### Slides

```진행상황
박노열
진행상황
• Gait analysis
• Femur Reconstruction
Gait analysis
3D rotation
X
X
Z
Z
Y
Y
3D rotation
• 두 Orientation간의 최단 차이
vˆ

Projection angle
Pelvic Tilt
Pelvic Obliquity
15
30
20
Down-Up
5
Pos-Ant
10
-5
-15
0
20
40
60
80
100
Pelvic Rotation
30
20
Ext - Int
10
0
-10
-20
-30
0
20
40
60
80
100
0
-10
0
20
40
60
80
100
Euler angle -> Projection angle
Y (sagittal)
X (coronal)
Z
(transverse)
Euler angle -> Projection angle
Y (sagittal)
β
α
X (coronal)
γ
Z
(transverse)
X’ Y’ Z’ =
cycz
czsxsy-cxsz
sxsz+cxczsy
cysz
cxcz+sxsysz
cxsysz-czsx
-sy
cysx
cxcy
Projection angle -> Euler angle
Y (sagittal)
(0,e,f
)
β
α
γ
Z
(transverse)
(a,b,0
)
X (coronal)
(g,0,i)
X’ Y’ Z’ = b e h
c f i
Projection angle -> Euler angle
Y (sagittal)
(0,e,f
)
β
α
γ
Z
(transverse)
(a,b,0
)
X (coronal)
(g,0,i)
X’ Y’ Z’ = b e h
c f i

tan α =

tan β =

tan γ =

Projection angle -> Euler angle
Y (sagittal)
(0,e,f
)
β
α
γ
Z
(transverse)

tan α =

tan β =

tan γ =

(a,b,0
)
X (coronal)
(g,0,i)
X’ Y’ Z’ = b e h
c f i
=
cycz
czsxsy-cxsz
sxsz+cxczsy
cysz
cxcz+sxsysz
cxsysz-czsx
-sy
cysx
cxcy
Projection angle -> Euler angle
• tan α =
• tan β =
• tan γ =

= tan
=
cos  tan
cos +tan  sin  sin
=
tan  sin +cos  sin
cos
Projection angle -> Euler angle
• =α
• y=
tan γ−sin α cos α tan β
arctan
sin α tan β tan γ+cos α
• x=
tan γ cos −cos α sin
arctan
sin α
– Quaternion 변환 후
– Dynamic time warping으로 계산
Result
normal1
normal2
normal3
normal4
normal5
cp1
cp2
cp3
cp4
normal1
0.00
9.55
2.51
4.11
9.27
13.72
19.58
10.97
13.93
normal2
9.55
0.00
9.69
9.64
5.68
10.68
12.59
7.75
11.46
normal3
2.51
9.69
0.00
4.10
9.35
14.59
19.25
11.69
14.71
normal4
4.11
9.64
4.10
0.00
11.25
16.48
20.85
12.88
15.96
normal5
9.27
5.68
9.35
11.25
0.00
7.15
10.94
7.10
9.13
cp1
13.72
10.68
14.59
16.48
7.15
0.00
11.71
8.93
8.98
cp2
19.58
12.59
19.25
20.85
10.94
11.71
0.00
14.19
13.53
cp3
10.97
7.75
11.69
12.88
7.10
8.93
14.19
0.00
12.07
cp4
13.93
11.46
14.71
15.96
9.13
8.98
13.53
12.07
0.00
Calibration
Pelvic Tilt
30
20
0
-10
0
20
40
60
80
100
1.5
1
0.5
0
-0.5
-1
-1.5
-2
-2.5
-3
1
7
13
19
25
31
37
43
49
55
61
67
73
79
85
91
97
Pos-Ant
10
Normal1
Normal2
Result
• Calibration 후
normal1
normal2
normal3
normal4
normal5
cp1
cp2
cp3
cp4
normal1
0.00
3.88
2.83
3.12
5.69
8.12
9.41
7.18
15.02
normal2
3.88
0.00
5.01
3.47
3.60
4.48
7.10
5.65
11.63
normal3
2.83
5.01
0.00
3.05
5.74
8.50
9.98
7.70
15.69
normal4
3.12
3.47
3.05
0.00
4.01
6.76
8.65
7.03
13.34
normal5
5.69
3.60
5.74
4.01
0.00
4.63
5.89
5.28
10.71
cp1
8.12
4.48
8.50
6.76
4.63
0.00
5.65
5.47
8.27
cp2
9.41
7.10
9.98
8.65
5.89
5.65
0.00
6.63
7.55
cp3
7.18
5.65
7.70
7.03
5.28
5.47
6.63
0.00
9.54
cp4
15.02
11.63
15.69
13.34
10.71
8.27
7.55
9.54
0.00
Result
normal1
normal2
normal3
normal4
normal5
cp1
cp2
cp3
cp4
normal1
0.00
9.55
2.51
4.11
9.27
13.72
19.58
10.97
13.93
normal2
9.55
0.00
9.69
9.64
5.68
10.68
12.59
7.75
11.46
normal3
2.51
9.69
0.00
4.10
9.35
14.59
19.25
11.69
14.71
normal4
4.11
9.64
4.10
0.00
11.25
16.48
20.85
12.88
15.96
normal5
9.27
5.68
9.35
11.25
0.00
7.15
10.94
7.10
9.13
cp1
13.72
10.68
14.59
16.48
7.15
0.00
11.71
8.93
8.98
cp2
19.58
12.59
19.25
20.85
10.94
11.71
0.00
14.19
13.53
cp3
10.97
7.75
11.69
12.88
7.10
8.93
14.19
0.00
12.07
cp4
13.93
11.46
14.71
15.96
9.13
8.98
13.53
12.07
0.00
normal1
normal2
normal3
normal4
normal5
cp1
cp2
cp3
cp4
normal1
0.00
3.88
2.83
3.12
5.69
8.12
9.41
7.18
15.02
normal2
3.88
0.00
5.01
3.47
3.60
4.48
7.10
5.65
11.63
normal3
2.83
5.01
0.00
3.05
5.74
8.50
9.98
7.70
15.69
normal4
3.12
3.47
3.05
0.00
4.01
6.76
8.65
7.03
13.34
normal5
5.69
3.60
5.74
4.01
0.00
4.63
5.89
5.28
10.71
cp1
8.12
4.48
8.50
6.76
4.63
0.00
5.65
5.47
8.27
cp2
9.41
7.10
9.98
8.65
5.89
5.65
0.00
6.63
7.55
cp3
7.18
5.65
7.70
7.03
5.28
5.47
6.63
0.00
9.54
cp4
15.02
11.63
15.69
13.34
10.71
8.27
7.55
9.54
0.00
Result
• Calibration 전 후 비교
normal1
normal2
normal3
normal4
normal5
cp1
cp2
cp3
cp4
Normal Avg CP Avg
6.36
14.55
8.64
10.62
6.41
15.06
7.27
16.54
8.88
8.58
12.52
9.87
16.64
13.14
10.08
11.73
13.04
11.52
normal1
normal2
normal3
normal4
normal5
cp1
cp2
cp3
cp4
Normal Avg CP Avg
3.88
9.93
3.99
7.22
4.16
10.47
3.41
8.94
4.76
6.63
6.50
6.46
8.20
6.61
6.57
7.21
13.28
8.45
Femur Reconstruction
Contribution
• Clinical Measurement 자동측정
• PCA를 통한 CM 추정
Experiments
• CM 실측과 자동측정 비교
– 자동측정의 정확성 입증
– 3D 측정 및 재배치로 인한 차이
NSA(deg)
femoral AV(deg)
AVG
5.07
5.21
STD
3.41
3.22
MIN
0.46
0.37
MAX
14.11
13.95
R value
0.614
0.893
p-value
<0.001
<0.001
Problems
• Neck shaft angle
X-ray에서의 각도
3D상에서의 각도
Problems
• Femoral AV
CT에서의 각도
재배치 후 각도
Experiments
• X-ray를 통한 Reconstruction
– 재구성된 Shape과 실제 Shape의 비교
• 실제 Shape과 유사함 입증
• Iterative Closest Point algorithm
– 두 Shape간의 Transform을 수렴 할 때까지 반복
– 재구성된 Shape의 CM을 실제 CM과 비교
• 측정된 CM과의 유사함 입증
Problem
• 합성된 X-ray의 부정확
– 잘못된 형태에 맞추려고 함.
– 실제 Shape의 실루엣을 이용
Result
• Node(vertex) : 1434
• ICP error
ICP error(mm)
AVG
1.10
STD
0.42
MIN
0.80
MAX
2.17
Result
• 자동 측정된 CM과 비교
NSA(deg)
femoral AV(deg) Shaft bowing(deg) Neck length(mm)
Age
AVG
2.04
2.48
0.48
2.06
1.83
STD
2.01
1.73
0.32
1.48
1.77
MIN
0.02
0.23
0.02
0.21
0.00
MAX
9.69
8.69
1.13
5.70
8.10
R value
0.793
0.973
0.956
0.711
0.921
p-value
<0.001
<0.001
<0.001
<0.001
<0.001
Result
• 실제 측정된 CM과 비교
AVG
STD
MIN
MAX
R value
p-value
NSA
4.93
2.75
0.18
11.48
0.700
<0.001
femoral AV
4.89
3.02
0.21
10.63
0.915
<0.001
Experiments
• 추가
– X-ray 수
– 다양한 각도의 X-ray
– Shape의 Node(vertex) 수
– PCA parameter의 수
```