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Related Experiment Video

Updated: Jul 7, 2026

Quantifying Intermembrane Distances with Serial Image Dilations
07:45

Quantifying Intermembrane Distances with Serial Image Dilations

Published on: September 28, 2018

Image reconstruction by convolution with symmetrical piecewise nth-order polynomial kernels.

E W Meijering1, K J Zuiderveld, M A Viergever

  • 1Image Sci. Inst., Utrecht Univ., The Netherlands. erik@cv.ruu.nl

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|February 13, 2008
PubMed
Summary

Researchers explored polynomial kernels for image reconstruction, aiming for practical alternatives to the ideal sinc-function. Cubic convolution showed significant improvement over linear interpolation, but higher-order kernels offered only marginal gains.

Related Experiment Videos

Last Updated: Jul 7, 2026

Quantifying Intermembrane Distances with Serial Image Dilations
07:45

Quantifying Intermembrane Distances with Serial Image Dilations

Published on: September 28, 2018

Area of Science:

  • Image processing
  • Digital signal processing
  • Numerical analysis

Background:

  • Image reconstruction relies on interpolation kernels, with the sinc-function being theoretically ideal but practically unusable.
  • Finite-extent kernels approximating the sinc-function are needed for efficient and precise image reconstruction.
  • Symmetrical piecewise nth-order polynomial kernels offer a potential solution balancing computational speed and mathematical accuracy.

Purpose of the Study:

  • To investigate the applicability of sine-approximating symmetrical piecewise nth-order polynomial kernels for image reconstruction.
  • To derive and evaluate polynomial kernels of first, third, fifth, and seventh orders.
  • To quantitatively assess reconstruction capabilities based on spatial/spectral behavior and image transformation tests.

Main Methods:

  • Derivation of nth-order polynomial kernels (1st, 3rd, 5th, 7th).
  • Analysis of spatial and spectral characteristics of the derived kernels.
  • Experimental evaluation using image translation, rotation, and magnification on real-life test images.

Main Results:

  • Cubic convolution (3rd order) demonstrated a significant improvement in image reconstruction compared to linear interpolation (1st order).
  • Higher-order polynomial kernels (5th and 7th order) provided only marginal improvements over cubic convolution.
  • The tested kernels effectively approximated the sinc-function's properties for practical image reconstruction.

Conclusions:

  • Symmetrical piecewise nth-order polynomial kernels are viable for image reconstruction, offering a practical alternative to the sinc-function.
  • Cubic convolution represents a good balance between performance and complexity for many image reconstruction tasks.
  • The benefits of increasing polynomial order beyond cubic are limited, suggesting diminishing returns for computational cost.