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Reversible, fast, and high-quality grid conversions.

Laurent Condat1, Dimitri Van De Ville, Brigitte Forster-Heinlein

  • 1Institute of Biomathematicsand Biometry, Helmholtz Zentrum München-German Research Center for Environmental Health, 85764 Neuherberg, Germany. laurent.condat@helmholtz-muenchen.de

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|April 9, 2008
PubMed
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A novel grid conversion method offers exact data recovery through symmetric reversibility. This fast, high-quality resampling technique is ideal for applications like hexagonal to Cartesian lattice conversion.

Area of Science:

  • Image processing
  • Computational geometry
  • Signal processing

Background:

  • Resampling between different 2-D periodic lattices is crucial for various imaging and data processing tasks.
  • Existing methods may lack exact reversibility or computational efficiency.

Purpose of the Study:

  • To introduce a new grid conversion method with symmetric reversibility.
  • To enable exact data recovery after resampling between lattices.

Main Methods:

  • Decomposition of lattice conversion into shear operations.
  • Implementation of translations using 1-D fractional delay operators.
  • Utilizing 1-D convolutions with specific filters for symmetric reversibility.

Main Results:

Related Experiment Videos

  • The proposed method achieves exact data recovery via symmetric reversibility.
  • The technique is computationally fast.
  • High-quality resampled images are produced.

Conclusions:

  • The new grid conversion method provides an efficient and accurate solution for resampling between 2-D periodic lattices.
  • Its symmetric reversibility ensures data integrity.
  • Potential applications include hexagonal-Cartesian grid conversion and fast affine transformations.