Linear interpolation revitalized

By Thierry Blu, Philippe Thévenaz, Michael A. Unser. IEEE Transactions on Image Processing, 2004

413 citations recorded by the source corpus.

We present a simple, original method to improve piecewise-linear interpolation with uniform knots: we shift the sampling knots by a fixed amount, while enforcing the interpolation property. We determine the theoretical optimal shift that maximizes the quality of our shifted linear interpolation. Surprisingly enough, this optimal value is nonzero and close to 1/5. We confirm our theoretical findings by performing several experiments: a cumulative rotation experiment and a zoom experiment. Both show a significant increase of the quality of the shifted method with respect to the standard one. We also observe that, in these results, we get a quality that is similar to that of the computationally more costly "high-quality" cubic convolution.

Subfields: Computational Mechanics, Computer Graphics and Computer-Aided Design, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/5d41f8a5844c9a65ac68c6387d6534907c325f43

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

1. Eric Dubois
2. Hussein H. Aly

In Computer Graphics and Computer-Aided Design

1. Eric Dubois
2. Hussein H. Aly

In Computer Vision and Pattern Recognition

1. Eric Dubois
2. Hussein H. Aly
3. Raanan Fattal
4. G. Yu
5. Stéphane Mallat
6. Mark W. Schmidt
7. T. Chen

Citations in the corpus

• Image up-sampling using total-variation regularization with a new observation model (2005, background): “Linear interpolators range from straightforward pixel repeat [which is also called zero-order hold (ZOH)], bilinear, or bicubic [3] interpolation to embedding in spline kernel spaces [4]–[7].”