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Least-squares image resizing using finite differences.

A Muñoz1, T Blu, M Unser

  • 1Biomed. Imaging Group, Swiss Federal Inst. of Technol., Lausanne. arrate.munoz@epfl.ch

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|February 8, 2008
PubMed
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This study introduces an optimal spline-based algorithm for digital image scaling, improving image quality by reducing artifacts and enhancing signal-to-noise ratio. The novel finite difference method offers efficient computation for arbitrary scaling factors.

Area of Science:

  • Digital Image Processing
  • Computational Mathematics
  • Computer Vision

Background:

  • Standard image interpolation methods often introduce artifacts like aliasing and blocking.
  • Arbitrary (noninteger) scaling factors pose challenges for traditional algorithms.
  • Improving signal-to-noise ratio (SNR) is crucial for image quality.

Purpose of the Study:

  • To develop an optimal spline-based algorithm for digital image enlargement and reduction.
  • To address the challenge of arbitrary noninteger scaling factors.
  • To improve image quality by minimizing artifacts and enhancing SNR.

Main Methods:

  • A projection-based approach utilizing a novel finite difference method.
  • Computation of inner products with B-spline basis functions of any degree n.

Related Experiment Videos

  • Algorithm complexity is independent of the scaling factor, ensuring efficiency.
  • Main Results:

    • The spline-based algorithm consistently outperforms standard interpolation procedures.
    • Significant reduction in artifacts such as aliasing and blocking.
    • Substantial improvement in the signal-to-noise ratio.

    Conclusions:

    • The proposed algorithm provides superior image scaling results compared to existing methods.
    • The method is computationally efficient and adaptable to various piecewise polynomial functions.
    • This approach offers a robust solution for high-quality digital image resizing.