BIOMEDICAL IMAGING GROUP (BIG)
Laboratoire d'imagerie biomédicale (LIB)

How a Simple Shift Can Significantly Improve the Performance of Linear Interpolation

T. Blu, P. Thévenaz, M. Unser

Proceedings of the 2002 Ninth IEEE International Conference on Image Processing (ICIP'02), Rochester NY, USA, September 22-25, 2002, pp. III.377–III.380.

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.

Thanks to a theoretical analysis, we determine the optimal shift that maximizes the quality of our shifted linear interpolation. Surprisingly enough, this optimal value is nonzero and it is close to 1 ⁄ 5.

We confirm our theoretical findings by performing a cumulative rotation experiment, which shows a significant increase of the quality of the shifted method with respect to the standard one. Most interesting is the fact that we get a quality similar to that of high-quality cubic convolution at the computational cost of linear interpolation. 

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