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Linear interpolation revitalized.

Thierry Blu1, Philippe Thévenaz, Michael Unser

  • 1Biomedical Imaging Group FSTI/IOA, Swiss Federal Institute of Technology Lausanne (EPFL), CH-1015 Lausanne EPFL, Switzerland. thierry.blu@epfl.ch

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|September 21, 2004
PubMed
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We introduce a novel method for piecewise-linear interpolation by shifting sampling knots. This simple technique significantly enhances interpolation quality, achieving results comparable to more complex methods.

Area of Science:

  • Computer Science
  • Applied Mathematics

Background:

  • Piecewise-linear interpolation is a fundamental technique in data approximation.
  • Standard interpolation methods can suffer from artifacts and reduced accuracy, especially with uniform knot placement.

Purpose of the Study:

  • To develop an improved method for piecewise-linear interpolation using uniform knots.
  • To theoretically determine and experimentally validate an optimal knot-shifting strategy.

Main Methods:

  • A novel approach involving a fixed shift of sampling knots while maintaining the interpolation property.
  • Theoretical derivation of the optimal shift value to maximize interpolation quality.
  • Experimental validation using cumulative rotation and zoom experiments.

Main Results:

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  • The optimal shift value is non-zero and approximately 1/5.
  • The proposed shifted linear interpolation method demonstrates significant quality improvements over the standard approach.
  • Achieved interpolation quality is comparable to computationally intensive cubic convolution methods.

Conclusions:

  • A simple, yet effective, method to enhance piecewise-linear interpolation has been developed.
  • The optimal knot shift offers a practical improvement for uniform knot interpolation.
  • This technique provides a computationally efficient alternative to high-quality interpolation methods.