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Title: ??????:HTML

1
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2
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3
10/8????????

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???miyazaki _at_ hiroshima-cu.ac.jp
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http//cat.middlebury.edu/stereo/data.html
http//vision.middlebury.edu/stereo/data/
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PDF????????????
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4
10/15????????

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http//cat.middlebury.edu/stereo/data.html
http//vision.middlebury.edu/stereo/data/
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5
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6
10/29???????2???????

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2???????????????????
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????OS,????(?????),?????????,???????????
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7
11/5??a????????

??11/24(????????)?18?
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???miyazaki _at_ hiroshima-cu.ac.jp
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??????,???????????????
a??????????????????????????????
????OS,????(?????),?????????,???????????
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8
11/26???????????????

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?)
??????HTMLGIFJPG, PDF/Word, ppt??????????,?????
??????
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???miyazaki _at_ hiroshima-cu.ac.jp
12/1 ??????????????????????,HTML/PDF/Word/ppt???
1/14??????????????????????,???????????(???PC?????
)
1/14 ????????????????????,?????????????????????
???.HTMLGIFJPG???.??????????????.
??,????,???????,??,???????
??????????????????,????????????????????
http//cat.middlebury.edu/stereo/data.html
http//vision.middlebury.edu/stereo/data/
????2???????????????????,a????????????????????????
,??????????????????????????
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????OS,????(?????),?????????,???????????
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9
12/3??ITS???12/1011

??12/15(???????)?18?
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????????
???miyazaki _at_ hiroshima-cu.ac.jp
ITS???????????????????????.?????????????????,???
??,????,???????,??,???????
ITS????1.5???????,??????

10
2 ????????????????????????????,?????????

10/08 02 ????????????????????????????????????(
??????????????)????????

11
?????
12
??????

?????????????????(max-flow/min-cut,Normalized
Cut, Swendsen-Wang Cut, ?)??????????????,??????max
-flow/min-cut??????????MRF??????????????????????
max-flow/min-cut?????Ford-Fulkerson???????Push-rel
abel???????????????????????????????,??????max-flow
/min-cut??????????MRF??????????????????????
max-flow/min-cut?????????????

13
?????????

???(???????)????
??????????,???????????????????????
?????????????????(640x480?2????????1?????)
???????,???????????????????????????

14
?????????

?????????????
?0,1,2,...0.1, 0.2, 0.3, ...??A, ??B, ??C, ...
???????????????????????????????0.1, 0.5, -7.1,
3.4, ...
?????????????????
??????????????????
?????????????????????????1?????????????
?????????????????????????????????????
?????????????????,????????????????

15
??????????????????

???????????????????????????
???????????????????
??????????????????,?????????????????????????
????????????????????????????,???????????
??????????????????????????

16
GC?BP

Graph cut (??????,?????,??????)?Belief
propagation (????????????,?????,?????,???????,????
????,?????)??????
???????
????,????,????,??,???????,
???????graph cut????belief propagation????????????
??,???????????????
???????????
?????????Markov Random Field(???????)????????????

17
3 ?????????,?????????

10/15 03 2??????????

18
???

?????????(xl,yl)????,???????
?????(xl,yl)?????????????????????
?????????????????
?????????????,??????????
???????(xr,yr)????(xl,yl)(xl-DISPMAX,yl)??????
DISPMAX?????????
???,tsukuba???????????15?????????????????
Middlebury??????(???)dmin.txt?(???230?)???????????
?
y????????????????
?????????,y??????????????????????????rectification

19
???

(xl,yl)?(xr,yr)???????????????????,?????????????
1???????????????????
??55(?33?77?)?????????????????
??????????????
SSD?SAD?0?????,????????
???-11???,????????
?????????????

(a) SAD (sum. of absolute difference)
(b) SSD (sum. of squared difference)
(c) Correlation
-
20
4 ???-???????,??????????????

10/22 04 ??????????

21
????????????

????????????????????
????????????????????????????????????????????2?????
???????????????????????????????????
?????? V s,o,p,q,r,t ???????????????? s ?? ??
t ?????? 5 ????????????????????

22
?1
?2
?3
23
???-???????

?1??????????????????????.
source?s,sink?t?????.
s??t??????????????????.
???????2?????.
???Ford-Fulkerson??????????????????.
???????????,???23????????????.
?3????????.
s-t?????,????s?t??????????????.
??????,???????,s??t?????????.
????????????????????????.
?????1274?????23??.
9???????????????????.
???????23???????????.

24
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????????????????
??????,?????????????????
???????????????
?????????????,API????????????
?????????????????
???????????

25
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?? ?????? 3???????
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26
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?????????????,?????1?1??????? ???1???,????????????
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27
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28
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29
????????????1?????
????????????????? ????????????0,????1?????
???
? ?
0
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30
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31
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32
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33
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34
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35
??????

http//www.cs.adastral.ucl.ac.uk/vnk/software.htm
l
http//www.cs.cornell.edu/rdz/graphcuts.html
http//www.cs.ucl.ac.uk/vladkolm/software.html
http//www.adastral.ucl.ac.uk/vladkolm/software.h
tml
http//www.csd.uwo.ca/faculty/olga/code.html
http//vision.middlebury.edu/MRF/code/
http//vision.middlebury.edu/MRF/eccv06/
http//www.caam.rice.edu/optimization/L1/pgc/
http//www.caam.rice.edu/wy1/ParaMaxFlow/
http//jerome.berbiqui.org/total-variation-code/
http//avglab.com/andrew/soft.html
http//research.microsoft.com/en-us/um/people/pkoh
li/code.html
http//maven.smith.edu/nhowe/research/code/
http//opencv.jp/
http//www.cs.ucl.ac.uk/staff/V.Kolmogorov/softwar
e.html

???????????????4????,??????????????
http//www.cs.ucl.ac.uk/staff/V.Kolmogorov/softwar
e.html?MAXFLOW??????????????

36
?????????????????????
sink
6
5
3
node0
node1
4
1
2
source
37
????
sink
1
4
1
1
1
8
1
node0
node1
node2
node3
1
8
1
1
1
4
4
source
38
????????????
?????????? typedef Graphltint,int,intgt
GraphType GraphType g new GraphType(/estimate
d of nodes/ 4, /estimated of edges/ 3)
g -gt add_node() g -gt add_node() g -gt
add_node() g -gt add_node() g -gt
add_tweights( 0, / capacities / 4, 1 ) g -gt
add_tweights( 1, / capacities / 1, 4 ) g -gt
add_tweights( 2, / capacities / 1, 1 ) g -gt
add_tweights( 3, / capacities / 4, 1 ) g -gt
add_edge( 0, 1, / capacities / 1, 1 ) g -gt
add_edge( 1, 2, / capacities / 8, 8 ) g -gt
add_edge( 2, 3, / capacities / 1, 1 ) int
flow g -gt maxflow() printf("Flow d\n",
flow) printf("Minimum cut\n") if
(g-gtwhat_segment(0) GraphTypeSOURCE) printf(
"node0 is in the SOURCE set\n") else printf("nod
e0 is in the SINK set\n") if (g-gtwhat_segment(1)
GraphTypeSOURCE) printf("node1 is in the
SOURCE set\n") else printf("node1 is in the
SINK set\n") if (g-gtwhat_segment(2)
GraphTypeSOURCE) printf("node2 is in the
SOURCE set\n") else printf("node2 is in the
SINK set\n") if (g-gtwhat_segment(3)
GraphTypeSOURCE) printf("node3 is in the
SOURCE set\n") else printf("node3 is in the
SINK set\n") delete g
39
2???????????????
sink
6
1
4
6
4
9
2
8
6
8
2
4
3
5
9
5
7
1
source
2
???
?
????????
2
??????????????, ????????????,????????????????
40
5 ????,???2???????

10/29 05 2??????????????

41
????
??2??
??1??
????????? ?????????
???????
?????? ???????
42
????
??2??
??1??
??,?????????(???)??????? ??????????????????????? ?
??????,???192?????1,???64?????2
?????????????????????????
?????????????192???????1 ?????????????64???????2
43
????
??2??
??1??
??????????????????? ??1????1,??2????2???
??????????
?????????????192???????1 ?????????????64???????2
???,??????????????????
44
????
??2??
??1??
?????1?????,??????????1??????? ??????????,????????
??????????
????????????????????????????
??????????????1???????1 ??????????????2???????2
45
????
??2??
??1??
??????????4???????????,????
????????????????2??????????????
?????2????????? ??????????????
?????2????????? ??????????????
C?0????? 0??C?????????,???????????????, ?????????2
??????????????
46
????
???
??2 ?
D(2,I(q))
D(2,I(p))
C
p
q
D(1,I(q))
D(1,I(p))
? ??1
???
????????????????1?,??2????????? ?????????????????,
??????????? ??????????????????,??????????????????
????????????????,maxflow????,?????????
47
??????
LazySnapping?Grabcut????,????????????
??????????????????????, ??????????????????? ??????
???,???????????????????????????
48
6 a??,????????

11/05 06 a??????????.??????????????????????

49
?????????????
??
????
????? ???
?????? ???
50
??????????

?????????????
?????
a????????

????????????,0255?????
???????????????????????, 256??(0255??)?????????
???????????????????????????, ?????????????????????
?
51
?????
??????
????fp?????Ip????????????????
???????
???????????a?b???????????????
c????????,?????????????????????????
d?????????????
c0?c1??????
d???????
???????????????????????
52
?????
(????)???????????? ???????????????????????????
??????????????????????? ?????????????????????????
53
???????
sink
sink
?????? ??????????
source
source
54
???????
????????????????,?????????????? ??????,???????????
?? ???????????????????, ?????????(x,y)??????????
????
x0
x1
x2
x3
??????????? 43
y0
(x,y)?(x1,y)?????????? 33
y1
(x,y)?(x,y1)?????????? 42
y2
55
???????
???????
???????????????????,????
A??????2??????????,????????
???,????1???????2??????
?????????
???
??
56
???????
sink
??p???q???????? ???a???
a
a
a
p
q
fp
fq

Q. ??????
??.?????????,
???0255?256????

??p????????fp ??q????????fq
source
Q. ??????????? A. ?????????.???????????????
57
???????
??p?????fp????a????????????????????? ??q?????fq???
?a?????????????????????
sink
Q. ???a??? A. ???????

Q. ??????
??.?????????,
???0255?256????

a
a
a
p
q

Q. ????????????
?????.a?????????????
????????

fp
fq
source
58
???????
??????????????? ????????????????????
sink
D????????V????????
?????????????????????
a
a
??????
a
p
q
???????
fp
fq
source
59
???????
??????
???????
???,??p????Ip?128 ??q????Iq?60 ??r????Ir?80 ?????p
????fp?192 ?????q????fq?75 ?????r????fr?70 ?????a(
??????????)?110 c1 ?????,
sink
a
a
a
p
q
fp
fq
source
60
???????
???????????????
Q. ???????? A. ????????????????
sink
??p????a????, ??q????fq?????, ??r????fr??????? ???
????????
30
18
a
a
0
a
50
0
q
apq
82
35
r
aqr
35
40
p
117
fp
fq
15
5
fr
10
64
????????(fp,fq,fr)211 ???????(a,fq,fr)83
source
61
???????
???????????????????????(?????)
sink
??????????
??a????110????, ??????(fp,fq,fr,...)? 110?????????
30
18
a
a
0
a
50
0
q
apq
82
35
r
aqr
35
40
p
117
fp
fq
15
5
fr
10
64
??,a?0255?? ????????
source
62
a??

for a0255
???????????????????
????????
?????????????

???????A?????B?????2?????????????? ???2??????????
a????????????256????,????????????
Q. ???????????????????? A. ????????????????????
63
a??

?????
for p???????
fp???
end for
E???????
for ???0???????
success0
for a0255
???????
?????????
for p???????(???640x480)
????,???,?????D(fp),?????D(a)???
end for
for (p,q)??????(???639x480640x479)
???a?,?????V(fp,fq),?????V(a,a)???
???p????a???????(???)?V(fp,a)???
???a????q???????(???)?V(a,fq)???
end for
?????????????????

64
????????? typedef Graphltfloat,float,floatgt
GraphType GraphType graph
?????????????? graph new GraphType(??????????64
0x480639x480640x479, ??????????639x480x2640x47
9x2) delete graph
?????????? graph-gtadd_node(??????????640x480639x
480640x479)
65
????????????????????? graph-gtadd_tweights( ?????,
??????????????, ??????????????)

Q. ????????
????????.?????????????????.
???,????n????????,???0n-1?????.

Q. ???????????????????
????????????????????.
???????????????,?????????????????.
?????????????????????????.
??????,??????????????,
?????????????????,????????????0n-1???,
????????????

66
??????????????????????? graph-gtadd_edge(?????i,
?????j, ???i?????j??????????, ???j?????i??????????
) ?????,????????????
????????????????????? graph -gt maxflow()
?????????????? if(graph-gtwhat_segment(?????)
GraphTypeSOURCE) ??????????????????????????? ???
????????????????????????????? if(graph-gtwhat_segme
nt(?????) GraphTypeSINK) ????????????????????
??????? ????????????????????????????????
Q. ??????????????? A. ?????????????????.???,?????
fp,?????a,???.
67

Q. ??????
???????????.??????????????.
??????????0255??????????????????.

Q. ???????????????????
??????????????.
???????RGB?????????????????.

Q. ???????????????
?????????????.
??,????????????,??????????.
??????????????,?????????????????,
?????????????????????.
???????,?????????????????.
??????????????,??????????????????????.
(????????????????????????????.???,
????????,??????????????,???????????
???????????????)

68
Q. ???????? A. ??????????????????.????????????????
????
??????
???????
Q. ??????? A. ?????????????.??????????
???,P?????????,N??????????????
???,?????,????640x480??, ???????639x480640x479
69
??????????????? ?????????????????????????? ???????
?? ?????????????????????????????????? ?????256x256
??????????????
?????,V(a,a)0???. fpfq???,V(fp,fq)0???. fpfq??
?,V(fp,a)V(a,fq)???.
a
a
a
a
a
p
q
p
q
fp
fq
fpfq
fqfp
????????? ??????????? a???????
70

Q. ????????????.?????????????????
??????????,?????????????.
??????????????,??????????.
????,?????????????????????.

?????
for p???????
fp???
end for
for ???02(???????????????????????)
for a0255
???????
?????????
for p???????(???640x480)
????,???,?????D(fp),?????D(a)???
end for
for (p,q)??????(???639x480640x479)
???a?,?????V(fp,fq),?????V(a,a)???
???p????a???????(???)?V(fp,a)???
???a????q???????(???)?V(a,fq)???
end for
?????????????????
?????????????????
??????

Q. ???????????semimetric???????????????????.
regular??????????????????????,?????????????
?????????????????????.
Q. QPBO, roof-duality??????????
???????????.
Q. ????????????????????????
A. ?????????,Miyazaki????????????????.

72
7 a???????,?????

11/12 07 a??????????????

73
???

?????????(xl,yl)????,???????
?????(xl,yl)?????????????????????
?????????????????
?????????????,??????????
???????(xr,yr)????(xl,yl)(xl-DISPMAX,yl)??????
DISPMAX?????????
???,tsukuba???????????15?????????????????
Middlebury??????(???)dmin.txt?(???230?)???????????
?
y????????????????
?????????,y??????????????????????????rectification

74
???

(xl,yl)?(xr,yr)???????????????????,?????????????
1???????????????????
??55(?33?77?)?????????????????
??????????????
SSD?SAD?0?????,????????
???-11???,????????
?????????????

(a) SAD (sum. of absolute difference)
(b) SSD (sum. of squared difference)
(c) Correlation
-
75
??????????

??????????????????
?????
a????????

???2????,??(disparity)0DISPMAX????? DISPMAX??????
???
???????????????????????, 0DISPMAX?????????
???????????????????????????, ?????????????????????
?
76
?????
??????
SAD?????? ????????
???????
??????????fp?fq??????????????? ?????(???)?????????
c????????,??????????????????????
d?????????????
c0?c1??????
T????????
d???????
???????????????????????
??????????????????? ?????????????????????????????
???????????,???????????
77
???????
sink
sink
?????? ??????????
source
source
78
???????
????????????????,?????????????? ??????,???????????
?? ???????????????????, ?????????(x,y)??????????
????
x0
x1
x2
x3
??????????? 43
y0
(x,y)?(x1,y)?????????? 33
y1
(x,y)?(x,y1)?????????? 42
y2
79
???????
sink
??p???q???????? ???a???
a
a
a
p
q
fp
fq

Q. ??????
??.????????,
???0DISPMAX??

??p????????fp ??q????????fq
source
Q. ??????????? A. ?????????.???????????????
80
???????
??p?????fp????a????????????????????? ??q?????fq???
?a?????????????????????
sink
Q. ???a??? A. ???????
a
a
a
p
q

Q. ????????????
?????.a?????????????
????????

fp
fq
source
81
???????
??????????????? ????????????????????
sink
D????????V????????
a
a
a
p
q
fp
fq
source
82
a??

?????
for p???????
fp???
end for
E???????
for ???0???????
success0
for a0DISPMAX
???????
?????????
for p???????(???640x480)
????,???,?????D(fp),?????D(a)???
end for
for (p,q)??????(???639x480640x479)
???a?,?????V(fp,fq),?????V(a,a)???
???p????a???????(???)?V(fp,a)???
???a????q???????(???)?V(a,fq)???
end for
?????????????????

Q. ???????????????
?????????????.
??,????????????,??????????.
??????????????????,???????,
??????????????????????????????????????.
??????????????????????OK.

?????????, ????????????, ?????????????????????????
??
84
8 ????????,????????

11/19 08 ????????????????

85
a???????????

for a063
???????????????????
????????
?????????????

a??
316???

for i011
a??????
???????????????????
????????
?????????????

????????
http//www.cg.info.hiroshima-cu.ac.jp/miyazaki/pu
blication/project/shadow/indexe.html
86
Approach based on alpha expansion
Alpha expansion
Hierarchical graph cut
1
5
1
5
3
3
1
5
1
5
5
1
2
alpha2
3
1
5
2
2
4
1
alpha2,4,...
3
5
1
2
4
4
2
1
5
alpha4
3
4
5
87
Hierarchical structure
32
16
32
48
16
48
8
16
24
32
40
48
56
16
32
48
8
24
40
56
8
16
24
32
40
48
56
88
Graph construction example
a
p
a
q
b
89
(No Transcript)
90
Algorithm
Alpha expansion
Hierarchical graph cut

A 0, 32, 16, 48,8, 40, 24,
56,4, 20, 36, 52, 12, 28, 44, 60, ...,3,
7, 11, ..., 63
for i 0 to 11 do
for all nodesedges do
add nodesedges using
solve max-flow/min-cut problem
Iterate 2 until convergence

A 0, 1, 2, ..., 63
for i 0 to 63 do
for all nodesedges do
add nodesedges using
solve max-flow/min-cut problem
Iterate 2 until convergence

91
(No Transcript)
92
063???????(n64)
A 0, 32, 16, 48,8, 40, 24,
56,4, 20, 36, 52, 12, 28, 44, 60, 2, 10,
18, 26, 34, 42, 50, 58, 6, 14, 22, 30, 38, 46,
54, 62, 1, 5, 9, 13, 17, 21, 25, 29, 33, 37,
41, 45, 49, 53, 56, 60, 3, 7, 11, 15, 19, 23,
27, 31, 35, 39, 43, 47, 51, 55, 59, 63
???????????????????,???????????????????? ??????2??
??????????? ??????(?????063)??????????? ?????????
???,?????????????????????????
93
Output of Hierarchical graph cut
Stereo matching Art
Stereo matching Laundry
Image restoration
Shadow removal
Input
Ground truth
Ishikawa 2003
a expansion
Hierarchical cut
94
Speed of hierarchical graph cut
Stereo matching Art Stereo matching Laundry Image restoration Shadow removal
Speed-up ?6.8 ?11.4 ?16.6 ?3.4
Error difference 4.6 3.0 -0.4 0.0
Hierarchical graph cut
Alpha expansion
1.1?107
1.7?106
Energy
Energy
0
1.5?106
sec
250
Iteration
7
95
?????????????
??
????
????? ???
?????? ???
96
??????????

?????????????
?????
????????

????????????,0255?????
???????????????????????, 256??(0255??)?????????
???????????????????????????, ?????????????????????
?
97
?????
??????
?????p?????Ip????????????????
???????
????????????p??pq???????????????
c????????,?????????????????????????
d?????????????
c0?c1??????
d???????
???????????????????????
98
???????
sink
sink
?????? ??????????
source
source
99
???????
????????????????,?????????????? ??????,???????????
?? ???????????????????, ?????????(x,y)??????????
????
x0
x1
x2
x3
??????????? 43
y0
(x,y)?(x1,y)?????????? 33
y1
(x,y)?(x,y1)?????????? 42
y2
100
???????
sink
??p???q???????? ???a???
ap
aq
a
p
q
ßp
ßq

Q. ??????
??.?????????,
???0255?256????

??p????????ßp ??q????????ßq
source
Q. ??????????? A. ?????????.???????????????
101
???????
??p?????ßp????ap????????????????????? ??q?????ßq??
??aq?????????????????????
sink
Q. ???a??? A. ???????

Q. ??????
??.?????????,
???0255?256????

ap
aq
a
p
q

Q. ????????????
?????.??????????????
?????????????

ßp
ßq
source
102
???????
???????????????
sink
D????????V????????
ap
e????????????? ????????????????2??
aq
a
p
q
ßp
ßq
source
103
???????

Q. max(a,b)???
a?b???????
??????????

???
sink
a
p
q
source
Q. 8?????? A. ????????(???1?)???
104
???????

Q. max(a,b)???
a?b???????
??????????

???
sink
a
p
q
source
Q. 8?????? A. ????????(???1?)???
105

?????
for p???????
ßp???
end for
A0,...,3,...,63
E???????
for ???0???????
success0
for i011
???????
?????????
for p???????(???640x480)
Ai???,ßp???????ap???
????,?????D(ßp),?????D(ap)???
end for
for (p,q)??????(???639x480640x479)
Ai???,ßp???????ap???
Ai???,ßq???????aq???
???a?,?????V(ßp,ßq),?????V(ap,aq)???

106
Q. a??????????? A. ?????i????,Ai???ß(??????)????
??????
????64???,?Ai????, A01, A11, A21,
A31, A42, A52, A64,
A74, A88, A98, A1016,
A1116 ????,?????????64??? (???? ??????)
?A64,20,36,52???? ??????ßp?13???? ap????20??
?
?????
???,_ _?????????????
107

Q. ??????
???????????.??????????????.
??????????0255??????????????????.

Q. ???????????????????
??????????????.
???????RGB?????????????????.

Q. ???????????????
?????????????.
??,????????????,??????????.
??????????????,?????????????????,
?????????????????????.
???????,?????????????????.
??????????????,??????????????????????.
(????????????????????????????.???,
????????,??????????????,???????????
???????????????)

108
??????????????? ?????????????????????????? ???????
?? ?????????????????????????????????? ?????256x256
??????????????
apaq??ßpßq???
?????????
a
a
ap
aq
a
p
q
p
q
ßp
ßq
ß
ß
109

Q. ????????????.?????????????????
??????????,?????????????.
??????????????,??????????.
????,?????????????????????.

(?????????????)
for ???02(???????????????????????)
for i011
(?????????????)
?????????????????
?????????????????
??????
end for
end for

110
?????????????????????????? ??????a????????????????
????? ???????????????????????????????, ???????????
??????????????
111
9 ?????????????,?????

11/26 09 ????????????????????

112
???

?????????(xl,yl)????,???????
?????(xl,yl)?????????????????????
?????????????????
?????????????,??????????
???????(xr,yr)????(xl,yl)(xl-DISPMAX,yl)??????
DISPMAX?????????
???,tsukuba???????????15?????????????????
Middlebury??????(???)dmin.txt?(???230?)???????????
?
y????????????????
?????????,y??????????????????????????rectification

113
???

(xl,yl)?(xr,yr)???????????????????,?????????????
1???????????????????
??55(?33?77?)?????????????????
??????????????
SSD?SAD?0?????,????????
???-11???,????????
?????????????

(a) SAD (sum. of absolute difference)
(b) SSD (sum. of squared difference)
(c) Correlation
-
114
Output of Hierarchical graph cut
Stereo matching Art
Stereo matching Laundry
Image restoration
Shadow removal
Input
Ground truth
Ishikawa 2003
a expansion
Hierarchical cut
115
??????????

??????????????????
?????
????????

???2????,??(disparity)0DISPMAX????? DISPMAX??????
???
???????????????????????, 0DISPMAX?????????
???????????????????????????, ?????????????????????
?
116
?????
??????
SAD?????? ????????
???????
??????????fp?fq??????????????? ?????(???)?????????
c????????,??????????????????????
d?????????????
c0?c1??????
T????????
d???????
???????????????????????
c0?c1
??????????????????? ?????????????????????????????
???????????,???????????
117
???????
sink
sink
?????? ??????????
source
source
118
???????
????????????????,?????????????? ??????,???????????
?? ???????????????????, ?????????(x,y)??????????
????
x0
x1
x2
x3
??????????? 43
y0
(x,y)?(x1,y)?????????? 33
y1
(x,y)?(x,y1)?????????? 42
y2
119
???????
sink
??p???q???????? ???a???
ap
aq
a
p
q
ßp
ßq

Q. ??????
??.????????,
???0DISPMAX??

??p????????ßp ??q????????ßq
source
Q. ??????????? A. ?????????.???????????????
120
???????
??p?????ßp????ap????????????????????? ??q?????ßq??
??aq?????????????????????
sink
Q. ???a??? A. ???????
ap
aq
a
p
q

Q. ????????????
?????.??????????????
?????????????

ßp
ßq
source
121
(No Transcript)
122
???????
???????????????
sink
D????????V????????
ap
e????????????? ????????????????2??
aq
a
p
q
ßp
ßq
source
123
???????

Q. max(a,b)???
a?b???????
??????????

???
sink
a
p
q
source
Q. 8?????? A. ????????(???1?)???
124
???????

Q. max(a,b)???
a?b???????
??????????

???
sink
a
p
q
source
Q. 8?????? A. ????????(???1?)???
125
Algorithm
Alpha expansion
Hierarchical graph cut

A 0, 32, 16, 48,8, 40, 24,
56,4, 20, 36, 52, 12, 28, 44, 60, ...,3,
7, 11, ..., 63
for i 0 to 11 do
for all nodesedges do
add nodesedges using
solve max-flow/min-cut problem
Iterate 2 until convergence

A 0, 1, 2, ..., 63
for i 0 to 63 do
for all nodesedges do
add nodesedges using
solve max-flow/min-cut problem
Iterate 2 until convergence

126
(No Transcript)
127

?????
for p???????
ßp???
end for
A0,...,3,...,63
E???????
for ???0???????
success0
for i011
???????
?????????
for p???????(???640x480)
Ai???,ßp???????ap???
????,?????D(ßp),?????D(ap)???
end for
for (p,q)??????(???639x480640x479)
Ai???,ßp???????ap???
Ai???,ßq???????aq???
???a?,?????V(ßp,ßq),?????V(ap,aq)???

128
063???????(n64)
A 0, 32, 16, 48,8, 40, 24,
56,4, 20, 36, 52, 12, 28, 44, 60, 2, 10,
18, 26, 34, 42, 50, 58, 6, 14, 22, 30, 38, 46,
54, 62, 1, 5, 9, 13, 17, 21, 25, 29, 33, 37,
41, 45, 49, 53, 56, 60, 3, 7, 11, 15, 19, 23,
27, 31, 35, 39, 43, 47, 51, 55, 59, 63
???????????????????,???????????????????? ??????2??
??????????? ??????(?????063)??????????? ?????????
???,?????????????????????????
129
Q. a??????????? A. ?????i????,Ai???ß(??????)????
??????
????64???,?Ai????, A01, A11, A21,
A31, A42, A52, A64,
A74, A88, A98, A1016,
A1116 ????,?????????64??? (???? ??????)
?A64,20,36,52???? ??????ßp?13???? ap????20??
?
?????
???,_ _?????????????
130

Q. ???????????????
?????????????.
??,????????????,??????????.
??????????????????,???????,
??????????????????????????????????????.
??????????????????????OK.

????????????????, ???????????? ???,?????????????,
????????????????????????
131
??????????????? ?????????????????????????? ???????
?? ?????????????????????????????????? ?????256x256
??????????????
apaq??ßpßq???
?????????
a
a
ap
aq
a
p
q
p
q
ßp
ßq
ß
ß
132