Page 210 - Digital Analysis of Remotely Sensed Imagery

174 Cha pte r F i v e

four neighbors are treated as weights. So the output pixel value is a
proximity-weighted average of its four nearest pixel values. The cal-
culation for the pixel shown in Fig. 5.13b is illustrated below. In this
example, the interpolation is performed horizontally first and verti-
cally next.
DN = 41 + (51 − 41) × 0.3/(0.3 + 0.7) = 44
1
DN = 34 + (42 − 34) × 0.3/(0.3 + 0.7) = 36.4
2
DN = 44 + (36.4 − 44) × 0.2/(0.2 + 0.8) = 42.48 = 42
After the first round of interpolation the results can be accu-
rate to one decimal point. However, it must be rounded to the
nearest integer after the second round of interpolation a pixel
value is not allowed to have any decimal points if the image is
saved as 8-bit unsigned. As shown in this example, there is little
difference (only 1 in this case) between the results resampled using
the nearest neighbor and bilinear interpolation methods, even
though bilinear involves more computation.

Cubic Convolution
In this method, 16 pixels surrounding the one under study are needed
for the interpolation. The output pixel is assigned the radiance aver-
aged from these 16 nearest neighbors after five interpolations. The
algorithm for the computation (Moik, 1980) is provided below:
DN(i, Δj) = Δj{Δj[Δj(DN(i, j + 3) − DN(i, j + 2) + DN(i, j + 1)
− DN(i, j)) + DN(i, j + 2) − DN(i, j + 3)
− 2DN(i, j + 1) + 2DN(i, j)] + DN(i, j + 2)
− DN(i, j)} + DN(i, j + 1) (5.23)
where Δj = distance increment in column and DN(i, j + k)(k = 0, 1,
2, 3) = pixel value at the kth pixel to the right in row i.
The above estimation is repeated 4 times, each time for one of the
four rows or columns. After the four values are interpolated, the
operation is repeated one more time in a perpendicular direction
(e.g., vertically) using Eq. (5.24). This equation looks identical to
Eq. (5.23) except that the initial pixel values are not raw but estimated
from the previous four interpolations.

DN(Δi, Δj) = Δi{Δi[Δi(DN(i + 3, Δj) − DN(i + 2, Δj)
+ DN(i + 1, Δj) − DN(i, Δj)) + DN(i + 2, Δj)
− DN(i + 3, Δj) − 2DN(i + 1, Δj) + 2DN(i, Δj)]
+ DN(i + 2, Δj) − DN(i, Δj)} + DN(i + 1, Δj) (5.24)

where Δi = distance increment in row, and DN(i + k, Δj) (k = 0, 1, 2, 3) =
pixel value at the kth pixel down in column Δj.