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# Matting - PowerPoint PPT Presentation

Matting. Roey Izkovsky Yuval Kaminka. Helping Superman fly since 1978. Outline. The matting problem Previous work New approaches: The iterative approach Jue Wang, Michael F.Cohen Closed form solution Anat Levin, Dani Lischinski,Yair Weiss Comparison and summary Bonus?. Outline.

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### Matting

Roey Izkovsky

Yuval Kaminka

Helping Superman fly since 1978

• The matting problem

• Previous work

• New approaches:

• The iterative approach Jue Wang,Michael F.Cohen

• Closed form solutionAnat Levin, Dani Lischinski,Yair Weiss

• Comparison and summary

• Bonus?

• The matting problem

• Previous work

• New approaches:

• The iterative approach Jue Wang,Michael F.Cohen

• Closed form solutionAnat Levin, Dani Lischinski,Yair Weiss

• Comparison and summary

• Bonus?

 Image and video editing

New background

Composite image

 Image and video editing

Input image

New image

• The separation of an image I into

• Foreground object image F

• Background image B

• Alpha matte α – the opacity

• Problem: extract F, B, α from image

hair

fur

• Under constrained problem:One equation, 3 unknowns

 We need to constrain the problem!

• The matting problem

• Previous work

• New approaches:

• The iterative approach Jue Wang,Michael F.Cohen

• Closed form solutionAnat Levin, Dani Lischinski,Yair Weiss

• Comparison and summary

• Bonus?

Two types:

Known background Natural image

matting matting

• Blue screen Matting

• Still under-constrained

• Solution: make more assumptions

• “Foreground contains no blue”

• Other foreground distribution assumption…

• Use two different backgrounds

• Main flaw: need to know the background…

Blue background

Composite image

• The assumptions:

• Smoothness of the alpha matte

• GMM for the Background and Foreground colors

• Initial estimate:trimap provided by the user

Background

Foreground

Unknown

Input image

Trimap

• The algorithms framework:

• Estimate F, B distributions from close pixels

• Find best α by some method

• Extrapolate F,B from close neighborhood

• Estimate α from calculated F, B values

• Estimate F, B distributions in area

• Find best α matching distributions

• P(F), P(B) from image samples

• P(C|F,B,α) using a distribution for C

• Main flaw: Accurate trimap required

• Tedious to provide manually

• Hard to extract automatically

 In particular, not feasible to videos

Input image

Trimap

Binary segmentation

Great.So let’s get started…

• The matting problem

• Previous work

• New approaches:

• The iterative approach Jue Wang,Michael F.Cohen

• Closed form solutionAnat Levin, Dani Lischinski,Yair Weiss

• Comparison and summary

• Bonus?

Trimap reduces to scribbles

Two new methods

• Iterative optimization approach

• Heuristic algorithmic optimization

• A closed form solution

• Mathematical approach

Trimap

Scribbles

### Iterative optimization approach

Jue Wang

Michael F. Cohen

• Score:

fit to image data +alpha matte smoothness

• Iteratively propagating estimated results.

• Initialize “work pixels” from scribbles

• Repeatedly:

• Expand work pixels

• Find best alpha matte

• Stop when finished

Uc = {user scribbles}

ui = 0

α = 0

ui = 0

α = 1

ui = 1

α = 0.5

Initialization

• Introducing:

• ui - uncertainty variable

• Uc – work pixels

Uc = {user scribbles + 15 pixel radius}

Our goal:

find α matte for Uc that minimizes the energy -

Smoothness

Data

N Possible values for B

Vd

Score for αp = α

Image color Ip

Vd

• Fit measure of αp to Ip

• Score for αp = α :

Fi , Bj – possible values for F, B in the pixel

wFi, wBj – corresponding weights

α = 0.4

u = 0.5

α = 0.8

u = 0.3

α = 0.4

u = 0.4

α = 0.2

u = 0.3

α = 0.9

u = 0.2

α = 0.3

u = 0.3

Vd

Fi , Bj – possible values for F, B in the pixel

wFi, wBj – corresponding weights

F Samples

B Samples

What happens when there are not enough F/B samples?

p

α = 0.5

u = 1.0

Vd

• Score for αp = α :

• Discretize

• and normalize

Vs

• Matte smoothness :

Uc = {user scribbles + 15 pixel radius}

Our goal: find α matte for Uc that minimizes the energy -

Uc Graph

Nodes = Pixels, Edges by 4-connectivity

GOAL: Minimize

BELIEF PROPAGATION

GOAL: Minimize

BELIEF PROPAGATION

t=0

y

mpq – message from p to q

q

p

Vector: p’s “opinion” for each

possible α for q

GOAL: Minimize

BELIEF PROPAGATION

t=1

y

mpq – new message pq

myp – previous message yp

q

p

GOAL: Minimize

BELIEF PROPAGATION

t=2,3,4…

y

q

p

GOAL: Minimize

BELIEF PROPAGATION

t=T (stopping time)

y

q

p

GOAL: Minimize

BELIEF PROPAGATION

t=T (stopping time)

y

q

p

Best state calculated for each node:

Found α matte for Uc that minimizes the energy -

Update F, B and uncertainty:

• Initialize Uc, F, B, u and alpha matte from scribbles

• Repeatedly:

• Expand Uc by another 15 pixel radius

• Find best alpha matte (BP)

• Update F,B,u for new matte

• Stop when total uncertainty is minimal

Initial matte

Propagation of α matte

Final matte

Input image

Extracted matte

Input image

Composite image

Extracted matte

The ambiguity bunny

Scribbles result

Trimap result

Ambiguity bunny with trimap

Ambiguity bunny with scribbles

• Minimal user input

• Applicable to video

• Sensitive to ambiguity in F, B

• Uses simple color-model

• Performance:

• 15-20 min. on a 640x480 image

• Factor 50 reported by better implementation

Fantastic.Let’s go on…

• The matting problem

• Previous work

• New approaches:

• The iterative approach Jue Wang,Michael F.Cohen

• Closed form solutionAnat Levin, Dani Lischinski,Yair Weiss

• Comparison and summary

• Bonus?

### Closed form solution

Anat Levin

Dani Lischinski

Yair Weiss

• Assumption: local smoothness in F, B

 cancel out unknowns from the matte equs.

• Solve for F,B and alphausing algebraic tricks.

Assumptions:

• F,B locally smooth.

 treat F,B as constant in a small window w

GOAL:

Minimize -

• Numerical stability

• Bias to smoother matte

wj

• GOAL:

• Minimize:

• Minimize:

3N Variables (N = image size) We can rid a, b by algebraic manipulation

• Minimize:

Theorem: for we have

Intuitively, L is some covariance matrix

• Minimize:

Proof: Rewrite in matrix form:

• Minimize:

Proof: Rewrite in matrix form:

By mean-least-squares, best a,b pair

for each window is:

• Some more manipulation give the required result

EXCITED?

T-SHIRT, NOW FOR ONLY \$1999

F2

F1

G

Closed form solution

• For color images:

• Simple: Do each channel separately

• Smart: Assume one alpha for R,G,B.Use redundancy to allow a “color-line” model per window

Color line model:

OUT: F, B Constant within a window

IN: F, B are on some line

• For color images:

• Simple: Do each channel separately

• Smart: Assume one alpha for R,G,B.Use redundancy to allow a “color-line” model per window

• For color images:

• Simple: Do each channel separately

• Smart: Assume one alpha for R,G,B.Use redundancy to allow a “color-line” model per window

Now, as before, cost is:

And a,b can be cancelled out.

Now problem reduced to finding best α for:

L is Huge size NxN (N = # image pixels)

But Sparse…

• The algorithm:

• Compute L

• Solve for given the scribbles.

• Solving a sparse set of bilinear equationswith constraints (Lagrange multipliers)

• Find F, B given the matte

• Adding smoothness assumptions on F, B

• Improvements:

• Use larger environment in low cost by “pyramids”

Extracted matte

Input image

Input image with scribbles

Problematic matte

Small eigenvectors of L are

correlated with minimal matte

L is positive definite.

Eigenbasis: v1,…,vN

Eigenvalues: λ1 > λ2 > … > λN > 0

Small eigenvectors of L are

correlated with minimal matte

Small eigenvectors of L are

correlated with minimal matte

 can guide user scribbles

Eigenvectors matching smallest eigenvalues

Resulting matte

Guided scribbles

• Minimal user input

• Provable optimality (under assumptions)

• Assumes only smooth F,B (no color model)

• Applicable to video (as we speak…)

• Problematic with textures

• Performance:

• 20-40 seconds for a 200x300 image

• Expensive in memory

Superb.Let’s sum up…

• The matting problem

• Previous work

• New approaches:

• The iterative approach Jue Wang,Michael F.Cohen

• Closed form solutionAnat Levin, Dani Lischinski,Yair Weiss

• Comparison and summary

• Bonus?

Input image

Matte ground truth

Closed form solution

Iterative approach

Poisson

Color ambiguity

Iterative approach Closed form

Sensitive Sensitive

Improving results…

Ambiguity bunny

Iterative approach

Bayesian

Closed form solution

Optimality?

Iterative approach Closed form

Provably optimal

But for the specific

(simplified) cost

Uses heuristics

to optimize

Textures

Iterative approach Closed form

F,B must satisfy

color-line model

Assumes only

Alpha matte smooth

Rough edges

Iterative approach Closed form

Input image with scribbles

Can handle rough

edges

Assumes

Alpha matte smooth

 matte results 

Running time

Iterative approach Closed form

20/40 seconds

Costly in memory

~20 sec.

(For medium size image)

Tests

Iterative approach Closed form

Extensively tested

quantitative results

No quantitative

results reported

• The matting problem

• Previous work

• New approaches:

• The iterative approach Jue Wang,Michael F.Cohen

• Closed form solutionAnat Levin, Dani Lischinski,Yair Weiss

• Comparison and summary

• Bonus?

Douglas E. Zongker ~ Dawn M. Werner ~ Brian Curless ~ David H. Salsin

C = F + (1- a)B + F

• F ~ Contribution of light from Environment that travels through the object

R – reflectance image

T – Texture image

Alpha Matte Environment Matte Photograph

Alpha Matte Environment Matte Photograph

• The matting problem

• Old methods: require trimap

• Two new methods from scribbles:

• Iterative optimization

• Assume: matte smooth, F,B locally similar

• Use heuristic optimization for alpha

• Close form solution

• Assume: F, B locally smooth (color-line model)

• Solve linear equations for alpha