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Understanding Synthetic Aperture Radar Images
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Understanding Synthetic Aperture Radar Images-Chris Oliver-SciTech Publishing (2004)
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8
Texture Exploitation
8.1 Introduction
Techniques for removing speckle from SAR images and deriving the RCS were
described in Chapters 6 and 7. Information is then carried at the single-pixel level.
However, this is not the only type of information contained in a SAR image. We
illustrate this in Figure 8.1 with an example of airborne SAR imagery from the
Tapajos region of the Amazon rain forest, obtained with the CCRS C-band
system, as part of the SAREX program
[1-3].
These 6-m resolution, 5-look data
were obtained with illumination from the right at an incidence angle of about
60 degrees. A highway runs diagonally from top right to bottom left. The region
to the left of this is comprised of primary forest; while that to the right is made up
of a mixture of primary forest, secondary forest, and clearings with pasture and
crops.
Suppose that the remote sensing task is to distinguish those regions that
correspond to primary forest from secondary forest and clearings. It is apparent
that the radar return in this image falls into two categories. One, corresponding
to secondary forest and clearings, has no fluctuations above those expected for
5-look speckle. This is caused by the fact that vegetation is sufficiently dense and
uniform so that the RCS is effectively constant. The other, corresponding to
primary forest, has appreciable excess fluctuations caused by tall trees penetrat-
ing the canopy and resulting in bright tree crowns with associated shadow.
Visually, it appears that there is no relevant information in the mean RCS. Some
regions of primary forest have a larger RCS than the secondary forest and
clearings; others have a smaller value. This follows from the fact that both
Figure 8.1 SAREX image of part of the Amazon rain forest in the Tapajos region.
returns correspond to wet vegetation canopies with essentially the same water
content, having the same RCS at the 6-cm wavelength used. Thus, the informa-
tion required to discriminate between the two clutter types resides in image
texture. This cannot be estimated from a single pixel but requires a finite
window to characterize local statistics. The situation is further complicated if
the texture is correlated, as we will show in Chapter 9.
We demonstrated in Chapter 5 that clutter textures could be described by
the normalized variance. Thus, single-point texture statistics can be utilized as a
means of characterizing clutter in image interpretation. This chapter is con-
cerned with establishing optimum means for extracting and exploiting this
textural information.
In Section 8.2 we discuss how texture information can be derived without
any knowledge of the data distribution. However, where prior knowledge of the
form of PDF is available, it should be exploited. Model-based texture parameter
estimation is discussed in Section 8.3. ML texture estimators for various forms
of PDF are derived in Section
8.3.1,
leading to texture measures that can be used
in texture characterization. Assuming that clutter textures are actually K-distrib-
uted, the associated statistical uncertainty in the estimation of the order parame-
ter for the different measures is derived in Section 8.3.2. The normalized log
measure is then exploited in a texture analysis of rain forest data in Section 8.3.3.
The issue of texture classification into regions of different parameter values is
addressed in Section 8.4. Section 8.5 provides an analysis and discussion of
techniques for optimum texture segmentation. Finally, we compare the quality
and speed of algorithms for texture exploitation in Section 8.6.
8.2 Model-Free Texture Exploitation
It is not possible to select texture measures that optimize the information
content without a specific model for the data. However, suboptimal results can
be obtained with noncommittal approaches. For example, the K-S test, intro-
duced in Section
8.2.1,
compares the CDF of two data sets. Alternatively,
moments of the data PDF might be compared. The ability to discriminate
between textures would then depend on the accuracy with which these moments
were estimated, as discussed in Section 8.2.2. The selection of which particular
moment to adopt is crucial. If the form of the PDF is known, then those
moments that optimize the information about the texture can be selected. In
Section 8.2.3 we demonstrate how some simple moments are optimized for
particular forms of PDF. In Section 8.2.4 we discuss how the form of the data
PDF can be approximated in terms of a mixture of simple analytic distributions,
each of which possesses an analytic solution.
8.2.1 The Kolmogorov-Smirnov Test
The K-S test investigates the null hypothesis that two data sets are taken from
the same distribution and depends on the maximum value of the absolute
difference between their CDFs. The probability that the K-S measure exceeds
that observed is approximately independent of the size of the sample (provided
this is greater than four) and the form of the data PDF and can be readily
calculated
[4,5].
The test can be applied to classification, as described in Section
8.4.2, with one input provided by theoretical or trained CDFs for the different
classes. In segmentation, discussed in Section 8.5, our interest is in determining
whether
two
data samples
are
members
of the
same (unknown) distribution
and
no analytic
PDF or
training data
are
necessary.
In
both situations,
if the
analytic
form
of the PDF is
known
a
priori,
it is
better that
it
should
be
incorporated
into model-based exploitation methods rather than using
the
noncommittal
K-S
test.
8.2.2 Estimating Moments
In Chapter
5 we
showed that
the
normalized variance
(the
square
of the
contrast)
of
intensity provided
a
means
of
discriminating between examples
of
field and woodland. Performance
is
then determined
by the
statistical uncer-
tainty
in
these estimates. Consider
the
variance
of an
uncorrelated random
intensity /with
an
estimate, defined over
a
window
of
TV
pixels,
by
—,,n-P-^i
n
-[^t,,]
(8..)
where
the
bars denote ^ample averages. Though both
/
and/
2
are
unbiased,
since
(l) = (I) and (l
2
) — (I
2
), the
estimated variance
var / is
biased since
((/)
2
)
¥=
(I)
2
. In
fact,
the
mean
and
variance
of
this estimator
are
given
by
(var/)
= (l -—
Jvar/
(8.2)
exactly,
and
var[^7]
=
^((/4)-4(/3)(/)-(P}
2
+ 8(P)(I)
2
- 4(I)
4
) (8.3)
to O(l/N), respectively.
For
"true" normalization this estimate
is
divided
by the
square
of the
true mean.
Alternatively,
a
self-normalized estimate
is
obtained
by
dividing
the
esti-
mated variance
by the
square
of the
estimated mean. Hence,
^
s
ii -
1
(8.4)
/2
/2
The uncertainty in this estimator depends on errors in both numerator and
denominator, which are clearly not independent. The expected
value
of this
estimator can be derived by perturbing both numerator and denominator about
their mean
value
[6] leading to
which is biased to O(l/N). The variance of the quantity can be derived
following
a similar process leading to
j^i]-±.№-turn
+
<u$-sen
(8
,>
L
P J N((lf (if (if (If )
Let us examine the difference between true and
self
normalizations for a
K-distributed intensity with order parameter v, by substituting appropriate
moments from (5.14). With true normalization the bias is
while
the variance is
var[var/|
4
/
?n
co a/-\
LJ^lh+-+^+^
(8.8)
(I)
4
NK v v
2
V
3
J
The self-normalized quantity, on the other hand, has a bias of
Bi
as s
/™l\ - var/ « - A f! + IY
1
+
6 ^
(89)
\
I
2
I (If NK vA vJ
and a variance of
-S
2
BH)H)H)
™
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