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The contourlet transform: an efficient directional multiresolution image representation.

Minh N Do1, Martin Vetterli

  • 1Department of of Electrical and Computer Engineering, Coordinated Science Laboratory, Beckman Institute, University of Illinois, Urbana, IL 61801, USA. minhdo@uiuc.edu

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|December 24, 2005
PubMed
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The contourlet transform, a new 2D image analysis tool, effectively captures edge geometry. This discrete-domain method offers efficient, flexible multiresolution and directional image expansion for enhanced visual information processing.

Area of Science:

  • Image processing
  • Computer vision
  • Applied mathematics

Background:

  • Separable 1D transforms (Fourier, wavelet) struggle with image edge geometry.
  • Existing 2D transforms like curvelets discretize continuous models.
  • Discrete data poses challenges for geometric analysis in images.

Purpose of the Study:

  • Develop a "true" 2D transform to capture intrinsic image geometry.
  • Construct a discrete-domain transform for efficient geometric analysis.
  • Introduce the contourlet transform for flexible, local, and directional image expansion.

Main Methods:

  • Construct a discrete-domain multiresolution and multidirection expansion using nonseparable filter banks.
  • Utilize a fast iterated filter bank algorithm with O(N) complexity for N-pixel images.

Related Experiment Videos

  • Establish a link between discrete filter banks and continuous contourlet expansions via directional multiresolution analysis.

    • Main Results:

    • The contourlet transform provides a flexible, local, and directional image expansion based on contour segments.
    • Achieves optimal approximation rates for piecewise smooth functions with smooth curve discontinuities.
    • Demonstrates potential in various image processing applications through numerical experiments.

    Conclusions:

    • The contourlet transform offers a powerful new tool for geometric image processing.
    • Its discrete-domain construction and efficiency make it suitable for practical applications.
    • Advances the field of sparse representation for images with complex geometric structures.