Vishnevskiy

2. Tθ
M
min

9. Tθ
M
min

10. • A AS
• X XS
ˆ
TAX : A → X
M
ˆ
TAX =Tθ M (Tθ (A), X )
ˆ ˆ
X XS = TAX (AS ).

11. • Tθ
• M
• min

12. Tθ
Tθ
M
min

13. Tθ
•
•
•
•

14. Tθ
•
•
•

15. Tθ
•
•
•
•

16. M
Tθ
M
min

17. M
•
•
•

18. M
M(A, X ) = ρ (A(T (p)), X (p)) dp
ΩX
1
• MMS (A, X ) = N (Ai − Xi )2
Ai Xi
• MNCC (A, X ) = −
A2
i Xi2
• MMI (A, X ) = H(A) + H(X ) − H(A, X )

19. M
•
•
•
•

20. min
Tθ
M
min

21. min
•
•

22. •
•
•
•
•

23. •
•
•

24. •
•
•
•

25. XS
• Dice(AS , XS ) = 2 |ASS|+|XS||
|A ∩XS
• H(AS , XS ) = max (h(AS , XS ), h(XS , AS )) ,
h(AS , XS ) = maxa∈AS minx∈XS ||a − x ||
XS
ˆ
M TAX (A), X .

26. T1,X
A1 X
T1,2 T2,X
A1 A2 X
T1,X
• T1,2 ◦ T2,X T1,X
• Dice(A2S , T1,2 (A1S )) + Dice(XS , T2,X (A2S )) Dice(XS , T1,X (A1S ))
d1,2 +d2,3
• d1,3 = 2
• d1,3 = d1,2 · d2,3

27. A
•
•
εAX1 + εX1 X3 + εX3 A = 3Dice (AS , TAX1 (TX1 X3 (TX3 A (AS ))))
...
εAX1 · εX1 X3 · εX3 A = Dice (AS , TAX1 (TX1 X3 (TX3 A (AS ))))
...
•

28. min x 2
 
εi1 + εj1 + εk1 − Di1 j1 k1
x =
 

εiC + εjC + εkC − DiC jC kC
N K E = N(N − 1)
C = K (N − 1)(N − 2)
ε ∈ RE ×1 P ∈ {0, 1}C×E .
min Pε − E 2
s.t. 0 ≤ ε ≤ 1.

29. min x 2
 
log εi1 + log εj1 + log εk1 − log Di1 j1 k1
x =
 
,
log εiC + log εjC + log εkC − log DiC jC kC
s.t. 0 < εp ≤ 1, p = 1, . . . , E .
P

30. 1
1 0.5 0.6 5
0. 0.6 0.6
0.5
0.3 0.3 0.1 0.9
3
0.5
0.3
0.3 0.8
5
0.3 0.7
0.1
7
Number of atlases
0.5 0.6
0.
5 0.5
9
0.5
0.6
11 0.4
0.5
3
0.
1 0.
6
13 0.3
0.
0.6
15 0.2
0.1
0.7
17
0.30.5
0.6
0
3 5 7 9 11 13 15 17 19 21 23 25 27 29
Number of targets

31. 1
1 0.3 0.5
0.6 0.5
0.6 0.7
0.5 7 0.7
0.6 0. 0.7 0 0.9
3 .8
0.7
0.8 0.8
0.8
0.7
0.8
5 0.8
0.8
0.7
0.
0.8
8
0.8
7
Number of atlases
0. 0.8
0.7
0.8 0.6
0.8
85
8
0.
0.
9 8 0.8
0.8
0.8 0.5
0.8
0.8
11 0.8 0.4
0.85 8
0.8
0.
5
13 0.3
0.8
0.
0.8
8
5 0.85
0.2
0.8
15
0.8 5 0.1
17 5 0.8
0.
85
0.8
3 5 7 9
0.85 0.8
11 13 15 17 19 21 23 25 27 0.7
29
0
Number of targets

32. 1
1 0.1
0.3 0.1 0.3 0.1
0.5 0.3 0.1
0.5
0.5
0.6 0.7 0.7 0.6 0.7 0.6 0.9
3
0.8
0.8
0.8
0.8
0.8
5
7
0.8 0.85
0.
0.7
0.8 5
0.8 0.8
0.85
7 5
Number of atlases
0.8
0.7
0.6
5 5
0.8
0.
0.85
9
8
0.5
8
0.
11 0.85 85 0.85
0.
0.4
0.8
85
0.85 5
5
5
0.
13 0.8
0.8
0.3
0. 0
85 .8
15 0.85 0.2
5
0.8
5
0.1
0.85
0.8
17
5
0.8
0.8 0.85
0.85
0.
0.8 0
85
3 5 7 9 11 13 15 17 19 21 23 25 27 29
Number of targets

33. •
•
•