these learned weights are utilized to reconstruct impervious
fraction map.
Accuracy Assessment
The general accuracy indicator used in this work is the R-
square, given by:
R
SSR
SST
2
=
(8)
in which
SSR
is the regression sum of squares and
SST
is the
total sum of squares. The higher R-square suggests the less
similarity difference among impervious fractions derived
by the proposed approach and reference data. Furthermore,
another three error measurements (1) root mean square error
(
RMSE
), (2) mean absolute error (MAE), and (3) systematic er-
ror (SE) are used to evaluate the accuracy of our technique in
detail, which are respectively given by:
RMSE
n
x
x
i
i
i
n
=
( )
−
( )
(
)
=
∑
1
1
2
Γ Γ
ˆ
,
(9)
MAE
n
x
x
i
i
n
i
=
( )
−
( )
=
∑
1
1
Γ Γ
,
(10)
SE
n
x
x
i
i
i
n
=
( )
−
( )
(
)
=
∑
1
1
Γ Γ
ˆ
,
(11)
where
Γ
represents the final output of our proposed method,
Γ
ˆ
is the reference impervious fractions (in this study, we inter-
preted the reference data from
Gaode Map Online
).
RMSE
and
MAE
predict the estimation errors, and SE indicates the overall
tendency of the estimation bias.
Experimental Results
Two different experiments were conducted. The next Section
presents the pixel-based
IS
estimation experiment, followed
by the parcel-based
IS
estimation experiment. 150 patches
(90 m × 90m) were randomly collected for accuracy assess-
ment. These samples are with a good coverage over the study
area among all the land use types including roads, residential
areas, business blocks, vegetation, and shadows.
Pixel-based Impervious Surface Estimation
Figure 7a illustrates the
IS
result estimated from physical
features and
POI
features. Meanwhile, we considered the road
distribution map (see Figure 5a) as an additional source of so-
cial data, and then fed all physical and social features into
IS
estimation model (The result is shown in Figure 7b). The frac-
tions of (7a) and (7b) both vary from 0 to 1, and the learned
weights of features are illustrated in Table 2. Figure 7c and
7d give the zoomed-in views of (7a) and (7b), respectively.
Three fitting curves are drawn in Figure 7e reference data
versus physical features (R-square = 0.6932), (7f) reference
data versus impervious fractions integrating physical features
and
POI
features (R-square = 0.8345), and (7g) reference data
versus impervious fractions integrating physical features and
all social features (R-square =0.8452), suggesting a strong
correlation between the impervious fractions we obtained
and the reference data. Three R-square values go from 0.6932
to 0.8345 and then up to 0.8345, which indicates the great
contributions brought by
POIs
and road network. Because of
the low coverage rate of road network and the randomness
of samples, it is not easy to substantiate the contributions of
road network by using the R-square value. However, by con-
sidering road distribution, we can capture each block clearly
in the resulting map (Figure 7d).
Parcel-based Impervious Surface Estimation
In this paper, we consider the mean value of pixels in each
parcel as the parcel-based physical features. Because of the
complicated internal structure of each parcel, the accuracy
of the parcel-based method is not as good as pixel-based
method. Figure 8a shows the obtained impervious map in-
tegrating physical features and
POI
features, while Figure 8b
takes the advantage of physical features,
POI
features and road
distribution. The learned weights are shown in Table 2. Also,
the enlarged views of these two maps with values varying
from 0 to 1 are illustrated in Figure 8c and 8d. The following
figures: (8e), (8f), and (8g) give the fitting curves of reference
data versus physical features, reference data versus
IS
result
using physical and
POI
features, and reference data versus
impervious fractions integrating physical and all social fea-
tures. Three R-square values are 0.6932, 0.7512, and 0.7529,
respectively. The experimental results suggest that parcel-
based methods contribute significantly to
IS
estimation. Fur-
thermore, parcel-based methods are also promising for higher
level decision making in urban planning and urban analysis.
Accuracy Assessment
To further evaluate the accuracy of our work, referring to Bau-
er
et al
. (2004), two types of land covers including developed
areas and less developed areas are conducted for verification
purposes. Based on the definition of impervious surface in
(Arnold, Jr. and Gibbons, 1996) and the exact conditions of
study area, pixels with values equal or larger than 0.4 are
sorted into developed area, and the rest are allocated to less
developed area. Meanwhile, in order to explore the benefits
of social knowledge, we use the physical features previously
extracted for comparison. Three considered error measure-
ments (including
RMSE
,
MAE
, and
SE
) are listed in Table 3,
revealing the persuasiveness and advancement of our method.
Table 2. Feature weights learned by multivariable linear
regression model.
Experiment I Experiment II
Pixel-based
(section 4.1)
Physical Features
0.91
0.76
Impervious POIs Features
0.59
0.49
Pervious POIs Features
-0.11
-0.13
Road Features
0.18
Parcel-
based
(section 4.2)
Physical Features
0.87
0.84
Impervious POIs Features
0.79
0.76
Pervious POIs Features
-0.09
-0.10
Road Features
0.04
Table 3. Accuracy comparison between the physical features
we extracted in 3.1 and our proposed method using
RMSE
,
MAE
and
SE
of two experiments.
Methods
Area
RMSE(%) MAE(%)
SE(%)
Physical
Features
Less Developed Area 12.09
6.70
-5.32
Developed Area
18.08
14.23
13.68
Overall
14.66
9.56
1.90
Pixel-
based
Less Developed Area 10.65
6.65
-5.68
Developed Area
11.49
9.03
6.41
Overall
10.98
7.55
-1.09
Parcel-
based
Less Developed Area 10.32
5.95
-4.78
Developed Area
11.79
9.28
4.94
Overall
10.90
7.21
-1.09
776
December 2018
PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
