Inverse B-spline interpolation |

For completeness, I include a 2-D forward interpolation example. Figure 19 shows a 2-D analog of function in Figure 4 and its coarsely-sampled version.

chirp2
Two-dimensional test function
(left) and its coarsely sampled version (right).
Figure 19. |
---|

Figure 20 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 21 and 22, 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
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.
Figure 20. |
---|

plccubspl
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.
Figure 21. |
---|

plckaispl
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.
Figure 22. |
---|

Inverse B-spline interpolation |

2014-02-15