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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.
**chirp2
**

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.

**plcbinlin
**

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.

**plccubspl
**

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.

**plckaispl
**

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.

** Next:** Beyond B-splines
** Up:** Forward Interpolation
** Previous:** B-splines
Stanford Exploration Project

9/5/2000