RADAR Texture Algorithms
Created by: Nathan Jennings
Created on: 05.29.2010
Mean
Sum(Xij) – the sum of the pixels
within a given “window” (e.g. 3x3) size.
n – number of pixels within the “window” (i.e. 9
for a 3x3 window)
Computes Mean value of a moving window. This algorithm is more of a filter than a
texture measure. The mean can be used in
RADAR processing to “smooth” the speckle that is inherent in raw RADAR
data. This algorithm was created for the
author to learn and trouble shoot the other texture measures:
1. Variance
2. Skewness
3. Kurtosis
The mean value of the moving window is used in
all of the texture algorithms listed.
This alforithm simply computes the mean of the moving window and writes
it out to an image.
Variance
Sum(Xij – M)2 – sum of the
squares of the difference between a pixel and the mean of a “window.”
M – Mean from above
n – number of pixels within a window.
Computes Variance Statistical Measure how
"variable" a distribution curve is.
A large variance indicates that pixels within a
local neighborhood are different from one another. A small variance indicate that pixels are
similar to one another and may have a normal distribution.
The resulting variance image can help in
determining some land cover types or assit
to "segment" the image into areas with
distinct texture patterns.
Skewness
Skewness =
Xij – pixel value
M – Mean (from above)
V – Variance (from above)
n – number of pixels in the “window”
Computes Skewness Statistical Measure how
"shifted" a distribution curve is.
A large positive skewness indicates a
"shift" to the right of the mean (i.e. the right side of the
distribution has a longer tail than the left side). A large negative value indicates a shift to
the left of the mean (i.e. the left side of the distribution has a longer tail
than the right). The resulting skewness
values can be positive or negative.
From an image processing "texture"
point of view large (positive or negative) skewness values indicates a trend in
the local neighborhood of brightness values.
A broad area of negative values can indicate that the original
brightness values
tend to be small, but similar. A broad area of positive values can indicate
that the original brightness values tend to be larger, but similar. The resulting skewness image can help in determining
some land cover types or assit to "segment" the image into areas with
distinct texture patterns.
Kurtosis
Xij – pixel value
M – Mean (from above)
V – Variance (from above)
n – number of
pixels in the “window”
Computes Kurtosis Statistical Measure how
"peaked" or "flat" a distribution curve is.
A high peak about the mean that falls off rapidly
and has "heavy" tails indicate high kurtosis.
From an image processing "texture"
point of view large kurtosis values indicates that many pixel values are near
the mean within a local neighborhood (e.g. 3x3, 5x5, 7x7 area) and a smaller
number of pixels are further away from the mean (i.e. are towards the tails of
the distribution curve). One can say
that most of the pixels in a local area are "similar" to one another,
but do have some pixels that are very different. The resulting kurtosis image can help in
determining some land cover types or assit to "segment" the image
into areas with distinct texture patterns.
The algorithm
functions can be found here:
Work Cited
Iron, J. R., and G. W. Petersen. 1981. Texture Transforms of
Remote Sensing Data. Remote Sensing of Environment 11:359-370.