available - Cornell University Program of Computer Graphics

Pigmented Colorants
Dependency on Media and Time
Jeffrey B. Budsberg • September 1, 2006 • Cornell University
Art Restoration
• Azor-Sadoch lunette
– Michelangelo.
Sistine chapel
ceiling, Vatican City
Color Matching
• The Expulsion from
Garden of Eden
– Masaccio.
Brancacci chapel,
Florence
Motivation
• The appearance of paint changes over time
• The painting medium drastically effects the
overall appearance
• What if there was a way to predict the
appearance of pigmented materials?
Overview
•
•
•
•
•
Painting
Paint optics
Experimental results
Kubelka Munk theory
Interactive viewer
Vasily Kandinsky, Improvization 7
Composition of a painting
• Support
– the surface upon which
the subsequent layers
reside
• Size
– permeation that protects
against deterioration
• Ground
– coated layer that provides
a uniform work surface
Composition of a painting
Composition of paint
• Pigment
– fine powdered colorant
material
• Binding Medium
– adheres colorant
particles to surface
• Vehicle
– facilitate spreading
across a surface
Malachite
- medium grade 20-100μm
- fine grade 20μm
Paint optics
• Subsurface scattering
inside paint layers
• Index of refraction η
can vary due to:
– composition
– time
ηair < η1 < η2
Full picture
• Light interaction in
paint is very complex
–
–
–
–
–
–
–
Media
Pigment
Ground
Surface definition
Film thickness
Layers
Other materials
Experiment
• 21 pigmented mixtures
• 8 binding media
• 6 time intervals
–
–
–
–
–
–
wet
1 day
1 week
1 month
3 months
6 months
• Capture diffuse reflectance: 350-700:10nm
a
b
c
d
e
f
g
h
i
j
k
Lapis lazuli
Cold glauconite
Chrome yellow
Gold ochre
Raw umber
Burnt sienna
Red ochre
Hematite
Cold hematite
Lampblack
Titanium dioxide
Binding Media
•
•
•
•
•
•
•
•
Watercolor
Gouache
Distemper
Tempera
Casein
Oil
Encaustic
Acrylic
Carbohydrate-based
Protein-based
Drying oils
Wax
Synthetic polymer
Sample preparation
Chrome yellow in distemper
Measurement
Monochromator
•
Czerny-Turner design
•
Yields tunable
monochromatic light
from broad spectrum
source
Effect of Media
–Pigment and Time constant
Effect of Media
Effect of Time
–Pigment and Media constant
Problem
• Only have a discrete set of measurement data
• Would like to see resulting appearance of:
–
–
–
–
arbitrary pigment mixtures
arbitrary time
for any media
under any illuminant
• Want to modify variables interactively
Additive/Subtractive mixing
Kubelka Munk theory
• Observed macroscopic light
effects in pigments
• Accurately approximate the
diffuse reflectance of
pigmented materials
• Related paint reflectance R
to absorption K and
scattering S coefficients
• For complete hiding, the
solution to their differential
equations is:
2
⎛ K ⎞ (1 − R∞ )
⎜ ⎟=
2 R∞
⎝S⎠
K-M theory
{
Rtotal
}d
i
Rk Tk Kk Sk
K ic i (1− R ) 2
∑
⎛K ⎞
∞
=
⎜ ⎟ = in
⎝ S ⎠ mix ∑ S c
2R∞
n
Pigmented mixtures
i
1
R=
Reflectance &
Transmittance
i i
1+
K
+ b tanh(bSd )
S
⎛ K ⎞⎛ K ⎞
b = ⎜ ⎟⎜
⎟
⎝ S ⎠⎝ S + 2 ⎠
T = bR sinh(bSd )
2
Compositing
Rtotal
T R
= R1 + 1 2
1 − R1 R2
Ttotal =
T1T2
1 − R1 R2
Kubelka Munk in Graphics
• K-M theory introduced to graphics for rendering and color
mixing [Hasse and Meyer 1992]
• Compositing weathered metallic patinas [Dorsey and
Hanrahan 1996]
• Rendering and compositing watercolor glazes [Curtis et al.
1997]
• Rendering wax crayons [Rudolf et al. 2003]
• None of these implementations offer real-time
rendering for interactive applications
[Curtis et al. 97]
• Plausible results, but no
measurements taken
• 3 wavelengths for
calculations
• Interactive at low quality
• More accurate colors/
detail in post-processing
[Baxter 04]
• Attempts to solve
previous K-M issues
• 71 measurements
using 11 pigments
• 8 wavelengths for
calculations
• Real-time interaction
on the GPU
• Poor wavelength
selection
⎡ x (λ ) ⎤
⎡X ⎤
⎢ Y ⎥ = R(λ )E (λ ) ⎢ y (λ )⎥ dλ
⎥
⎢
⎢ ⎥ ∫
⎢⎣ z (λ ) ⎥⎦
⎢⎣ Z ⎥⎦
Mixing Comparison
• Linear RGB
incorrect
• 3 KM not enough
• 8 KM better…
• but the amount of
reflectance data
limits accuracy
Yellow ochre and Prussian blue under D65
Our system
• Similar to Baxter’s IMPaSTo system
• 8 wavelengths for calculations maximizing x , y , z
• Real-time interaction on the GPU
• 1008 time-dependent reflectance spectra Æ K&S
• Not only arbitrary mixing, but over time
• Different binding media
Simulated canvas
Local (point):
• concentrations
•x, y, h
• normal
Global (canvas):
• time
• media
• light
world space
screen space
Rendering pipeline
Data
ci
normal
time
media
light
K-M
(K/S)mix
Reflectance
Transmittance
Composite
Lighting
SpectraÆ
XYZ
Convert
ÆRGB
ÆsRGB
GPU
Display
System features
pigment interpolation
time interpolation
different lighting
different media
Applications
• Artist
– Creative vision
• Art historian
– Restoration
– Conservation
• Industry
– Printing
– Colored materials
• Graphics
– Weathering
Questions