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Related Experiment Videos

Directionlets: anisotropic multidirectional representation with separable filtering.

Vladan Velisavljević1, Baltasar Beferull-Lozano, Martin Vetterli

  • 1School of Computer and Communication Sciences, Swiss Federal Institute of Technology Lausanne (EPFL), Switzerland. vladan.velisavljevic@telekom.de

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|July 13, 2006
PubMed
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A new anisotropic multidirectional wavelet transform (M-DIR WT) offers improved image representation by better capturing edges and contours. This directionlet transform achieves superior nonlinear approximation compared to standard wavelets.

Area of Science:

  • Image Processing
  • Signal Analysis
  • Applied Mathematics

Background:

  • Standard wavelet transform (WT) has limitations in representing anisotropic image features due to isotropic basis functions.
  • 1-D discontinuities (edges, contours) lead to non-sparse representations in standard WT.
  • A need exists for transforms that efficiently capture complex, multidirectional geometrical structures.

Purpose of the Study:

  • Introduce a novel lattice-based, perfect reconstruction, critically sampled anisotropic multidirectional (M-DIR) wavelet transform.
  • Develop a transform that overcomes the limitations of standard WT for representing anisotropic image structures.
  • Evaluate the efficiency of the proposed transform for nonlinear image approximation.

Main Methods:

  • Developed a new anisotropic M-DIR WT based on a lattice structure.

Related Experiment Videos

  • Ensured the transform retains separable filtering, subsampling, and computational simplicity.
  • Designed anisotropic basis functions (directionlets) with directional vanishing moments.

    • Main Results:

    • The proposed anisotropic M-DIR WT efficiently represents anisotropic geometrical structures.
    • Achieved a nonlinear approximation power of O(N(-1.55)) for images.
    • Demonstrated performance superior to standard WT's O(N(-1)) approximation rate at similar computational complexity.

    Conclusions:

    • The novel anisotropic M-DIR WT is an efficient tool for image processing, particularly for representing edges and contours.
    • Directionlets provide a more effective representation for anisotropic image features than standard wavelets.
    • This transform offers a significant improvement in nonlinear approximation capabilities for images.