGoogle Scholar
  20. 20.
    Tsai RY, Huang TS: Multiframe image restoration and registration. In Advances in Computer Vision and Image Processing. Volume 1. JAI Press, Greenwich, Conn, USA; 1984:317–339. chapter 7Google Scholar
  21. 21.
    (Shekarforoush) Foroosh H, Zerubia JB, Berthod M: Extension of phase correlation to subpixel registration. IEEE Transactions on Image Processing 2002, 11(3):188–200. 10.1109/83.988953CrossRefGoogle Scholar
  22. 22.
    (Shekarforoush) Foroosh H, Berthod M, Zerubia J: Subpixel image registration by estimating the polyphase decomposition of cross power spectrum. Proceeding of IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR '96), June 1996, San Francisco, Calif, USA 532–537.CrossRefGoogle Scholar
  23. 23.
    Hoge WS: A subspace identification extension to the phase correlation method [MRI application]. IEEE Transactions on Medical Imaging 2003, 22(2):277–280. 10.1109/TMI.2002.808359CrossRefGoogle Scholar
  24. 24.
    Kim SP, Su WY: Subpixel accuracy image registration by spectrum cancellation. Proceeding of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '93), April 1993, Minneapolis, Minn, USA 5: 153–156.Google Scholar
  25. 25.
    Stone HS, Orchard MT, Chang E-C, Martucci SA: A fast direct Fourier-based algorithm for subpixel registration of images. IEEE Transactions on Geoscience and Remote Sensing 2001, 39(10):2235–2243. 10.1109/36.957286CrossRefGoogle Scholar
  26. 26.
    Wolberg G, Zokai S: Robust image registration using log-polar transform. Proceeding of International Conference on Image Processing (ICIP '00), September 2000, Vancouver, British Columbia, Canada 1: 493–496.Google Scholar
  27. 27.
    Kuglin CD, Hines DC: The phase correlation image alignment method. Proceeding of IEEE International Conference on Cybernetics and Society, September 1975, New York, NY, USA 163–165.Google Scholar
  28. 28.
    Castro EDe, Morandi C: Registration of translated and rotated images using finite Fourier transforms. IEEE Transactions on Pattern Analysis and Machine Intelligence 1987, 9(5):700–703.CrossRefGoogle Scholar
  29. 29.
    Zemanian AH: Distribution Theory and Transform Analysis. Dover, New York, NY, USA; 1965.zbMATHGoogle Scholar
  30. 30.
    Oppenheim AV, Schafer RW: Discrete Time Signal Processing. 1st edition. Prentice-Hall, Englewood Cliffs, NJ, USA; 1989.zbMATHGoogle Scholar
  31. 31.
    Tikhonov A, Arsenin A: Solutions of Ill-Posed Problems. Winston & Sons, Washington, DC, USA; 1977.zbMATHGoogle Scholar
  32. 32.
    Golub GH, Heath M, Wahba G: Generalized cross-validation as a method for choosing a good ridge parameter. Technometrics 1979, 21(2):215–223. 10.2307/1268518MathSciNetCrossRefGoogle Scholar
  33. 33.
    CMU Vision and autonomous systems center's image database.
  34. 34.
    Wright GA: Magnetic resonance imaging. IEEE Signal Processing Magazine 1997, 14(1):56–66. 10.1109/79.560324CrossRefGoogle Scholar
  35. 35.
    Skolnik MI: Radar Handbook. 2nd edition. McGraw-Hill, New York, NY, USA; 1990.Google Scholar
  36. 36.
    Stein M: Introduction to Matrices and Determinants. Wadsworth, Belmont, Calif, USA; 1967.Google Scholar

Copyright information

© Balci and Foroosh. 2006

Authors and Affiliations

  • Murat Balci
    • 1
  • Hassan Foroosh
    • 1
  1. 1.School of Computer ScienceUniversity of Central FloridaOrlandoUSA

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