standard deviation values of the visible blue band, visible
green band, and visible red band, respectively.
β
B
1
to
β
B
2
,
β
G
1
to
β
G
2
, and
β
R
1
to
β
R
2
represent the corresponding coefficients.
β
B
0
,
β
G
0
, and
β
R
0
represent the corresponding intercept parameters.
Models 6 and 7 (or Equations 7 to 8) analyze which feature
combination (i.e., spectral features [mean values] versus tex-
ture features [standard deviation values]) contributes more to
the
ODR
prediction capability, and these two models are:
ODR
=
β
S
0
+
β
S
1
PC
S
1
+
β
S
2
PC
S
2
+
β
S
3
PC
S
3
(7)
ODR
=
β
T
0
+
β
T
1
PC
T
1
+
β
T
2
PC
T
2
+
β
T
3
PC
T
3
(8)
PC
S
1
to
PC
S
3
indicate the three principal components de-
rived from the mean values of each of the three visible bands,
and
β
S
1
to
β
S
3
represent corresponding coefficients.
PC
T1
to
PC
T3
indicate the three principal components extracted from the
standard deviation value of each of the three visible bands,
and
β
T
1
to
β
T
3
represent corresponding coefficients.
β
S
0
and
β
T
0
represent the intercept parameters.
Validation
In order to test the validity and robustness of the method for
predicting
ODR
operationally, we held out 25 of the sites from
the identified regression model with the highest certainty
described in the previous section. Among the 50 study sites,
25 of them were selected using a random sample stratified by
distress rate and used to develop the regression models while
the other 25 were used to validate the predicted
ODR
values
by root mean squared error (
RMSE
), mean absolute error, and
standard error.
Results and Discussion
Table 4 shows the linear regression results using all six
principal components (
PC
A
1
to
PC
A
6
) and by using only two
principal components (
PC
A
1
to
PC
A
2
). It revealed that remov-
ing
PC
A
3
to
PC
A
6
decreased the R-squared value and increased
the
RMSE
for all three datasets. It proved that
PC
A
3
to
PC
A
6
are
useful components despite containing less than 1 percent of
the original information. This suggests that all six principal
components should be used for operational inference of
ODR
.
Table 4 and Figure 2 show the model fit results (sample
size = 50) of the 6-inch, 12-inch, and 24-inch models when
using all six principal components. The 6-inch linear re-
gression model is valid at a 95 percent confidence interval
(the joint P-value (Prob >F) is less than 0.001). The adjusted
R-squared value is 0.9439 and the
RMSE
is 24.087. This er-
ror number is acceptable since the
ODR
assessed by manual
evaluation can exhibit an error of up to 84 or up to 50 percent
in terms of variability (Bogus
et al.,
2010). This implies that
natural color aerial photographs with 6-inch spatial resolution
can be used to assess and predict overall pavement surface
distress rates
.
The 12-inch linear regression model is valid at a 95 per-
cent confidence interval (joint P-value (Prob >F) is less than
0.001). The adjusted R-squared value is 0.7958, and the
RMSE
is 45.843 which is approximately double that of the 6-inch
model. This implies that with a higher error, natural color
digital aerial photographs with 12-inch resolution can also be
used to assess and predict overall pavement surface distress
rates. However, 12-inch models still exhibit less error than
manual evaluation (45.843 <84).
The 24-inch linear regression model is valid at a 95 per-
cent confidence interval (joint P-value (Prob >F) is less than
0.001). The adjusted R-squared value is 0.6771 and
RMSE
is
57.645. This implies that natural color aerial photographs
with 24-inch resolution can still be used to assess and predict
overall pavement surface distress rates, but with the highest
error of the resolutions assessed. However, it is still bet-
ter than the manual evaluation (57.645 <84), and it has the
T
able
2. P
earson
C
orrelation
R
esults of
the
M
ean
V
alue
and
S
tandard
D
eviation
V
alue of
the
6-I
nch
, 12-I
nch
,
and
24-I
nch
N
atural
C
olor
D
igital
A
erial
P
hotography
Dataset
Variables
ODR
M1
STD1
M2
STD2
M3
STD3
6-inch
ODR
1.0000
M1
-0.9586
1.0000
STD1
0.9043
-0.8938
1.0000
M2
-0.9512
0.9958
-0.8781
1.0000
STD2
0.9075
-0.9016
0.9987
-0.8871
1.0000
M3
-0.9333
0.9859
-0.8456
0.9922
-0.8565
1.0000
STD3
0.9263
-0.9148
0.9926
-0.9020
0.9953
-0.8764
1.0000
12-inch
ODR
1.0000
M1
-0.7337
1.0000
STD1
0.8245
-0.6640
1.0000
M2
-0.6993
0.9904
-0.6423
1.0000
STD2
0.8243
-0.6766
0.9977
-0.6575
1.0000
M3
-0.6832
0.9699
-0.6192
0.9881
-0.6390
1.0000
STD3
0.8379
-0.6665
0.9892
-0.6518
0.9935
-0.6420
1.0000
24-inch
ODR
1.0000
M1
-0.7246
1.0000
STD1
0.5457
-0.5072
1.0000
M2
-0.7220
0.9863
-0.4397
1.0000
STD2
0.5718
-0.5323
0.9977
-0.4669
1.0000
M3
-0.7030
0.9455
-0.3497
0.9833
-0.3793
1.0000
STD3
0.6022
-0.5236
0.9868
-0.4550
0.9923
-0.3657
1.0000
Note: 1 indicates the visible red band; 2 indicates the visible green band; 3 indicates the visible blue band; M indicates mean; STD indicates
standard deviation; and ODR indicates overall distress rate.
714
September 2015
PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
