cs148: introduction to computer graphics and imaging image...

CS148: Introduction to Computer Graphics and Imaging

Image Compositing

Colbert Challenge

CS148 Lecture 14 Pat Hanrahan, Fall 2009

Key Concepts

Optical compositing and mattes The alpha channel Compositing operators Premultipled alpha Matte extraction

Optical Compositing


Image Composition

Defn: Combine foreground element with background

Examples:   Graphics arts: Selections and masks, stencils,

friskets and masking tape   Animation: cels, multiplane camera   Film: optical printing, blue screen matting   Video: chroma-keying   Computer graphics: alpha channel


Animation Cels

Appraised on Antiques Roadshow http://www.pbs.org/wgbh/roadshow/archive/200804A11.html


Multiplane Camera – Walt Disney

http://disneyandmore.blogspot.com/2007/09/walt-disney-multiplane-camera-and.html


Optical Printing

From: “Special Optical Effects,” Zoran Perisic

From: “Industrial Light and Magic,” Thomas Smith (p. 181)


Composing Two Elements

Background

Foreground Traveling Matte

Holdout Matte

*

* +

+ =

=

The Alpha Channel


The Alpha Channel

A alpha channel is an additional image that defines:   The transparency or opacity of an image   The presence or absence of imagery

  Geometric coverage: soft-edge

  Or both coverage and transparency

Alpha channels may be   Binary masks: all or none   Mattes: 0.0 to 1.0 (0 to 255)


Fragment: Color + Coverage

Pixel

C=(R,G,B)

a = A = Coverage = Area = Opacity = 1 - Transparency A

Color c of pixel is an area-weighted average of C

c = A C

Area-weighted color = pre-multiplied (with A) color

Convention: capital, not multiplied; lower, multiplied

Image Composition


OVER Operator

OVER

Foreground Background

=

Composite

aF CF

Composite color: c = AF CF + AB CB = (aF CF )+ (1-aF) (aB CB)

Composite alpha: a = AF + AB = aF + (1-aF ) aB

aB CB AF = aF AB = (1-aF ) aB


OVER Operator

OVER

Foreground Background

=

Composite

aF CF

Composite color: c = cF + (1-aF)cB

Composite alpha: a = aF + (1-aF ) aB

aB CB AF = aF AB = (1-aF ) aB


Region Coverage

+ = 4 Regions

aB aA


Porter-Duff Compositing Algebra

How many ways can two pixels be combined?

4 Regions

Region 1: 1 possibility - 0

Region 2: 2 possibilities - A or 0

Region 3: 2 possibilities - B or 0

Region 4: 3 possibilities - A, B or 0

Operators: 12 total possibilities

1 2

34


Porter-Duff Compositing Algebra

c = FAcA+FBcB


OpenGL Blending Modes

Specify src (foreground) and dst (background) F’s

Porter-Duff 0, 1, As, Ad, 1-As, 1-Ad,

Other useful modes min(As,1-Ad) – Why?


Assumptions

Uncorrelated Correlated Anticorrelated


Premultiplied Alpha

Represent as c = aC = (ar,ag,ab,a)

Advantages   Closure

  Recovering C from c would require divide by a   Display c ; c over K = c + (1-aC ) K = c   One formula for compositing color and alpha

c = cF + (1-aF) cB

  Less arithmetic Associated: OVER (1 sub, 4 muls, 4adds) Unassociated: OVER (1 sub, 7 muls, 4 adds)


Interpolating RGBA

Two ways of interpolating an image 1.  Interpolate a and C; then multiply c = a*C 2.  Interpolate premultiplied colors c These lead to different answers

For example, suppose we interpolate (C, a) = (1,0,0,0) and (0,1,0,1) at ½.

1.  (1/2(1+0),1/2(0+1),1/2(0+0),1/2(0+1)) = (1/2,1/2,0,1/2); then we multiply by a to get (1/4,1/4,0,1/2)

2.  First we multiply to get (0,0,0,0) and (0,1,0,1); then we interpolate to get (0,1/2,0,1/2)


Which Way is Correct?

Interpolating composited images Composite foreground over the background and

then interpolate Interpolate foreground and background and then

composite These should yield the same result!

Only true if we interpolate c (method 2 on prev. slide)

Matte Extraction


Blue Screen


“Pulling a Matte” - Matte Creation

From digitized images   Image processing

  Set of colors marked transparent, region growing …   Demonstration: Photoshop Magic Wand

  Video or chroma-keying   Range of luminances marked transparent

  Blue-screen matting (Petro Vlahos)   Separate blue background from foreground image


Blue/Green-Screen Matte Extraction

Given: C - Observed color (RGB) CB - Backing color = blue or green (RGB)

Compute foreground color and alpha (RGBA) cF = (aF RF, aF GF, aF BF, aF)


Blue/Green-Screen Matte Extraction

Compositing equation: C = cF + (1-aF) CB

R = (aF RF) + (1-aF) RB

G = (aF GF) + (1-aF) GB

B = (aF BF) + (1-aF) BB

Knowns: (R,G,B) and (RB, GB, BB) Unknowns: (RF, GF, BF, aF ) or (rF, gF, bF, aF )

3 equations in 4 unknowns


Petros Vlahos Algorithm

Divide color space into two regions

The separating plane is given by the equation G = k2 B That is, colors with lots of green are outside

B

G

K

G = k2 B

CB

C Outside

C Inside



Observed colors may be inside the region or outside Colors inside are opaque Colors outside are composited with Cb

B

G

G = k2 B

CB

C Outside

C Inside

K



Outside colors cF are on a line between CB and C C = aF CF + (1-aF) CB = cF + (1-aF) CB => cF = C - (1-aF) CB

But where? We don’t know aF

B

G CB

CF

1-aF C aF

K



Outside colors are assumed to be on the plane

N cF = N C - (1-aF) A CB = 0 We now have a 4th equation and can solve for 4 unks.

B

G

K

G = k2 B

CB

CF

1-aF C N = (0,1,-k2) aF


Things to Remember

Classic techniques: masks, mattes, optical printing Definition of the alpha channel as opacity/coverage Premultiplied alpha Porter-Duff image compositing algebra Vlahos matte extraction algorithm

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