2-D example

For completeness, I include a 2-D forward interpolation example. Figure  shows a 2-D analog of function in Figure  and its coarsely-sampled version.

 

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Figure 19 Two-dimensional test function (left) and its coarsely sampled version (right).

Figure  compares the errors of the 2-D nearest neighbor and 2-D linear (bi-linear) interpolation. Switching to bi-linear interpolation shows a significant improvement, but the error level is still relatively high. As shown in Figures  and , B-spline interpolation again outperforms other methods with comparable cost complexity. In all cases, I constructed 2-D interpolants by orthogonal splitting. Although the splitting method reduces computational overhead, the main cost factor is the total interpolant size, which squares when going from 1-D to 2-D.

 

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Figure 20 2-D Interpolation errors of nearest neighbor interpolation (left) and linear interpolation (right). Top graphs show 1-D slices through the center of the image.

 

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Figure 21 2-D Interpolation errors of cubic convolution interpolation (left) and third-order B-spline interpolation (right). Top graphs show 1-D slices through the center of the image.

 

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Figure 22 2-D Interpolation errors of 8-point windowed sinc interpolation (left) and seventh-order B-spline interpolation (right). Top graphs show 1-D slices through the center of the images.