9.7 Resampling and Interpolation

9.7 Resampling and Interpolation

In the final stage of geometric correction a geo-coded image will be produced by resampling. There are two techniques for resampling as shown in Figure 9.7.1, and given as follows-

(1) Projection from input image to output image
Each pixel of the input image is projected to the output image plane. In this case, an image output device with random access such as flying spot scanner is required.
(2) Projection from output image to input image
Regularly spaced pixels in the output image plane are projected into the input image plane and their values interpolated from the surrounding input image data. This is a more general method.

Usually the inverse equation to transform from the output image coordinate system to the input image coordinate system, is not possible to determine because the geometric equation is very complex. In such a case, the following methods can be adopted-

(1) Partition into small areas
As a small area can be approximated by the lower order polynomials, such as affine or pseudo affine transformation, the inverse equation can be easily determined. Resampling can be undertaken for each small area, one by one.
(2) Line and pixel functions
A line function can be determined approximately to search for a scan line number which is closest to the pixel to be resampled, while a pixel function can be determined to search for the pixel number.
In resampling as shown in Figure 9.7.1(b), a projected point in an input image plane does not coincide with the input image data. Therefore the spectral data should be interpolated, and the following methods can be used-

(1) Nearest neighbor (NN)
As shown in Figure 9.7.2 (a), the nearest point will be sampled. The geometric error will be a half pixel at maximum. It has the advantage of being easy and fast.
(2) Bi-linear (BL)
As shown in Figure 9.7.2 (b), the bi-linear function is applied to the surrounding four points. The spectral data will be smoothed after the interpolation.
(3) Cubic convolution (CC)
As shown in Figure 9.7.2 (c), the spectral data will be interpolated by a cubic function using the surrounding sixteen points.The cubic convolution results in sharpening as well as smoothing, though the computation takes a longer time when compared with the other methods.