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Rate-distortion optimized tree-structured compression algorithms for piecewise polynomial images.

Rahul Shukla1, Pier Luigi Dragotti, Minh N Do

  • 1Audio-Visual Communications Laboratory, Swiss Federal Institute of Technology Lausanne CH-1015, Lausanne, Switzerland. rahul.shukla@epfl.ch

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|March 15, 2005
PubMed
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This study introduces novel tree-structured coding algorithms for signal segmentation, achieving optimal rate-distortion performance. The new methods outperform classic wavelet schemes and JPEG2000 for image compression.

Area of Science:

  • Digital Signal Processing
  • Image Compression
  • Data Encoding Algorithms

Background:

  • Traditional signal coding methods face limitations in achieving optimal rate-distortion (R-D) behavior for complex signals.
  • Wavelet-based schemes, while effective, do not always provide the theoretically optimal R-D performance for certain signal classes.

Purpose of the Study:

  • To develop novel coding algorithms utilizing tree-structured segmentation for improved rate-distortion performance.
  • To achieve theoretically correct asymptotic R-D behavior for piecewise polynomial signals.
  • To enhance image compression efficiency beyond existing standards like JPEG2000.

Main Methods:

  • Development of a binary-tree segmentation algorithm for 1D signals, approximating segments with polynomial models.

Related Experiment Videos

  • Implementation of a rate-distortion (R-D) optimized prune and join scheme for adaptive bit allocation.
  • Extension of the scheme to 2D signals using a quadtree structure for image compression.
  • Joint encoding of neighboring segments to achieve exponentially decaying R-D behavior.

    • Main Results:

    • The proposed 1D scheme achieves optimal asymptotic R-D behavior and O(N log N) computational complexity.
    • The 2D quadtree-coding scheme demonstrates exponentially decaying R-D behavior for specific image models.
    • Numerical results show the quadtree scheme outperforms JPEG2000 by approximately 1 dB for real images at low bit rates (0.15 bpp).

    Conclusions:

    • Tree-structured segmentation with R-D optimized prune and join strategies offers superior coding performance.
    • The developed algorithms provide significant improvements in image compression efficiency, especially at low bit rates.
    • The computational complexity remains efficient at O(N log N), making the algorithms practical for real-world applications.