the
approximation coefficients
. In the single-step
DWT
, the
original signal goes through the filter once. The image can be
well reconstructed by using the approximation coefficients
and setting other coefficients to 0 (Li 2002). In this study, only
the single-level decomposition was performed with different
wavelets—bior1.1 (
DWT1
), coif1 (
DWT2
), db1 (
DWT3
), rbio1.1
(
DWT4
), and sym2 (
DWT5
).
Nonlinear Spectral Transformation
In addition to linear spectral transformation methods, we
examined four major nonlinear transformation techniques:
CR
(Kruse 1988), spatial filtering transformation (
LP
,
HP
,
GLP
, and
GHP
filters),
NSMA
(Wu 2004), and tie spectral transformation
(Asner and Lobell 2000). These transformation methods are
summarized in Table 1, and described in the following.
CR
is a method of spectral reflectance normalization (see
Kruse 1988). During
CR
, straight-line segments connect every
peak of local spectra to construct a convex hull. The first and
last peaks in the local spectra are set to 1 in the continuum
removal data, while other data points in the original spec-
tral curve are assigned as less than 1. This can enhance the
absorption features from a spectral curve, eliminating slope
effects, topography, illumination, and the grain-size effect.
Spatial filtering is another type of spectral transformation.
Generally, it involves using a moving window to construct a
filter. The center value of the original pixel is replaced by a
mathematical computation with the pixel value and corre-
sponding filter value (moving window value). The filter can
be defined as
HP
or
LP
, which highlights the corresponding
frequency and suppresses the other type of frequency. That is,
an
HP
filter is likely to highlight heterogeneous areas and com-
press the information of homogenous areas; conversely, an
LP
filter emphasizes smooth areas instead of rough. In this study,
four filters were examined:
LP
,
HP
,
GLP
, and
GHP
.
NSMA
was proposed by Wu (2004). With
NSMA
, reflectance
is divided by the mean value of the corresponding pixel in
all bands. Brightness can be eliminated or reduced through
NSMA
, improving the separability of urban land cover classes.
Finally, tie spectral transformation was introduced by Asner
and Lobell (2000). They used the 2080-nm wave band as the tie
point, then implemented the tie transformation through apply-
ing other bands minus the tie point. Results indicated that tie
spectra could reduce the variation caused by soil moisture, leaf
and litter area index, tissue optics, and canopy architecture.
Only shortwave infrared were examined in that study. There-
fore, it is still necessary to explore the potential tie points in
visible and near-infrared wave bands in urban and suburban
areas. Thus, in this study all bands were viewed as potential tie
points and each tie transformation was calculated respectively.
Experiments
Study Areas and Data Sources
Three cities in the United States were examined in this study
(Figure 1): Janesville, Wis., Asheville,
N.C.
, and Columbus,
Ohio. Janesville is on the western shore of Lake Michigan,
within the humid continental climate. It has long nights in
Figure 1. Study areas of Janesville, Wis.; Asheville, N.C.; and Columbus, Ohio.
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