that other texture measures including range and variety have
a strong correlation with standard deviation and therefore,
only standard deviation was selected as the texture measure.
Table 1 shows the Pearson’s correlation results
.
For each image dataset, (6-inch, 12-inch, and 24-inch digital
aerial photographs), mean and standard deviation values of each
band (visible blue, visible green, and visible red) were selected
as independent variables, resulting in a total of six variables.
Pearson’s correlation analyses were performed to examine if
there is correlation among these six variables. The results in
Table 2 show that in each dataset these six variables have signifi-
cant correlation with
ODR
. However, there is also significant cor-
relation among these six variables, which violates the assump-
tion of variable independence by linear least squares regression.
PCA
was used on mean and standard deviation values of each
band of the three datasets to eliminate the correlation among
the six variables (Pearson, 1901). These principal components
were used as independent variables for the various linear
regression models described below. Table 3 shows the resultant
loadings for each principal component obtained from the
PCA
.
Linear Regression
Various multiple linear least squares regression models were
built based on reference pavement surface
ODR
data and the
principal components extracted from the 6-inch, 12-inch, and
24-inch multispectral, digital aerial photographs. The ultimate
goal is the identification of the regression model with the
highest correlation to predict pavement surface
ODR
values
.
The regression model that uses six principal components
obtained from all three visible bands, Model 1 in Table 4, can
be expressed as the following equation (Equation 2):
ODR
=
β
0
+
β
1
PC
A
1
+
β
2
PC
A
2
+
β
3
PC
A
3
+
β
4
PC
A
4
+
β
5
PC
A
5
+
β
6
PC
A
6
(2)
where
β
0
represents the intercept parameter,
PC
A
1
to
PC
A
6
rep-
resent the six principal components derived from mean and
standard deviation of each band, and
β
1
to
β
6
represent the
corresponding coefficients
.
As shown in Table 3,
PC
A
1
and
PC
A
2
collectively contain
more than 99 percent of the information contained in the
aerial imagery. In order to test the significance of the rest prin-
cipal components (
PC
A
3
to
PC
A
6
), the first two principal compo-
nents (
PC
A
1
and
PC
A
2
) were considered as a break point and
PC
A
3
to
PC
A
6
were removed from the linear regression, resulting in
Model 2 (or Equation 3):
ODR
=
β
0
+
β
1
PC
A
1
+
β
2
PC
A
2
(3)
To analyze which spectral band (visible blue, visible green,
and visible red) contributes more or is more significant to the
prediction of
ODR
, three linear regression models were created
(Models 3 to 5, or Equations 4 to 6) and they are:
ODR
=
β
B
0
+
β
B
1
PC
B
1
+
β
B
2
PC
B
2
(4)
ODR
=
β
G
0
+
β
G
1
PC
G
1
+
β
G
2
PC
G
2
(5)
ODR
=
β
R
0
+
β
R
1
PC
R
1
+
β
R
2
PC
R
2
(6)
PC
B
1
to
PC
B
2
,
PC
G
1
to
PC
G
2
, and
PC
R
1
to
PC
R
2
represent the two
principal components extracted from the mean values and
T
able
1. P
earson
C
orrelation
R
esults
of
T
exture
M
easurement
of
the
6-I
nch
, 12-I
nch
,
and
24-I
nch
N
atural
C
olor
D
igital
A
erial
P
hotography
.
Dataset
Variables
R1
STD1
V1
R2
STD2
V2
R3
STD3
V3
6-inch
R1
1.0000
STD1
0.8738
1.0000
V1
0.9790
0.9222
1.0000
R2
0.9952
0.8809
0.9816
1.0000
STD2
0.8746
0.9977
0.9234
0.8823
1.0000
V2
0.9729
0.9267
0.9969
0.9805
0.9300
1.0000
R3
0.9869
0.8491
0.9720
0.9876
0.8536
0.9691
1.0000
STD3
0.8877
0.9888
0.9362
0.8954
0.9926
0.9417
0.8784
1.0000
V3
0.9669
0.8938
0.9884
0.9711
0.8999
0.9891
0.9795
0.9247
1.0000
12-inch
R1
1.0000
STD1
0.7680
1.0000
V1
0.9001
0.9403
1.0000
R2
0.9949
0.7697
0.9007
1.0000
STD2
0.7676
0.9972
0.9411
0.7733
1.0000
V2
0.8995
0.9342
0.9961
0.9061
0.9395
1.0000
R3
0.9814
0.7474
0.8900
0.9898
0.7541
0.8971
1.0000
STD3
0.7709
0.9874
0.9466
0.7783
0.9919
0.9450
0.7720
1.0000
V3
0.8831
0.9117
0.9861
0.8924
0.9197
0.9901
0.8998
0.9400
1.0000
24-inch
R1
1.0000
STD1
0.8041
1.0000
V1
0.8915
0.9559
1.0000
R2
0.9956
0.7996
0.8826
1.0000
STD2
0.8034
0.9962
0.9514
0.8043
1.0000
V2
0.8857
0.9518
0.9930
0.8837
0.9535
1.0000
R3
0.9742
0.7631
0.8535
0.9845
0.7744
0.8585
1.0000
STD3
0.7977
0.9830
0.9451
0.8017
0.9906
0.9495
0.7900
1.0000
V3
0.8695
0.9302
0.9780
0.8722
0.9368
0.9843
0.8731
0.9518
1.0000
Note: 1 indicates the visible red band; 2 indicates the visible green band; 3 indicates the visible blue band; R indicates range, STD indicates
standard deviation, and V indicates variety
.
PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
September 2015
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