Faces and Image-Based Lighting

Faces and Image-Based Lighting

Digital Visual Effectsg Yung-Yu Chuang

with slides by Richard Szeliski, Steve Seitz, Alex Efros, Li-Yi Wei and Paul Debevec

Outline

• Image-based lighting

• 3D acquisition for faces

• Statistical methods (with application to face super-resolution)p )

• 3D Face models from single images

• Image based faces

• Image-based faces

• Relighting for faces

Image-based lighting Image based lighting

Rendering

• Rendering is a function of geometry, reflectance lighting and viewing reflectance, lighting and viewing.

• To synthesize CGI into real scene, we have to t h th b f f t

match the above four factors.

• Viewing can be obtained from calibration or structure from motion.

• Geometry can be captured using 3D y p g photography or made by hands.

• How to capture lighting and reflectance?

• How to capture lighting and reflectance?

Reflectance

• The Bidirectional Reflection Distribution Function

Given an incoming ray and outgoing ray – Given an incoming ray and outgoing ray

what proportion of the incoming light is reflected along outgoing ray?

surface normal surface normal

Answer given by the BRDF:

Rendering equation

) ω , p ( _i Li

ωi

) ω , p ( _i Li

p ωo

) ω p,

( _o

Lo

5D light field )

(

L L ( )

5D light field

 ) ω p,

( _o

Lo L_e(p,ω_o)

i i i

i

o,ω ) (p,ω )cosθ ω

ω p,

2 ( L_i d



 ₂



(p, _o, _i) _i(p, _i) _{i i}



s

^

Complex illumination

 ) ω p,

( _o

Lo L_e(p,ω_o)



s^{2 f(p,ωo,ωi)Li(p,ωi)cosθi dωi}







 ) ω p,

( _o

B ₂ f(p,ω_o,ω_i)L_d(p,ω_i)cosθ_idω_i



s



 ) ω ( _o

Bp _{2 ,ω} (ω_i) (ω_i)cosθ_i ω_i

o L d

f _d

s p



p q

Point lights

Classically, rendering is performed assuming point light sources

light sources

directional source

Natural illumination

People perceive materials more easily under natural illumination than simplified illumination natural illumination than simplified illumination.

I t R D d T d Ad l

Images courtesy Ron Dror and Ted Adelson

Natural illumination

Rendering with natural illumination is more expensive compared to using simplified expensive compared to using simplified illumination

directional source natural illumination

Environment maps

Miller and Hoffman 1984 Miller and Hoffman, 1984

HDR lighting

Examples of complex environment light Examples of complex environment light

Complex illumination

 ) ω p,

( _o

Lo L_e(p,ω_o)



s^{2 f(p,ωo,ωi)Li(p,ωi)cosθi dωi}







 ) ω p,

( _o

B ₂ f(p,ω_o,ω_i)L_d(p,ω_i)cosθ_idω_i



s



 ) ω ( _o

Bp _{2 ,ω} (ω_i) (ω_i)cosθ_i ω_i

o L d

f _d

s p



reflectance lighting B th h i l f ti Both are spherical functions

Function approximation

• G(x): the function to approximate

• B₁(x), B₂(x), … B_n(x): basis functions

• We want

) ( )

( x c B x

G ^{( ) } 

ⁿ _{i i}

^{( )}

1

x B c x

G

_i

i



i



• Storing a finite number of coefficients c_i gives an approximation of G(x)

Function approximation

• How to find coefficients c_i? Mi i i

– Minimize an error measure

• What error measure?

– L₂ error



^{[ ( ) ( )]}2²

2 ^



^



I i

i i

L G x cB x

E

• Coefficients



^{G x B x dx}

B G

c ^{ }



( ) ( )

X

i i

i G B G x B x dx

c ( ) ( )

Function approximation

• Basis Functions are pieces of signal that can be used to produce approximations to a function

produce approximations to a function

 ^{  c}

¹

  ^{ c}

²







2

 c

  ^{ c}

³

Function approximation

• We can then use these coefficients to reconstruct an approximation to the original signal

approximation to the original signal

1



c 

  c

2



2



c

₃

^ 

c

Function approximation

• We can then use these coefficients to reconstruct an approximation to the original signal

approximation to the original signal

  ^



^N

^c

ⁱ

^B

ⁱ

^{  x}



i i i 1

Orthogonal basis functions

• Orthogonal Basis Functions

Th f ili f f ti ith i l – These are families of functions with special

properties

    

 





 

 ^B

ⁱ

^{x B}

^j

^{x dx} _ ¹ _{0 i} ⁱ _{ j} ^j

 _{0 i j}

– Intuitively, it’s like functions don’t overlap each other’s footprint

A bit lik th F i t f b k

• A bit like the way a Fourier transform breaks a functions into component sine waves

Integral of product

   



 F x G x dx I     

  ^{x }  ^{f B x}

F ( ) ^G   ^{x }  ^{g B ( x )}

    

 ^{   }

  ^ 

i

i

i

B x

f x

F ( )   ^ 

j

j

j

B x

g x

G ( )

      

  



 

 

i j

j j i

i

B x g B x dx

f dx

x G x

F ( ) ( )



 ^{  }







i i j

i j

i

g B x B x dx f g dx F G

f ( ) ( )  ˆ ˆ



i j i

 ) ω (

B^p(ωo)



f (ω )L (ω )cosθ dω B _{2 ,ω} (ω_i) (ω_i)cosθ_i ω_i

o L d

f _d

s p



Basis functions

• Transform data to a space in which we can capture the essence of the data better capture the essence of the data better

• Spherical harmonics, similar to Fourier

t f i h i l d i i d i PRT transform in spherical domain, is used in PRT.

Real spherical harmonics

• A system of signed, orthogonal functions over the sphere

the sphere

• Represented in spherical coordinates by the f ti

function

   

 2 K

^m

P

^m

 0

     

   

 











^

0

0 ,

cos sin

2

, cos cos

2

, m

m P

m K

P m K

y

_l^m _l ^m

m l m

l m

l

 







      

 

 





 0 0 ,

cos

, cos sin

2 ,

0

0

m

m P

K

P m K

y

l l

l l

l











where l is the band and m is the index within the band



Real spherical harmonics Reading SH diagrams

This di i direction

– + +

Not this direction

Reading SH diagrams

This di i direction

– + +

Not this direction

The SH functions



0

y

0₀

y



1

y

1

 y

₁¹

1

y

2

y

₂²

0

y

2 1

2

y

 2

2

y



The SH functions Spherical harmonics

Spherical harmonics

0

^m Y (   )

0

Y _lm ( , )  

1

1

l

1

_y z x

22

xy yz 3 z

²

 1 zx x

²

 y

²

-1

-2 0 1 2

SH projection

• First we define a strict order for SH functions

  ^{l m}

l

i   1 

• Project a spherical function into a vector of

• Project a spherical function into a vector of SH coefficients

   





_i

i

f s y s ds

c     

S

i i

SH reconstruction

• To reconstruct the approximation to a function N2

  ^   

~

^N

i

i

y s

c s

f

0 i

• We truncate the infinite series of SH functions to give a low frequency approximationg q y pp

Examples of reconstruction

An example

• Take a function comprised of two area light sources

sources

– SH project them into 4 bands = 16 coefficients





3290679 0930 0908 1. ,





 









238 0 0 425

0642 0001 0317 0837 0940 0 0417 0 0278 0679 0930 0908 0

, . , . , . ,

. , , . , , . ,

. , . , . ,

.



0.425,0,0.238

Low frequency light source

• We reconstruct the signal

U i l th ffi i t t fi d l f

– Using only these coefficients to find a low frequency approximation to the original light source

SH lighting for diffuse objects

• An Efficient Representation for Irradiance Environment Maps Ravi Ramamoorthi and Pat Environment Maps, Ravi Ramamoorthi and Pat Hanrahan, SIGGRAPH 2001

A ti

• Assumptions

– Diffuse surfaces – Distant illumination

– No shadowing, interreflection

 ) (p,ω_o

B ₂ f(p,ω_o,ω_i)L_d(p,ω_i)cosθ_idω_i



ss

) n ( ) ( Ep



 n) B(p,

irradiance is a function of surface normal

Diffuse reflection

B   E B   E

di i fl

radiosity (image intensity)

reflectance (albedo/texture)

irradiance (incoming light)

= ×

k li h quake light map

Irradiance environment maps

L n

Illumination Environment Map Irradiance Environment Map



^p

^{  }

^p

 ^

 L  n  d  n

E ) (



Spherical harmonic expansion

Expand lighting (L), irradiance (E) in basis functions

 l

( , )

^l _{lm lm}

( , ) L     

^{ }

L Y  

0 l ml

 

 l

0

( , )

_{lm lm}

( , )

l l

E      E Y  

0 l ml

= .67 + .36 + …

Analytic irradiance formula

Lambertian surface



acts like low-pass

filter 2 / 3

E _lm A L _{l lm} ^A

^{l  / 4}

E  A L

₀ ^{ / 4}

0 1 2

l

cosine term

 

21

2 2

( 1) !

2 ( 2)( 1) 2 !

l

l l l

A l l even

l l

 ^{   }

  

    2  ( )( ) 2 ! 

9 parameter approximation

i Order 0

Exact image Order 0

1 term

m

RMS error = 25 % ⁰ Y_lm( , ) 

l m

1 2

y z x

-1

-2 0 1 2

2 _xy yz 3z²1 zx x²y²

9 Parameter Approximation

i Order 1

Exact image Order 1

4 terms

m

RMS Error = 8% ⁰ Y_lm( , ) 

l m

1 2

y z x

-1

-2 0 1 2

2 _xy yz 3z²1 zx x²y²

9 Parameter Approximation

i Order 2

Exact image Order 2

9 terms

m

RMS Error = 1% ⁰ Y_lm( , ) 

l m

For any illumination, average error < 3% [Basri Jacobs 01]

1 2

y z x

error < 3% [Basri Jacobs 01]

-1

-2 0 1 2

2 _xy yz 3z²1 zx x²y²

Comparison

Incident Irradiance map Irradiance map illumination

300x300

p Texture: 256x256

Hemispherical

p Texture: 256x256 Spherical Harmonic Integration 2Hrs Coefficients 1sec Time 300 300 256 256    Time 9 256 256  

Complex geometry

Assume no shadowing: Simply use surface normal Assume no shadowing: Simply use surface normal

y

Natural illumination

For diffuse objects, rendering with natural illumination can be done quickly

illumination can be done quickly

directional source natural illumination

Video

Acquiring the Light Probe

HDRI Sky Probe

Clipped Sky + Sun Source Lit by sun only y y

Lit by sky only y y y Lit by sun and sky y y

Illuminating a Small Scene

Real Scene Example

• Goal: place synthetic objects on tableGoal: place synthetic objects on table

Light Probe / Calibration Grid g

Modeling the Scene

light-based model light-based model

real scene

The Light-Based Room Model

Rendering into the Scene

• Background PlateBackground Plate

Rendering into the scene

• Objects and Local Scene matched to SceneObjects and Local Scene matched to Scene

Differential rendering

• Local scene w/o objects, illuminated by modelLocal scene w/o objects, illuminated by model

Differential rendering

=

- =

Differential rendering

+ +

Differential Rendering

• Final ResultFinal Result

Environment map from single image? Eye as light probe! (Nayar et al)

Results Application in “Superman returns”

Capturing reflectance Application in “The Matrix Reloaded”

3D acquisition for faces 3D acquisition for faces

Cyberware scanners

face & head scanner whole body scannery

Making facial expressions from photos

• Similar to Façade, use a generic face model and view dependent texture mapping

and view-dependent texture mapping

• Procedure

1. Take multiple photographs of a person 2. Establish corresponding feature points 3. Recover 3D points and camera parameters 4. Deform the generic face model to fit points 5. Extract textures from photos

Reconstruct a 3D model

input photographs

generic 3D pose more deformed

generic 3D face model

p

estimation features model

Mesh deformation

– Compute displacement of feature points Apply scattered data interpolation – Apply scattered data interpolation

generic model displacement deformed model

Texture extraction

• The color at each point is a weighted combination of the colors in the photos combination of the colors in the photos

• Texture can be:

– view-independent – view-dependent

• Considerations for weighting

– occlusion – smoothness

– positional certaintyp y – view similarity

Texture extraction Texture extraction

Texture extraction

view-independent view-dependent

Model reconstruction

Use images to adapt a generic face model Use images to adapt a generic face model.

Creating new expressions

• In addition to global blending we can use:

R i l bl di – Regional blending – Painterly interface

Creating new expressions

New expressions are created with 3D morphing:

+ =

+

/2 /2

Applying a global blend

Creating new expressions

+

x

+

x

=

Applying a region-based blend

Creating new expressions

+ + +

+ + +

=

Using a painterly interface

Drunken smile Animating between expressions

Morphing over time creates animation:

“neutral” “joy”

Video Spacetime faces

Spacetime faces

black & white cameras color cameras

video projectors

time

time

Face surface Face surface

time

stereo

time

stereo active stereo

time

spacetime stereo

stereo active stereo

Spacetime Stereo

time

surface motion surface motion

time=1

Spacetime Stereo

time

surface motion surface motion

time=2

Spacetime Stereo

time

surface motion surface motion

time=3

Spacetime Stereo

time

surface motion surface motion

time=4

Spacetime Stereo

time

surface motion surface motion

time=5

Spacetime Stereo

time

surface motion surface motion

Better

• spatial resolution

• temporal stableness time

• temporal stableness

Spacetime stereo matching Video

Fitting FaceIK

Animation 3D face applications: The one

3D face applications: Gladiator

extra 3M extra 3M

Statistical methods Statistical methods

Statistical methods

para observed

f(z)+

z y

para- meters

observed signal )

| ( max

* P z y

z  max P ( z | y )

^Example: super-resolution

z

z

) ( )

|

max P ( y z P z



super-resolution de-noising

de-blocking

) max (

y P



z de-blocking

Inpainting

) ( )

| (

min L y z L z

z





^…

Statistical methods

para observed

f(z)+

z y

para- meters

observed signal )

( )

| ( min

* L y z L z

z  min L ( y | z )  L ( z )

z

z



)

2

(z f

data y  a-priori



2

evidence knowledge

Statistical methods

There are approximately 10²⁴⁰ possible 1010 There are approximately 10 possible 1010 gray-level images. Even human being has not seen them all yet. There must be a strong seen them all yet. There must be a strong statistical bias.

Takeo Kanade Takeo Kanade

Approximately 8X10¹¹ blocks per day per person.

Generic priors

“S th i d i ”

“Smooth images are good images.”





x

x V z

L ( )  ( ( ))

x

) 2

(d  d

Gaussian MRF  

(d) d

Gaussian MRF

T d

d 

 ²

T d

T d T d T T

d d











 

) (

) 2

( ₂

Huber MRF 

Generic priors Example-based priors

“E i ti i d i ”

“Existing images are good images.”

six 200200 Images  Images  2,000,000 pairs

pairs

Example-based priors

L(z)

Example-based priors

high-resolution

low-resolution

Model-based priors

“Face images are good images when Face images are good images when working on face images …”

Parametric

model Z=WX+ L(X)

model

) ( )

| ( min

* L y z L z

z  (y | )  ( )

z

 X *  min L ( y | WX   )  L ( X )

 















*

*

) ( )

| ( min WX z

X L WX

y L

X

x

 

PCA

• Principal Components Analysis (PCA):

approximating a high dimensional data set approximating a high-dimensional data set with a lower-dimensional subspace

**

**

** **

** **

** ****

** **

**

** First principal componentFirst principal component Second principal component

Second principal component

Original axes Original axes

**

** ** **

**

******** **

**

****

** **

Data points Data points

PCA on faces: “eigenfaces”

Average

Average First principal componentFirst principal component Average

Average face face

Other Other components components

For all except average, For all except average,o a e cept a e age,o a e cept a e age,

“gray” = 0,

“gray” = 0,

“white” > 0,

“white” > 0,

“black” < 0

“black” < 0black < 0black < 0

Model-based priors

“Face images are good images when Face images are good images when working on face images …”

Parametric

model Z=WX+ L(X)

model

) ( )

| ( min

* L y z L z

z  (y | )  ( )

z

 X *  min L ( y | WX   )  L ( X )

 















*

*

) ( )

| ( min WX z

X L WX

y L

X

x

 

Super-resolution

(a) (b) (c) (d) (e) (f)

(a) Input low 24×32 (b) Our results (c) Cubic B-Spline (a) Input low 24×32 (b) Our results (c) Cubic B Spline (d) Freeman et al. (e) Baker et al. (f) Original high 96×128

Face models from single images

Face models from single images

Morphable model of 3D faces

• Start with a catalogue of 200 aligned 3D Cyberware scans

Cyberware scans

• Build a model of average shape and texture

• Build a model of average shape and texture, and principal variations using PCA

Morphable model

shape examplars texture examplars

Morphable model of 3D faces

• Adding some variations

Reconstruction from single image

Rendering must be similar to the input if we guess right

g g

Reconstruction from single image

prior

shape and texture priors are learnt from database ρ is the set of parameters for shading including camera pose, lighting and so onp , g g

Modifying a single image

Animating from a single image Video

Exchanging faces in images Exchange faces in images

Exchange faces in images Exchange faces in images

Exchange faces in images Morphable model for human body

Image-based faces (lip sync.)

Video rewrite (analysis)

Video rewrite (synthesis) Results

• Video database

2 i t f JFK – 2 minutes of JFK

• Only half usable

• Head rotation

• Head rotation

training video R d li Read my lips.

I never met Forest Gump.

Morphable speech model Preprocessing

Prototypes (PCA+k-mean clustering)

W fi d I d C f h t t i

We find I_i and C_i for each prototype image.

Morphable model

analysis

I ^{α β}

analysis synthesis

Morphable model

analysis synthesis

Synthesis

Results Results

Relighting faces Relighting faces

Light is additive

lamp #1 lamp #2

Light stage 1.0 Light stage 1.0

64x32 lighting directions

Input images Reflectance function

occlusion flare

Relighting Results

Changing viewpoints Results

3D face applications: Spiderman 2 Spiderman 2

real synthetic

real synthetic

Spiderman 2

video video

Light stage 3

Light stage 6 Application: The Matrix Reloaded

Application: The Matrix Reloaded References

• Paul Debevec, Rendering Synthetic Objects into Real Scenes:

Bridging Traditional and Image-based Graphics with Global Illumination and High Dynamic Range Photography

Illumination and High Dynamic Range Photography, SIGGRAPH 1998.

• F. Pighin, J. Hecker, D. Lischinski, D. H. Salesin, and R.

Szeliski Synthesizing realistic facial expressions from Szeliski. Synthesizing realistic facial expressions from photographs. SIGGRAPH 1998, pp75-84.

• Li Zhang, Noah Snavely, Brian Curless, Steven M. Seitz, S ti F High R l ti C t f M d li g d Spacetime Faces: High Resolution Capture for Modeling and Animation, SIGGRAPH 2004.

• Blanz, V. and Vetter, T., A Morphable Model for the S th i f 3D F SIGGRAPH 1999 187 194 Synthesis of 3D Faces, SIGGRAPH 1999, pp187-194.

• Paul Debevec, Tim Hawkins, Chris Tchou, Haarm-Pieter Duiker, Westley Sarokin, Mark Sagar, Acquiring the R fl t Fi ld f H F SIGGRAPH 2000 Reflectance Field of a Human Face, SIGGRAPH 2000.

• Christoph Bregler, Malcolm Slaney, Michele Covell, Video Rewrite: Driving Visual Speeach with Audio, SIGGRAPH 1997.

• Tony Ezzat, Gadi Geiger, Tomaso Poggio, Trainable Videorealistic Speech Animation, SIGGRAPH 2002.