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)
 
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