the winter and cool temperatures in summer. Flat plain is
its major landscape in Janesville. Asheville is the largest city
in western North Carolina. It is in the Blue Ridge Mountains
where two rivers, the Swannanoa and French Broad, merge
together. It is in a humid subtropical climate area, which
means it is cool in winter and not as hot as in summer as
other eastern cities. Mountainous characteristics are sig-
nificant in the Asheville area, and residential buildings are
constructed based on its local terrain. Columbus, the largest
city in Ohio, has relatively flat topography. Like Janesville, its
climate is humid continental. Winter is cold and dry, while
summer is hot and muggy. The three study areas are mainly
occupied by commercial buildings, freeways, parking lots,
residential houses, soil, and vegetation (tree and grass).
Two scenes of
Landsat-8
Operational Land Imager imagery
(Janesville: June 3, 2014; Columbus: September 14, 2015) and
a scene of
Landsat-5
Thematic Mapper imagery (Asheville:
June 2, 2009) were used in this study. Image preprocessing
was applied, such as radiometric calibration, atmospheric
correction using Fast Line-of-sight Atmospheric Analysis of
Hypercube with corresponding parameters, and reprojection
to Universal Transverse Mercator (Janesville: Zone 16; Ashe-
ville and Columbus: Zone 17). Historical high spatial resolu-
tion images (Columbus: August 22, 2015; Janesville: June
12, 2014; Asheville: May 30, 2009) acquired on Google Earth
were utilized to assess the mapping accuracy.
Method
The main objective of this study was to test whether there is a
significant difference after applying a spectral transformation
and to figure out which scheme performs better. Thus, we re-
peatedly applied
SMA
on each transformed scheme 100 times
using different spectra. Such repeated tests can reveal each
transformed scheme’s reliability. We then used paired-sample
t
tests to examine whether the differences were significant
and to figure out which scheme performs better. Generally, the
entire process comprises four steps: spectral transformation,
sample selection,
SMA
and accuracy assessment, and paired-
sample
t
test. First, each transformation scheme was applied
on the original data to create the transformed i
training samples were collected from the trans
for the construction of a spectral library, and te
were selected from the original image and digitized in the
corresponding areas of a high-resolution image for accuracy
assessment. Third,
SMA
was applied on each transformed im-
age and the
MAE
of each test was calculated. Finally, paired-
sample
t
tests were applied on the
MAE
sets of untransformed
and transformed schemes to test their differences.
Spectral Transformation
Spectral transformations were applied to the original data set
using the corresponding methods. In particular,
DA1–3
,
PCA
,
ICA
,
MNF
,
TC
,
CR
,
GHP
,
GLP
,
HP
, and
LP
were calculated directly
from
ENVI
and its extension models.
BN
was computed us-
ing Equation 3 while
NSMA
was calculated using the method
depicted in Wu (2004).
DWT1
–5 were calculated using
MATLAB
’s
dwt2 function. Tie1–7 (Tie2–7 in Asheville) were created with
the method described by Asner and Lobell (2000).
Sample Selection
Training samples were collected from the transformed images.
Four land cover classes were selected as training samples in
this study: vegetation (V), high-albedo impervious surface
area (ISAh), low-albedo impervious surface area (ISAl), and
soil (S). They were collected from the transformed images
with the assistance of high spatial resolution images to avoid
incorrect pixels. We had 50 training samples of each class for
each location, and each training-sample set was used for cor-
responding spectral-library construction.
Testing samples were collected from the original image to
assess each scheme’s performance. We selected 64, 60, and
50 testing samples, respectively, for Janesville, Asheville, and
Columbus. Each testing sample is 3 × 3 pixels (90 × 90 m) to
avoid the geometric error impact acquired from reprojection
and data acquisition. Fractions of impervious surface area
within the testing samples were calculated through digitizing
the corresponding area in high spatial resolution images.
SMA
and Accuracy Assessment
Fully constrained linear
SMA
was applied to transformed and
untransformed data using the V-ISAh-ISAl-S end-member
model. Each transformed scheme was tested 100 times using
randomly selected spectra in the corresponding spectral library.
The performance of each transformed scheme was evalu-
ated with
MAE
, which was calculated based on comparison
between estimated and referenced ISA fractions. Estimated
fractions of ISA were calculated by the sum of ISAh and ISAl
fractions in the same pixel.
Paired-Sample
t
Test
Paired-sample
t
tests were used to test whether there were sig-
nificant differences in
MAE
between transformed and untrans-
formed schemes. Unlike analysis of variance, paired-sample
t
tests compare the differences test by test, which is more reli-
able for indicating the performance of transformed schemes.
Paired-sample
t
tests provide the variables of mean difference
and their significant value. Mean difference is calculated
by subtracting the
MAE
of transformed schemes from that of
untransformed ones. Positive values mean the
MAE
of untrans-
formed schemes is larger than that of transformed schemes,
while negative values represent the opposite. Significant
values indicate the significance of the test result. In addition,
the number of improved tests and their improved percentages
were counted to demonstrate their performance. The number
of improved tests is calculated by counting the number of
tests which have a lower
MAE
than untransformed schemes.
The improved percentage is the average
MAE
of the improved
test. In addition, box plots and statistical description were ap-
e general performance of each scheme.
mances of transformed and untransformed
schemes are illustrated with box plots and descriptive statisti-
cal analysis for the three study areas (Figures 2–4). A sum-
mary of the
MAEs
for the three study areas is as follows.
• Janesville area. The
MAE
of the original data is 0.11, which
is less than those of most transformed schemes—except
NSMA
.
NSMA
has the lowest
MAE
, of 0.10.
MAE
values of
PCA
,
TC
,
GLP
, Tie4, and Tie5 are similar to that of the untrans-
formed scheme (0.11). Transformed schemes of
DA1–3
,
ICA
,
MNF
,
BN
, Tie1–3, Tie6, Tie7, and
DWT
have slightly higher
MAEs
than the untransformed scheme, varying from 0.12
to 0.14.
CR
,
GHP
, and
HP
, have relatively higher
MAEs
: 0.20,
0.18, and 0.18, respectively.
• Asheville area. The
MAE
of the untransformed scheme is as
same as in Janesville (0.11).
DA1–3
,
MNF
, and Tie3–7 have
slightly lower
MAEs
compared to the untransformed scheme,
with values around 0.10.
GHP
and
HP
have very high
MAE
values, of 0.21 both. Other schemes’
MAEs
are slightly
higher than that of the untransformed scheme.
• Columbus area. The
MAE
of the untransformed scheme in
Columbus is about 0.14, which is worse than in Janesville
or Asheville.
GHP
and
HP
illustrate extreme high
MAEs
in
this study area, at 0.25 both.
DA1–2
,
ICA
,
MNF
,
CR
,
GLP
,
LP
,
NSMA
, Tie3, Tie5,
DWT1
, and
DWT5
have small
MAEs
, between
0.11 and 0.13.
DA3
,
PCA
,
TC
, Tie1, Tie2, Tie6, Tie7, and
DWT2
–4 have similar
MAEs
to the untransformed scheme.
524
July 2019
PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
