Page 209 - Digital Analysis of Remotely Sensed Imagery

Image Geometric Rectification 173

38 46 DN 1 53 56
x

41 51 41 DN 1 51 36 41 DN 2 51 55
x
41 0.3 0.2 0.7 42
+ + +
42
0.8
34 42 34 42 32 34 DN 3 42 48
x
DN 2
28 30 DN 4 36 40
x
(a) (b) (c)
FIGURE 5.13 Mechanism of sampling pixel values using various methods. (a)
Nearest neighbor; (b) bilinear; (c) cubic convolution.

Nearest Neighbor
In this method, the output pixel is assigned the pixel value of its
closest adjoining pixel in the input image. For instance, the posi-
tion of an output pixel falls within four pixels that have radiomet-
ric values of 41, 51, 34, and 42, respectively (Fig. 5.13a). Since the
calculated position (r = 0.2, c = 0.3) is closest to the upper left pixel
that has a value of 41, the output pixel receives a value of 41. This
resampling method is simple to understand and implement. It does
not require complex computation. Most of all, it does not involve
altering the input pixel value. The output value at the new location
is the same as that in the input image, or change with distance if the
four corner pixels have different values. This problem is success-
fully overcome in the bilinear method.

Bilinear Interpolation
This method is underpinned by the assumption that pixel value var-
ies linearly from one location to another. Thus, the pixel value at a
location can be interpolated from its immediately neighboring pixels
through distance-weighted averaging. Bilinear interpolation involves
three linear interpolations of four neighboring pixel values. Since the
input pixel is surrounded by two pixels above and below it, to its left
and to its right, two interpolations have to be undertaken in one of
these two directions first. After the radiometric value in either direc-
tion is interpolated, the final pixel value is linearly interpolated from
the two interpolated values in a perpendicular direction. The sequence
of executing the interpolation in a particular direction bears no sequence
with the final interpolated results. In all interpolations, the horizontal
and vertical distances between the pixel under consideration and its