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