Page 259 - Digital Analysis of Remotely Sensed Imagery

Image Enhancement 221

where DN = convoluted output pixel value
out
DN(i, j) = pixel value in the input image at location (i, j)
in
i (i = 1, 2, 3) = row index
j (j = 1, 2, 3) = column index
w = value of the element at location (i, j) in the
ij
kernel
W = sum of all kernel elements
d = kernel size, usually an odd number ranging
from 3 to 9

The kernel is applied to the image in a moving window manner.
The operation moves on to the next pixel in the same row after the
current one has been convoluted. This is repeated until the next-to-
last pixel in the row, and then continues with the first pixel in the
following row. The output image has a lower dimension than the
input image because the first and last rows/columns do not have a
complete neighborhood if the kernel size is 3 × 3. This reduced dimen-
sion may be restored to that of the input image by duplicating the
first and last rows/columns of the output image.

6.3.3 Image Smoothing
Also called low-pass filtering or low spatial frequency (defined as infre-
quent grayscale changes that occur gradually over a relatively large
number of pixel distance) filtering, image smoothing is a process of sup-
pressing noise in the input image that may arise during image acquisi-
tion and transmission. Radiometric noises in an image are manifested
as abnormally larger or smaller pixel values than those in the neighbor-
hood. Since the genuine pixel value is unknown, noise cannot be com-
pletely eliminated through image smoothing. Instead, this noise is sup-
pressed to a certain degree by dividing it among all pixels within the
kernel. There are several methods for suppressing the noise. A com-
mon method is to replace the noise-infected pixel with the mean of all
pixel values inside the kernel. Essentially, the noise is shared by all
pixels in the kernel. Another method is to filter the noise-infested pixel
out by substituting it with a statistical parameter of all pixels (e.g.,
median). Low-pass filtering makes use of the low-pass kernel that is
characterized by an equal weight for all elements:

⎛ 111⎞
1 ⎜ 111 ⎟
9 ⎜ ⎟
⎝ 111⎠

During low-pass filtering, the pixel values are averaged among
those in the kernel. High-frequency features (e.g., edges) are subdued
in the smoothed image. Thus, every pixel in the window shares a por-
tion of the abnormality that may exist in the value of the pixel under