343
whole
onents
ponents
Components
then the four
-i; j = 1, 4 )
les less than
= 10, 20, 30,
and data can
it is possible
data on an
action cosines
requirement.
•d reflectance
>s
n determined
:hnique (Mitai
with a corre
cted, whose
i observations
pies for each
del for large
ie number of
of India has
i/lunsell colour
roma 1 to 6.
been observed
ons described
so been deter-
model based
been evolved
. The values
>del, six more
falling within
ollected from
ill these sam-
e values were
in sizes were
idicted values
mined in the
between the
Table 2. Regression analysis of diamter on transformed data
Number of samples = 5
num variance
ixed axes in
Regression Constants for diameter on
ppc 3
Regression constants for diamter on PPC
x and SPC
ied regression
ctor variables
ig them, will
Hence, the
SI.No
Dia
< d x>
C
X
M
X
<fy
GjT.x
r
A
X
B
X
C
X
<Ty.xl.x2
r
1
d 10
0.224
0.167
0.158
0.133
0.683
-6.11
5.30
-1.37
0.137
0.79
btained, have
2
d 20
0.293
0.369
0.293
0.196
0.815
-13.95
12.17
-3.36
0.147
0.93
ultiple linear
n found that
3
d 30
0.391
0.568
0.474
0.345
0.776
-23.28
20.14
-5.55
0.191
0.96
fourth PPC
4
d 40
0.469
0.785
0.648
0.463
0.785
-32.64
28.30
-7.92
0.140
0.99
pendent vari-
of 0.94 for
5
d 50
0.786
0.919
0.867
0.728
0.686
-44.60
38.28
-10.46
0.094
0.99
-linear model
6
d 60
1.299
1.065
1.121
1.019
0.615
-57.51
49.40
-13.46
0.132
0.99
7
d 7Q
2.291
1.049
1.102
1.000
0.616
-54.90
48.29
-13.35
0.234
0.98
8
d 80
4.110
0.468
0.498
0.456
0.609
-21.24
21.42
-5.94
0.167
0.97
9
d 90
6.317
-0.223
0.378
0.403
0.382
-2.44
6.06
-0.99
0.312
0.81
- Slope coefficient
- y intercept
regression coefficient
standard deviation of diameters
- standard error of estimate
A x , B^, C x - partial regression coefficients
<Ty xl x2 ~ stan< ^ arc l error °f estimate
r J - multiple correlation coefficient
Table 3. Grain size prediction model by optimization
Number of samples = 5
SI. No.
Description of model
Correlation coefficient of diameter with
Transformed
data
Original data in
Band-7|
Band-6 |
Band-5 1
Band-4
1
«10 =<0.22B 7
- 0.55B 6 + 0.62B 5 - 0.50B^) 1.08 + 1.53
1.0
-0.21
-0.20
-0.22
-0.40
2
d 20 =<0.24B 7 -
0.52B 6 + 0.60B 3 - 0.55B^) 1.65 + 2.42
1.0
0.13
0.13
0.07
-0.09
3
d 3Q =(0.24B ?
- 0.52B 6 + 0.61B 5 - 0.54B^) 2.75 + 3.61
1.0
0.23
0.24
-0.18
0.01
4.
d, 0 =<0.25B 7
- 0.51B 6 + 0.59B 5 - 0.57B 4 ) 3.31 + 4.65
1.0
0.34
0.30
0.21
0.10
5
d 5Q =<0.25B 7
- 0.54B 6 + 0.60B 5 - 0.53B^) 4.97 + 6.28
1.0
0.40
0.29
0.19
0.17
6
d 60 = (0 - 2 ' ,B 7
- 0.54B 6 + 0.61B 5 - 0.51B 4 ) 6.29 + 7.49
1.0
0.51
0.39
0.29
0.30
7
d 7Q =<0.25B 7
- 0.53B 6 + 0.60B 3 - 0.53B^) 5.44 + 7.81
1.0
0.58
0.45
0.34
0.36
8
d 80 =<0.26B 7
- 0.53B 6 + 0.59B 5 - 0.54B^) 2.27 + 6.70
1.0
0.57
0.38
0.24
0.34
9
d 90 =<0.21B 7
- 0.64B 6 + 0.67B 5 - 0.28B 4 ) 2.37 + 6.63
1.0
0.46
0.17
0.10
0.48
Table 4. Regression analysis of diameter on original and transformed data
Number of samples = 14
SI.No
Dia
r- values with original data in
Regression
constants for the model
Band-7
Band-6
Band-5
Band-4
C
X
M
X
<r y
ffT.x
r
1
d 10
-0.94
-0.88
-0.80
-0.61
1.21
0.05
0.22
0.07
0.95
2
d 20
-0.92
-0.85
-0.69
-0.61
2.25
0.12
0.45
0.09
0.98
3
d 30
-0.92
-0.85
-0.70
-0.52
3.35
0.18
0.67
0.15
0.98
4
-0.90
-0.82
-0.67
-0.53
5.02
0.32
1.07
0.32
0.96
5
d 50
-0.87
-0.79
-0.63
-0.53
6.74
0.46
1.49
0.54
0.94
6
d 60
-0.83
-0.74
-0.58
-0.50
8.37
0.64
1.87
0.77
0.92
7
d 70
-0.74
-0.67
-0.51
-0.51
9.62
0.81
2.17
1.17
0.85
8
d 80
-0.67
-0.62
-0.48
-0.51
11.24
0.93
2.45
1.44
0.82
9
d 90
-0.51
-0.49
-0.40
-0.64
12.00
1.03
2.15
1.36
0.80