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Centered pyramids.

P Brigger1, F Muller, K Illgner

  • 1Nat. Center for Res. Resources, Nat. Inst. of Health, Bethesda, MD 20892-5766, USA. pbrigger@imageminds.com

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|February 13, 2008
PubMed
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This study introduces improved centered image pyramids that offer better approximation power than traditional quadtree pyramids. These new pyramids combine the benefits of centered topology with more faithful image representation for enhanced multiresolution analysis.

Area of Science:

  • Computer Vision
  • Image Processing
  • Multiresolution Analysis

Background:

  • Quadtree-like pyramids offer advantageous centered topology for multiresolution image representation.
  • Existing quadtree pyramids suffer from poor approximation due to their piecewise-constant image model.

Purpose of the Study:

  • To construct improved centered image pyramids using general approximation functions.
  • To combine the benefits of centered topology with enhanced image representation at coarser levels.

Main Methods:

  • Developed a general framework for designing least squares pyramids using filtering and decimation.
  • Derived explicit formulas for filter coefficients for continuous (L(2)) and discrete (l(2)) norms.
  • Defined centered pyramids and provided filter coefficients for odd spline approximation functions.

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Main Results:

  • The proposed method improves approximation powers compared to traditional quadtree pyramids.
  • The new pyramids maintain advantages of centered topology, including symmetry and accurate label up-projection.
  • Demonstrated the effectiveness of the new centered pyramid construction.

Conclusions:

  • Improved centered image pyramids offer a more faithful image representation at coarser levels.
  • These pyramids enhance multiresolution analysis by combining topological advantages with better approximation.
  • The developed framework and formulas facilitate the design of advanced image pyramids.