Image Processing Reference
In-Depth Information
Next, the following values are obtained.
=
(
)=
(
)=
(
)=
y
96.15,
y
1
0
95.89,
y
1
1
106.00,
y
1
2
86.56,
(
)=
(
)=
(
)=
(
)=
y
2
0
96.78,
y
2
1
97.00,
y
2
2
94.67,
y
3
0
93.56,
(
)=
(
)=
(
)=
(
)=
y
3
1
96.44,
y
3
2
98.44,
y
4
0
97.00,
y
4
1
94.22,
y
4
(
)=
y
5
(
)=
y
5
(
)=
y
5
(
)=
2
97.22,
0
94.11,
1
96.00,
2
98.33,
y
1,2
(
)=
y
1,2
(
)=
y
1,2
(
)=
y
1,2
(
)=
0, 0
96.00,
0, 1
96.00,
0, 2
95.67,
1, 0
106.67,
y
1,2
(
)=
108.00,
y
1,2
(
)=
103.33,
y
1,2
(
)=
y
1,2
(
)=
1, 1
1, 2
2, 0
87.67,
2, 1
87.00,
y
1,2
(
)=
y
1,3
(
)=
y
1,3
(
)=
y
1,3
(
)=
2, 2
85.00,
0, 0
93.33,
0, 1
96.00,
0, 2
98.33,
y
1,3
(
1, 0
)=
102.00,
y
1,3
(
1, 1
)=
108.00,
y
1,3
(
1, 2
)=
108.00,
y
1,3
(
2, 0
)=
85.33,
y
1,3
(
2, 1
)=
85.33,
y
1,3
(
2, 2
)=
89.00,
y
1,4
(
0, 0
)=
96.67,
y
1,4
(
0, 1
)=
94.00,
y
1,4
(
0, 2
)=
97.00,
y
1,4
(
1, 0
)=
104.67,
y
1,4
(
1, 1
)=
104.00,
y
1,4
(
1, 2
)=
109.33,
y
1,4
(
2, 0
)=
89.67,
y
1,4
(
2, 1
)=
84.67,
y
1,4
(
2, 2
)=
85.33.
Last, by using (19)-(21),
μ
=
(
)=
−
(
)=
(
)=
−
ˆ
96.15,
α
1
ˆ
0
0.26,
α
1
ˆ
1
9.85,
α
1
ˆ
2
9.59,
(
)=
(
)=
(
)=
−
(
)=
−
α
2
ˆ
0
0.63,
α
2
ˆ
1
0.85,
α
2
ˆ
2
1.48,
α
3
ˆ
0
2.59,
(
)=
(
)=
(
)=
(
)=
−
α
3
ˆ
1
0.30,
α
3
ˆ
2
2.30,
α
4
ˆ
0
0.85,
α
4
ˆ
1
1.93,
ˆ
(
)=
ˆ
(
)=
−
ˆ
(
)=
−
ˆ
(
)=
α
4
2
1.07,
α
5
0
2.04,
α
5
1
0.15,
α
5
2
2.19,
ˆ
0.52,
ˆ
0.74,
ˆ
ˆ
β
1,2
(
0, 0
)=
−
β
1,2
(
0, 1
)=
−
β
1,2
(
0, 2
)=
1.26,
β
1,2
(
1, 0
)=
0.04,
ˆ
ˆ
1.19,
ˆ
ˆ
β
1,2
(
)=
β
1,2
(
)=
−
β
1,2
(
)=
β
1,2
(
)=
−
1, 1
1.15,
1, 2
2, 0
0.48,
2, 1
0.41,
ˆ
0.07,
ˆ
ˆ
0.19,
ˆ
β
1,2
(
2, 2
)=
−
β
1,3
(
0, 0
)=
0.04,
β
1,3
(
0, 1
)=
−
β
1,3
(
0, 2
)=
0.15,
ˆ
1.41,
ˆ
ˆ
0.30,
ˆ
β
1,3
(
)=
−
β
1,3
(
)=
β
1,3
(
)=
−
β
1,3
(
)=
1, 0
1, 1
1.70,
1, 2
2, 0
1.37,
ˆ
1.52,
ˆ
ˆ
0.07,
ˆ
β
1,3
(
2, 1
)=
−
β
1,3
(
2, 2
)=
0.15,
β
1,4
(
0, 0
)=
−
β
1,4
(
0, 1
)=
0.04,
ˆ
ˆ
2.19,
ˆ
0.07,
ˆ
β
1,4
(
0, 2
)=
0.04,
β
1,4
(
1, 0
)=
−
β
1,4
(
1, 1
)=
−
β
1,4
(
1, 2
)=
2.26,
ˆ
ˆ
ˆ
β
1,4
(
2, 0
)=
2.26,
β
1,4
(
2, 1
)=
0.04,
β
1,4
(
2, 2
)=
−
2.30.
Although there are software packages that can be used to estimate the effects on the basis of
(19)-(21), as yet no software can be used for an arbitrary monotonic set
A
. Therefore, it is often
necessary to implement the procedure for estimating the effects, which requires a considerable
amount of time.
3.4 Analysis of variance
When there are many factors, a comprehensive view of whether an interaction in
A
can be
disregarded is needed. The test procedure involves an analysis of variance. For a detailed
explanation of analysis of variance, refer to (Toutenburg & Shalabh, 2009).
The statistics needed in analysis of variance are the following.
SS
Mean
is the correction term
(the sum of squares due to the mean),
SS
F
l
is the sum of squares due to the effect of
F
l
,
SS
F
l
×
F
m
is the sum of squares due to the interaction effect of
F
l
×
F
m
, and
SS
Error
is the sum of squares
due to error. These can be computed as follows.
1
q
k
Y
2
,
SS
Mean
=
(22)
q
1
ϕ
=
0
Y
l
(
ϕ
)
−
SS
Mean
,
−
1
q
k
−
1
SS
F
l
=
(23)