well as shape variations. In the
CCSM
procedure, a reference
spectrum is compared to a “test” spectrum by calculating the
linear correlation coefficient between the two spectra at dif-
ferent match positions (Van Der Meer and Bakker, 1997; Datt,
2000). The cross correlogram function can be created by plot-
ting the correlation coefficients against match positions. The
location of the correlation maximum also indicates the degree
of similarity between the test spectrum and the reference
spectrum. The cross correlogram shape for high similarity is
parabolic and symmetric around match position 0 with a peak
correlation near to 1; on the contrary, the cross correlogram
shape for low similarity is skewed with the correlation peak
shifted towards either positive or negative match positions
(Datt, 2000). Cross correlograms were calculated and inspect-
ed visually for different canopy type combinations (Figure 2),
where “canopy type combination” refers to the comparison
between a test spectrum (i.e., an averaged spectrum of sam-
ples from one tamarisk canopy type) and a reference spectrum
(i.e., an averaged spectrum of samples from a second tamarisk
canopy type) when applying
CCSM
.
The Instability Index
ISI
was used to identify wavelengths that were least sensi-
tive to spectral variability for tamarisk canopy classifica-
tion (Somers
et al
., 2008).
ISI
was calculated as the ratio of
the within-class variability to the between-class variability
(Somers et al., 2010):
. (
ISI
m
m m
R R
i
z
m
j z
m
z i
j i
z i
j i
=
−
+
−
=
−
= +
∑ ∑
(
)
)
,
,
,
,
1
1 96
1
1
1
δ δ
(1)
where
R
z,i
and
R
j,i
are the reflectance values at wavelength
i
for class
z
and class,
j
, respectively, and
δ
z,i
and
δ
j,i
are the
standard deviations at the same wavelengths of class
z
and
j
,
respectively, and
m
is the number of classes. An
ISI
value that
is below one indicates the between-class variability exceeds
the within-class variability, while an
ISI
value which is above
one signifies the opposite trend. Wavelengths with an
ISI
value below one are expected to contain useful information
for spectral feature separation and should be selected for fur-
ther analysis (Somers
et al
., 2010).
Low
ISI
values were found for four spectral regions within
the canopy spectra. Two of these spectral regions (red and
NIR
) corresponded to spectral regions covered by the high
spatial resolution WorldView-2 multispectral instrument.
WorldView-2 provides one panchromatic band (0.5 m spatial
resolution) and eight multispectral bands (2 m spatial resolu-
tion) with an average revisit time of 1.1 days (Table1;
http://
digitalglobe.com
). Considering the size and distribution of
tamarisk stands along riparian corridors, WorldView-2 is one
of the most suitable sensors for high spatial resolution remote
monitoring of tamarisk defoliation and mortality, but lacks
SWIR
bands found on coarser spatial resolution sensors. Field-
measured spectra were convolved using a sensor response
function in ENVI software
) to
simulate WorldView-2 multispectral spectra.
ISI
was also
applied to select bands from the simulated WorldView-2 spec-
tra. Following this convolution step, four sets of spectra were
used for random forests classification analysis: full-range field
spectra, feature-selected field spectra, simulated WorldView-2
spectra with all eight bands, and feature-selected World-
View-2 spectra with only bands 5 through 8 (Table 1).
T
able
1. W
avelength
R
anges
of
M
ultispectral
B
ands
of
the
W
orld
V
iew
-2
S
ensor
(
nm
)
Band1 (coastal)
400-450
Band5 (red)
630-690
Band2 (blue)
450-510
Band6 (red edge)
705-745
Band3 (green)
510-580
Band7 (NIR1)
770-895
Band4 (yellow)
585-625
Band8 (NIR2)
860-1,040
Random Forests
The random forests (
RF
) algorithm was used to classify the
tamarisk canopy field spectra and simulated WorldView-2
spectra.
RF
is a machine learning algorithm based on tradi-
tional decision tree classification. It randomly selects input
variables from a large number of available variables and
generates a large ensemble of independent tree classifiers that
vote for class membership (Breiman, 2001).
RF
provides an
internal unbiased estimate of the training set error called the
out-of-bag (
OOB
) error (Breiman, 2001). During the process
of
RF
classification, each tree classifier was constructed from
bootstrapped samples comprising about two-thirds of the orig-
inal dataset. Samples not used in the tree construction were
put in the tree classifier to get a classification. In the end,
a class is given to the largest number of votes from the
OOB
sample. The ratio of the times that a class is not the true class
across all bootstrap iterations is called the
OOB
error estima-
tion (Breiman, 2001). In addition, standard methods for evalu-
ating classification accuracies such as confusion matrices and
the kappa coefficient (Congalton, 1991a and 1991b; Congalton
(a)
(b)
(c)
(d)
Figure 2. Cross correlograms using each tamarisk canopy type: (a) green, (b) brown desiccated, (c) yellow desiccated, and (d) dead as
the reference over the 350-2,500 nm region.
202
March 2015
PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
