Computer-Generated Watercolor

Cassidy J. CurtisSean E. AndersonJoshua E. SeimsKurt W. FleischerDavid H. Salesin

Outline

• Introduction

• Related work

• Background

• Overview

• Watercolor simulation

• Rendering

• Applications

• Results

• Conclusion

Introduction

• Various artistic effects of watercolor

Related work

• Simulating artists’ traditional media and tools– Watercolor : [David Small 1991]– Sumie : [Guo and Kunii 1991]

• Commercial package– Fractal Design Painter

Background

• Properties of watercolor– Watercolor paper– Pigment– Binder– Surfactant

Background• Watercolor Effects

• a) dry-brush• b) Edge darkening• c) Backruns• d) granulation and separation of pigments• e) Flow patterns• f) color glazing

Overview

• Computer-generated watercolor

1. Fluid (and pigment) simulation for each glaze

2. Rendering

Glaze: physical properties, area

Fluid simulation

• Three-layer model

Fluid simulation

• Paper Generation

– Height field model ( 0 < h < 1 )– Based on pseudo-random process– Fluid capacity c: proportional to h

minminmax )( ccchc

Fluid simulation

• Main loop

Applying Capillary Flow

Moving Water

Moving Pigments

Transferring Pigments

For e

ach

time

step

Fluid simulation

• Main loop

Applying Capillary Flow

Moving Water

Moving Pigments

Transferring Pigments

For e

ach

time

step

Moving water• conditions of water

1. To remain within the wet-area mask

2. To flow outward into nearby region

3. To be damped to minimize oscillating waves

4. To be perturbed by the texture of the paper

5. To be affected by local changes

6. To present the edge-darkening effect

Navier-Stoke Eq.

Viscous drag k

Paper slope h

Mass conserv.

Flow outward

Applying Capillary Flow

Moving Water

Moving Pigments

Transferring Pigments

Fluid simulation

• Configuration– Staggered grid

),5.0(),( jivu ),5.0(),( jivu

)5.0,(),( jivu

)5.0,(),( jivu

...),,( dgp

i,j

Applying Capillary Flow

Moving Water

Moving Pigments

Transferring Pigments

Fluid simulation

• Updating the water velocities– Governing Equation (2D Navier-Stoke Eqn.)

y

pv

y

vv

x

vu

t

v

x

pu

y

uv

x

uu

t

u

2

2

Applying Capillary Flow

Moving Water

Moving Pigments

Transferring Pigments

Fluid simulation

• Derivation of Navier-Stoke Eqn.(1/5)

– Basic Eqn.:

– For unit volume:

dt

dmmFV

x

dt

dF

V

Applying Capillary Flow

Moving Water

Moving Pigments

Transferring Pigments

Fluid simulation

• Derivation of Navier-Stoke Eqn.(2/5)

– Two kind of measurements

fluid

solid

)(tVControl volume

,(tV ),, zyx

Applying Capillary Flow

Moving Water

Moving Pigments

Transferring Pigments

Fluid simulation

• Derivation of Navier-Stoke Eqn.(3/5)

– Eulerian view

dt

zyxtd ),,,(V

t

z

zt

y

yt

x

xt

VVVV

wz

vy

uxt

VVVV

VVV

)(

t

Applying Capillary Flow

Moving Water

Moving Pigments

Transferring Pigments

Fluid simulation

• Derivation of Navier-Stoke Eqn.(4/5)

– Governing Eq.:

– Forces:• Gravity:

• Viscosity:

• Pressure:

dt

dF

V

g

V2

p

Applying Capillary Flow

Moving Water

Moving Pigments

Transferring Pigments

Fluid simulation

• Derivation of Navier-Stoke Eqn.(5/5)– Navier-Stoke Eqn.

– For 2D case,

y

pv

y

vv

x

vu

t

v

x

pu

y

uv

x

uu

t

u

2

2

pVVVV

2)(

t

Applying Capillary Flow

Moving Water

Moving Pigments

Transferring Pigments

Fluid simulation

• Updating the water velocities– Numerical integration for u

x

pu

y

uv

x

uu

t

u

2

t

uu jiji

,5.,5.

)()( ,1,,5.,,1,5. jijijijijiji uuvuuu

jiji pp ,,1

jijijijiji uuuuu ,5.1,5.1,5.,5.1,5.1 4

Applying Capillary Flow

Moving Water

Moving Pigments

Transferring Pigments

Fluid simulation

• Updating the water velocities– Applying paper slope effect:

– Applying Drag Force:

Applying Capillary Flow

Moving Water

Moving Pigments

Transferring Pigments

h VV

VF

Fluid simulation

• Mass conservation (1/3)– Divergence free condition

0

y

v

x

u

Applying Capillary Flow

Moving Water

Moving Pigments

Transferring Pigments

Fluid simulation

• Mass conservation (2/3)– Relaxation (iterative procedure)

y

v

x

u

Applying Capillary Flow

Moving Water

Moving Pigments

Transferring Pigments

Fluid simulation

• Mass conservation (3/3)– Relaxation (iterative procedure)

y

v

x

u

Applying Capillary Flow

Moving Water

Moving Pigments

Transferring Pigments

jivu ,),(

)(y

v

x

u

Fluid simulation

• Edge darkening – To flow outward

• Remove some water at the boundary

MM )1( pp

Applying Capillary Flow

Moving Water

Moving Pigments

Transferring Pigments

coeff. Darkening :

mask BlurredGaussian :

mask Wet :

M

M

Fluid simulation

• Edge darkening

MM )1( pp

Applying Capillary Flow

Moving Water

Moving Pigments

Transferring Pigments

dry wet

0

0

00

0

0

0

0

0

1

1

1 1

1

1

1

1

1

M

.1

.1

.10

.4

.4

.4

0

0

.6

.6

.6 1

.9

.9

.9

1

1

M’

0

0

00

0

0

0

0

0

.4

.4

.4 0

.1

.1

.1

0

0

(1-M’)M

Fluid simulation

• Main loop

Applying Capillary Flow

Moving Water

Moving Pigments

Transferring Pigments

For e

ach

time

step

Fluid simulation

• Moving Pigments – To move as specified by the velocity field u,v

jig ,

jiji gu ,,5.0 jiji gu ,,5.0

jiji gv ,5.0,

jiji gv ,5.0,

Applying Capillary Flow

Moving Water

Moving Pigments

Transferring Pigments

Fluid simulation

• Moving Pigments – To move as specified by the velocity field u,v

),0max(),0max(

),0max(),0max(

),0max(

),0max(

),0max(

),0max(

,5.0,,5.0,

,,5.0,,5.0,,

,5.0,1,1,

,5.0,1,1,

,,5.0,1,1

,,5.0,1,1

jijijiji

jijijijijiji

jijijiji

jijijiji

jijijiji

jijijiji

gvgv

gugugg

gvgg

gvgg

gugg

gugg

Applying Capillary Flow

Moving Water

Moving Pigments

Transferring Pigments

Fluid simulation

• Main loop

Applying Capillary Flow

Moving Water

Moving Pigments

Transferring Pigments

For e

ach

time

step

Fluid simulation

• Transferring Pigments– Adsorption and desorption

Adsorption ,h

wh /1,1Desorption

Applying Capillary Flow

Moving Water

Moving Pigments

Transferring Pigments

Fluid simulation

• Main loop

Applying Capillary Flow

Moving Water

Moving Pigments

Transferring Pigments

For e

ach

time

step

Fluid simulation

• Backruns – Diffusing water through the capillary layer

• Spreading slowly into a drying region

• Transfer water to its dryer neighbors until they are saturated

Applying Capillary Flow

Moving Water

Moving Pigments

Transferring Pigments

Fluid simulation

• Drybrush effect– By excluding any lower pixel than threshold

Rendering

• Optical properties of pigments– Optical composition – subtractive color mixing

Rendering

• Optical properties of pigments– Kubelka-Munk (KM) Model– To compute Reflectance R and Transmittance T

using K and S

unit length

absorbed

K

backscatteredS

Rendering

• Optical properties of pigments– Kubelka-Munk (KM) Model

bSdbbSda

bT

bSdbbSda

bSdR

coshsinh

coshsinh

sinh

1 and , /)( where 2 abSKSa

Rendering

• Optical properties of pigments– Kubelka-Munk (KM) Model– For multiple layers

21

21

21

22

11

1

1

RR

TTT

RR

RTRR

Rendering

• Optical properties of pigments– Kubelka-Munk (KM) Model

We need S and K values

Make user choose them intuitively

Rendering

• Optical properties of pigments– User selects Rw and Rb

Rendering

• Optical properties of pigments– User selects Rw and Rb

1 and ,1

2

1

)1(

)1(

)1)((coth

1

2

21

abR

RRRawhere

aSK

Rb

aRab

bS

w

wbw

w

w

Applications

• 1. Interactive painting with watercolors

• 2. Automatic image “watercolorization”

• 3. Non-photorealistic rendering of 3D models

Applications

• 1. Interactive painting with watercolors

Applications

• 2. Automatic image “watercolorization”

– Color separation

– Brushstroke Planning

Applications

• 2. Automatic image “watercolorization”– Color separation

• Determine the thickness of each pigment by brute-force search for all color combinations

Applications

• 2. Automatic image “watercolorization”– Brushstroke planning

Applications

• 3. Non-photorealistic rendering of 3D models– Using “photorealistic” scene of 3D model

Results

Results

Results

Results

Conclusion

• Various artistic effects of watercolor– Water and pigment simulation– Pigment Rendering

• Application– Interactive system– Automatic “watercolorization” of 2D and 3D

Further work

• Other effects– Spattering and drybrush

• Automatic rendering– Applying automatic recognition

• Generalization – Integration of Wet-in-wet and backruns

• Animation issues– Reducing temporal artifacts