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Turbo-charged linear interpolation


We demonstrate a new method that improves the quality of piecewise linear interpolation significantly, without adding much to the computation. The underlying principle is to shift the spline discontinuities by a fixed amount τ. This shifted model is then used to interpolate the signal.

The optimal shift τopt for our new method can be determined analytically:
optimal shift

The applet compares the following interpolation methods by performing a cumulative rotation experiment that magnifies errors:

  • Bilinear interpolation or cubic convolution (Keys)
  • and the new turbo-charged one: bilinear interpolation with shifted knots.
Instruction to use the applet
  1. Choose an input image in the list.
  2. Choose an number of rotations (iterations).
  3. Press ">" to run one step or ">>" to run all the steps.
  4. You can retrieve the optimum value of the shift by clicking on the "Best." button.
Toolbar in the image display
pointer_on Get the coordinates and value of a pixel.
info_on Get the maximum, minimum and the mean value of the image.
frame Open a new window containing the image.
zoomin_on Zoom out by a factor 2.
(N/A on Netscape)
zoomout_on Zoom in by a factor 2. (N/A on Netscape)
move Move the zoomed part of the image. (N/A on Netscape)


T. Blu, P. Thévenaz, M. Unser, "How a Simple Shift Can Significantly Improve the Performance of Linear Interpolation," Proceedings of the 2002 IEEE International Conference on Image Processing (ICIP'02), Rochester NY, USA, September 22-25, 2002, pp. III.377-III.380.

T. Blu, P. Thévenaz, M. Unser, "Linear Interpolation Revitalized," IEEE Transactions on Image Processing, vol. 13, no. 5, pp. 710—719, May 2004.


A package of C routines that implement shifted linear interpolation.