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Related Experiment Videos

Low bit-rate image coding using adaptive geometric piecewise polynomial approximation.

Roman Kazinnik1, Shai Dekel, Nira Dyn

  • 1School of Mathematical Sciences, Tel-Aviv University, Ramat Aviv, Tel-Aviv 69978, Israel.

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|September 6, 2007
PubMed
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A new geometric piecewise polynomial (GPP) image coding algorithm offers superior performance, especially for graphic and cartoon images. GPP outperforms wavelet coding at low bit rates, achieving better PSNR and visual quality.

Area of Science:

  • Digital image processing
  • Image compression algorithms
  • Approximation theory

Background:

  • Wavelet-based coding is a state-of-the-art method for image compression.
  • Existing methods face challenges in achieving high fidelity at very low bit rates, particularly for specific image types.
  • Adaptive multivariate piecewise polynomial approximation offers potential for improved image representation.

Purpose of the Study:

  • To introduce and evaluate a novel image coding algorithm based on geometric piecewise polynomials (GPP).
  • To compare the performance of the GPP algorithm against established methods like wavelet coding and JPEG2000.
  • To demonstrate the effectiveness of GPP for image compression, especially in low bit-rate scenarios and for specific image content.

Main Methods:

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  • The GPP algorithm utilizes adaptive multivariate piecewise polynomial approximation.
  • A key stage involves image segmentation minimizing a smoothness-based functional, similar to the Mumford-Shah functional.
  • The segmented image is lossy encoded, partitioned, and approximated by low-order polynomials on subdomains.

    • Main Results:

    • The GPP algorithm outperforms state-of-the-art wavelet coding in the low bit-rate range.
    • Significant improvements were observed on graphic and cartoon images compared to wavelet-based methods.
    • At 0.05 bpp on the 'Cameraman' image, GPP achieved 21.5 dB PSNR versus JPEG2000's 20 dB.
    • At 0.03 bpp on the 'Lena' image, GPP matched JPEG2000 PSNR with superior visual quality.

    Conclusions:

    • The GPP method represents a significant advancement in image coding, particularly for low bit rates.
    • GPP demonstrates superior performance on images with geometric structures and for graphic/cartoon content.
    • This algorithm offers a competitive alternative to existing compression techniques, providing better visual quality at reduced bit rates.