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Natural lighting Directional lighting
11ON̂ 22ON̂ kˆ ONk
11n
2nPn
2 P
0
0
...
0
...
...
Env. map Normal space
Matrix
completion
OutputLocal ambiguity Angular distance matrix Global ambiguity
Integrability constraint
SVD,Constant albedo
Input images Equivalent directional lighting
N̂ N
Shortest path
Patch extraction
21 nn ,
21 nn , P2nn ,
P2nn ,P1
nn ,
P1nn ,
...1l 1N
Patchsize
Env.Maps
r = 1 r = 10 r = 30 r = 50 r = 80
Normal space
Surface
�1
�1 �1
�2�2
�2�3
�3 �3(�4)
�4 �5
�5
SPHERE
BEAR
BUNNY
Environment maps
GT normal Rendered images
Up to rotation Complete solution Up to rotation Complete solution Up to rotation Complete solution
6.89
6.24
6.06
7.35
6.51
6.37
6.04
5.67
5.53
6.55
6.16
6.09
9.29
8.51
7.93
10.69
9.70
8.18
6.29
6.12
6.05
7.99
7.83
6.25
12.69
12.26
11.31
15.04
13.78
12.24
10.02
9.90
9.07
12.91
12.04
10.26
7.49 56.41
6.87 54.40
8.89
5.91
13.27
6.52
13.55
10.67
16.01
13.89
OursRendered images PF14
OursInput images YY13 Ours HJ15GT
Input image
20.69 28.99
18.23 26.31 0
10
20
30
40
50
60
Error map