A Multiplication-Free Algorithm and A Parallel Architecture for Affine Transformation

  • Wael Badawy
  • Magdy Bayoumi


Affine transformation is widely used in image processing. Recently, it is recommended by MPEG-4 for video motion compensation. This paper presents a novel low power parallel architecture for texture warping using affine transformation (AT). The architecture uses a novel multiplication-free algorithm that employs the algebraic properties of the AT. Low power has been achieved at different levels of the design. At the algorithmic level, replacing multiplication operations with bit shifting saves the power and delay of using a multiplier. At the architecture level, low power is achieved by using parallel computational units, where the latency constraints and/or the operating latency can be reduced. At the circuit level, using low power building blocks (such as low power adders) contributes to the power savings. The proposed architecture is used as a computational kernel in video object coders. It is compatible with MPEG-4 and VRML standards. The architecture has been prototyped in 0.6 μm CMOS technology with three layers of metal. The performance of the proposed architecture shows that it can be used in mobile and handheld applications.

affine transformation texture mapping video object MPEG-4 low power VLSI 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    M.F. Goodchild, “Geocoding and Geosampling,” in Spatial Statistics and Models, G.L. Gaile and C.J. Willmott (Eds.), Reidel Publishing Company, Dordrecht, Holland, 1984, pp. 33-53.CrossRefGoogle Scholar
  2. 2.
    P.J.L. van Beek, A.M. Tekalp, and A. Puri, “2D Mesh Geometry and Motion Compression for Efficient Object-Based Video Representation,” Int. Conf. On Image Processing '97, Santa Barbara, CA, Oct. 1997.Google Scholar
  3. 3.
    S. Brofferio and F. Rocca, “Interframe Redundancy Reduction of Video Signals Generated by Translating Objects,” IEEE Trans. Commun. vol. Com-25, 1977, pp. 448-455.CrossRefGoogle Scholar
  4. 4.
    A.M. Tekalp, P.J.L. van Beek, C. Toklu, and B. Gunsel “2D Mesh-Based Visual Object Representation for Interactive Synthetic/Natural Video,” in Proc. of the IEEE (special issue), vol. 86,no. 6, 1998, pp. 1029-1051.Google Scholar
  5. 5.
    K.J. Ray Liu et al. “Algorithm-Based Low Power and High-Performance Multimedia Signal Processing,” in Proc. of IEEE, vol. 86,no. 6, 1998, pp. 1155-1202.CrossRefGoogle Scholar
  6. 6.
    R.M. Haralick, “Automatic Remote Sensor Image Processing,” in Topics in Applied Physics, vol. 11: Digital Picture Analysis. New York: Springer-Verlag, 1976, pp. 5-63.CrossRefGoogle Scholar
  7. 7.
    G. Wolberg, Digital Image Warping, Los Alamitos, CA: Computer Society Press, 1990.Google Scholar
  8. 8.
    G.J. Holzmann, Beyond Photography-The Digital Darkroom, Englewood Cliffs, NJ: Prentice-Hall, 1998.Google Scholar
  9. 9.
    H. Bruzewitz, “Motion Compensation with Triangles,” in Proc. 3rd Int. Conf. 64 kbit Coding of Moving Video, Rootterdam, The Netherlands, 1990.Google Scholar
  10. 10.
    G.J. Sullivan and R.L. Baker, “Motion Compensation for Video Compression Using Control Grid Interpolation,” in Proc. IEEE ICASSP, vol. 4, 1991, pp. 2713-2716.Google Scholar
  11. 11.
    Y. Nakaya and H. Harashima, “An Iterative Motion Estimation Method Using Triangular Patches for Motion Compensation,” in Proc. SPIE Visual Communications and Image Processing, vol. 1605, 1991, pp. 546-557.Google Scholar
  12. 12.
    Y. Nakaya and H. Harashima, “Motion Compensation Based on Spatial Transformations,” IEEE Trans. Circuits Syst. Video Technol., vol. 4, 1994, pp. 339-356.CrossRefGoogle Scholar
  13. 13.
    J. Nieweglowski, T. Campbell, and P. Haavisto, “A Novel Video Coding Scheme Based on Temporal Prediction Using Digital Image Warping,” IEEE Trans. Consumer Electron., vol. 39, 1993, pp. 141-150.CrossRefGoogle Scholar
  14. 14.
    C. Toklu, A. Erdem, M.I. Sezan, and A.M. Tekalp, “Tracking Motion and Intensity Variations Using Hierarchical 2-D Mesh Modeling for Synthetic Object Transfiguration,” Graphic Models and Image Processing, vol. 58, 1996, pp. 553-573.CrossRefGoogle Scholar
  15. 15.
    A. Nosratinia, N. Mohsenian, M.T. Orchard, and B. Liu, “Interslice Coding of Magnetic Resonance Images Using Deformable Triangular Patches,” in Proc. IEEE ICIP, vol. 2, Austin, TX, 1994, pp. 898-892.Google Scholar
  16. 16.
    A. Nosratinia, N. Mohsenian, M.T. Orchard, and B. Liu, “Interframe Coding of Magnetic Resonance Images,” IEEE Trans. Medical Imaging, vol. 15, 1996, pp. 639-647.CrossRefGoogle Scholar
  17. 17.
    N. Mohsenian, A. Nosratinia, B. Liu, and M.T. Orchard, “Adaptive Entropy Constrained Transform Coding of Magnetic Resonance Image Sequences,” IEEE Trans. Nuclear Sci., vol. 42, 1995, pp. 2309-2316.CrossRefGoogle Scholar
  18. 18.
    P.E. Eren, C. Toklu, and A.M. Tekalp, “Object-Based Manipulation and Composition Using 2D Meshes in VRML,” in Proc. IEEE Signal Processing 1st Workshop Multimedia Processing, Princeton, NJ, 1997, pp. 257-261.Google Scholar
  19. 19.
    A. Nosratinia, “New Kernels for Fast Mesh-Based Motion Estimation,” IEEE Trans. On Circuits and Syst. For Video Technol., vol. 11,no. 1, 2001, pp. 40-51.CrossRefGoogle Scholar
  20. 20.
    C.L. Huang and C.Y. Hsu, “A New Motion Compensation Method for Image Sequence Coding Using Hierarchical Grid Interpolation,” IEEE Trans. Circuits Syst. Video Technol., vol. 4, 1994, pp. 42-52.CrossRefGoogle Scholar

Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Wael Badawy
    • 1
  • Magdy Bayoumi
    • 2
  1. 1.Department of Electrical and Computer EngineeringUniversity of CalgaryCalgaryCanada
  2. 2.The Center for Advanced Computer StudiesUniversity of LouisianaLafayetteUSA

Personalised recommendations