poisson matting - image system laboratory...2016/02/03 · alpha channel matting 2019-04-10 7 -...
TRANSCRIPT
2019-04-10
Poisson Matting
ISL
안재원
※ Sun, Jian, et al. "Poisson matting." ACM Transactions on Graphics (ToG) 23.3 (2004): 315-321.
Matting
Poisson Equation
Poisson Matting
Result
2019-04-10
2
Matting2019-04-10
3
- Intro
3
I : 획득 영상J : 원본 영상t : 전달량A : 대기광Matting equation
))(1()()()( xtAxtxJxI
※ Haze Image Model
Matting2019-04-10
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- Matting example
Matting2019-04-10
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- Matting equation
I : 획득 영상F : Foreground
B : BackGround
𝛼 : Alpha channel
))(1()()()( xtAxtxJxI
※ Haze Image Model
BαFαI )1(
※ Matting equation
Matting2019-04-10
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- Matting
Input Image User Trimap
Unknown
Background
Foreground
Probabilistic Model
Bayesian Model
Poisson Model
Closed Form Model
Alpha channel
Matting2019-04-10
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- Problem
Poisson Equation2019-04-10
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- Usage
<The Poisson Equation>
1. Shadow removal
2. Tone mapping
3. Image editing
4. Surface reconstruction
Poisson Equation2019-04-10
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- Equation
T
nx
f
x
ff ),,(
1
- Gradient
nx
f
x
ff
1
- Divergence
f 2
),(),()(2
2
2
2
yxfyxyx
- The Poisson Equation
Second order PDE(Partial Differential Equation)
)( BF
Idiv
- Estimate Alpha channel
Poisson Matting2019-04-10
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- Intro
<Assumption>
- Locally smooth(foreground, background)
<Overview>
1. Start with a user trimap
2. Estimate alpha values in unknown area.
3. Refine trimap
4. Back to ‘2.’
0F
0B
Background ForegroundUnknown Background ForegroundUnknown
Poisson Matting2019-04-10
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- Calculating 𝛼
BαFαI )1(
※ Matting equation
BαFααBFI )1()(
Background ForegroundUnknown
αBFI )(
)( BF
Iα
1. Alpha channel 과 image의 gradient는 비례함.
2. 적분을 통해 Alpha channel을 구할 수 있음.
Poisson Matting2019-04-10
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- Calculating 𝛼
ppp
p
p dpBF
I2
*
)(minarg
pB
pF : Nearest foreground pixel
: Nearest background pixel
- Variational problem(Guided interpolation)
- Poisson Equation
BF
Idiv
※ Pérez, Patrick, Michel Gangnet, and Andrew Blake. "Poisson image editing."ACM Transactions on Graphics (TOG). Vol. 22. No. 3. ACM, 2003.
Poisson Matting2019-04-10
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- Calculating 𝛼
- Poisson Equation
BF
Idiv ),(
2
2
2
2
yxfyx
h
h
h
h
),(),(4),(),(),(),(
2yxf
h
yxhyxhyxyhxyhx
),(
),(
),(
),(
),(
),(
11411 yxf
hyx
hyx
yx
yhx
yhx
Poisson Matting2019-04-10
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- Calculating 𝛼
6
52
4
8
7
93
1
410
141
014
410
141
014
410
141
014
100
010
001
000
000
000
000
000
000
100
010
001
100
010
001
100
010
001
),(
),(
),(
),(
),(
),(
),(
),(
),(
),(
),(
),(
),(
),(
),(
),(
),(
),(
99
88
77
66
55
44
33
22
11
99
88
77
66
55
44
33
22
11
yxf
yxf
yxf
yxf
yxf
yxf
yxf
yxf
yxf
yx
yx
yx
yx
yx
yx
yx
yx
yx
연립방정식을 풀어 Unknown영역의 Alpha channel값을 구한다.
),(
),(
),(
),(
),(
11411
hyx
hyx
yx
yhx
yhx
Poisson Matting2019-04-10
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- Optimization
FFF BBB
- New trimap
pppF FIinp ,95.0|
pppB BIinp ,05.0|
- Refinement
- 2~3회 반복.
Result2019-04-10
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- Intro
Result2019-04-10
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- Intro
Q & A
2019-04-10