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Tone mapping
Digital Visual EffectsYung-Yu Chuang
with slides by Fredo Durand, Lin-Yu Tseng, and Alexei Efros
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Tone mapping
• How should we map scene luminances (up to 1:100,000) to display luminances (only around 1:100) to produce a satisfactory image?Linear scaling?, thresholding?
10-6 106
10-6 106
Real worldradiance
Displayintensity
dynamic range
Pixel value 0 to 255
CRT has 300:1 dynamic range
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The ultimate goal is a visual match
We do not need to reproduce the true radiance as longas it gives us a visual match.
visual adaption
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Eye is not a photometer!
• Dynamic range along the visual pathway is only around 32:1.
• The key is adaptation
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Eye is not a photometer!
Are the headlights different in two images? Physically,they are the same, but perceptually different.
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We are more sensitive to contrast
• Weber’s law
%1~b
b
II
background intensity
Just-noticeableDifference (JND)
flash
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How humans deal with dynamic range
• We're more sensitive to contrast (multiplicative)– A ratio of 1:2 is perceived as the same contrast as a
ratio of 100 to 200– Makes sense because illumination has a
multiplicative effect– Use the log domain as much as possible
• Dynamic adaptation (very local in retina)– Pupil (not so important)– Neural– Chemical
• Different sensitivity to spatial frequencies
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Preliminaries
• For color images
• Log domain is usually preferred.
w
wd
w
wd
w
wd
d
d
d
LBL
LGL
LRL
BGR
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HDR Display
• Once we have HDR images (either captured or synthesized), how can we display them on normal displays?
HDR display system, Sunnybrook Technology, SIGGRAPH2004
DLP800:1
LCD300:1
diffuser Theoretically, 240,000:1.
Due to imperfectoptical depth, 54,000:1 measured
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Sunnybrook HDR display
Slide from the 2005 Siggraph course on HDR
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How it works
Slide from the 2005 Siggraph course on HDR
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Brightside HDR display
37”200000:1
Acquired by Dolby
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Tone mapping operators
• Spatial (global/local)• Frequency domain• Gradient domain
• 3 papers from SIGGRAPH 2002 Photographic Tone Reproduction for Digital Images Fast Bilateral Filtering for the Display of High-
Dynamic-Range Images Gradient Domain High Dynamic Range Compression
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Photographic Tone Reproduction for Digital Images
Erik Reinhard Mike Stark Peter Shirley Jim Ferwerda
SIGGRAPH 2002
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Global v.s. local
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Photographic tone reproduction
• Proposed by Reinhard et. al. in SIGGRAPH 2002• Motivated by traditional practice, zone system
by Ansel Adams and dodging and burning• It contains both global and local operators
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Zone system
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The Zone system• Formalism to talk about exposure, density• Zone = intensity range, in powers of two• In the scene, on the negative, on the print
Source: Ansel Adams
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The Zones
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The Zone system• You decide to put part of the system in a given
zone• Decision: exposure, development, print
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Dodging and burning• During the print• Hide part of the print during exposure
– Makes it brighter
From The Master Printing Course, Rudman
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Dodging and burning
From Photography by London et al. dodging burning
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Dodging and burning• Must be done for every single print!
Straight print After dodging and burning
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Global operator
yxww yxL
NL
,)),(log(1exp
),(),( yxLLayxL ww
m
Approximation of scene’s key (how light or dark it is).Map to 18% of display rangefor average-key scene
User-specified; high key or low key
),(1),(),(yxL
yxLyxLm
md
transfer function to compress
high luminances
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Global operator
),(1),(
),(1),(),(
2
yxLyxL
yxLyxLyxL
m
white
mm
d
It seldom reaches 1 since the input image does not have infinitely large luminance values.
Lwhite is the smallest luminance
to be mapped to 1
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low key (0.18) high key (0.5)
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Dodging and burning (local operators)
• Area receiving a different exposure is often bounded by sharp contrast
• Find largest surrounding area without any sharp contrast
),(),(),( yxGyxLyxL smblurs
blurs
blurs
blurs
s LsayxLyxLyxV
2
1
2),(),(),(
y)(x,:maxmax sVs
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Dodging and burning (local operators)
• A darker pixel (smaller than the blurred average of its surrounding area) is divided by a larger number and become darker (dodging)
• A brighter pixel (larger than the blurred average of its surrounding area) is divided by a smaller number and become brighter (burning)
• Both increase the contrast
),(1),(),(
maxyxL
yxLyxL blurs
md
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Dodging and burning
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Frequency domain
• First proposed by Oppenheim in 1968!• Under simplified assumptions,
image = illuminance * reflectancelow-frequencyattenuate more
high-frequencyattenuate less
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Oppenheim
• Taking the logarithm to form density image• Perform FFT on the density image• Apply frequency-dependent attenuation filter
• Perform inverse FFT• Take exponential to form the final image
kfkfccfs
1
)1()(
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Fast Bilateral Filtering for the Display of High-Dynamic-Range Images
Frédo Durand & Julie Dorsey
SIGGRAPH 2002
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A typical photo
• Sun is overexposed• Foreground is underexposed
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Gamma compression
• X X
• Colors are washed-outInput Gamma
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Gamma compression on intensity
• Colors are OK, but details (intensity high-frequency) are blurred
Gamma on intensityIntensity
Color
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Chiu et al. 1993
• Reduce contrast of low-frequencies• Keep high frequencies
Reduce low frequencyLow-freq.
High-freq.
Color
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The halo nightmare
• For strong edges• Because they contain high frequency
Reduce low frequencyLow-freq.
High-freq.
Color
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Durand and Dorsey
• Do not blur across edges• Non-linear filtering
OutputLarge-scale
Detail
Color
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Edge-preserving filtering
• Blur, but not across edges
• Anisotropic diffusion [Perona & Malik 90]– Blurring as heat flow– LCIS [Tumblin & Turk]
• Bilateral filtering [Tomasi & Manduci, 98]
Edge-preservingGaussian blurInput
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Contrast reductionInput HDR image
Contrast too high!
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Contrast reduction
Color
Input HDR image
Intensity
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Contrast reduction
Color
Intensity Large scale
FastBilateral Filter
Input HDR image
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Contrast reduction
Detail
Color
Intensity Large scale
FastBilateral Filter
Input HDR image
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Contrast reduction
Detail
Color
Intensity Large scale
FastBilateral Filter
Reducecontrast
Large scale
Input HDR image
Scale in log domain
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Contrast reduction
Detail
Color
Intensity Large scale
FastBilateral Filter
Reducecontrast
Detail
Large scale
Preserve!
Input HDR image
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Contrast reduction
Detail
Color
Intensity Large scale
FastBilateral Filter
Reducecontrast
Detail
Large scale
Color
Preserve!
Input HDR image Output
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Bilateral filter is slow!
• Compared to Gaussian filtering, it is much slower because the kernel is not fixed.
• Durand and Dorsey proposed an approximate approach to speed up
• Paris and Durand proposed an even-faster approach in ECCV 2006. We will cover this one when talking about computational photogrphy.
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Oppenheim bilateral
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Gradient Domain High Dynamic Range Compression
Raanan Fattal Dani Lischinski Michael Werman
SIGGRAPH 2002
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Log domain
• Logorithm is a crude approximation to the perceived brightness
• Gradients in log domain correspond to ratios (local contrast) in the luminance domain
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The method in 1D
log derivativeattenuate
integrateexp
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The method in 2D
• Given: a log-luminance image H(x,y)• Compute an attenuation map
• Compute an attenuated gradient field G:
• Problem: G may not be integrable!
H
HyxHyxG ),(),(
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Solution
• Look for image I with gradient closest to G in the least squares sense.
• I minimizes the integral:
22
2,
yx GyIG
xIGIGIF
dxdyGIF ,
yG
xG
yI
xI yx
2
2
2
2Poissonequation
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Solvey
Gx
GyI
xI yx
2
2
2
2
)1,(),(),1(),( yxGyxGyxGyxG yyxx
),(4)1,()1,(),1(),1( yxIyxIyxIyxIyxI
.. 1 … 1 -4 1 … 1 ..
I
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Solving Poisson equation• No analytical solution• Multigrid method• Conjugate gradient method
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Attenuation
• Any dramatic change in luminance results in large luminance gradient at some scale
• Edges exist in multiple scales. Thus, we have to detect and attenuate them at multiple scales
• Construct a Gaussian pyramid Hi
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Attenuation
gradient magnitudelog(Luminance) attenuation map
1),(
),(
yxHyx k
kH 1.0
8.0~
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Multiscale gradient attenuation
interpolate
interpolate
X =
X =
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Final gradient attenuation map
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Performance• Measured on 1.8 GHz Pentium 4:
– 512 x 384: 1.1 sec– 1024 x 768: 4.5 sec
• Can be accelerated using processor-optimized libraries.
0
4
8
12
16
0 1000000 2000000 3000000
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Bilateral[Durand et al.]
Photographic[Reinhard et al.]
Gradient domain[Fattal et al.]
Informal comparison
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Informal comparison
Bilateral[Durand et al.]
Photographic[Reinhard et al.]
Gradient domain[Fattal et al.]
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Bilateral[Durand et al.]
Photographic[Reinhard et al.]
Gradient domain[Fattal et al.]
Informal comparison
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Evaluation of Tone Mapping Operators using a High Dynamic Range Display
Patrick Ledda Alan Chalmers Tom Troscinko Helge Seetzen
SIGGRAPH 2005
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Six operators
• H: histogram adjustment• B: bilateral filter• P: photographic reproduction• I: iCAM• L: logarithm mapping• A: local eye adaption
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23 scenes
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Experiment setting
HDR displaytonemapping
result tonemapping
result
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Preference matrix
• Ranking is easier than rating.• 15 pairs for each person to compare. A total of
345 pairs per subject.
preference matrix (tmo2->tmo4, tom2 is better than tmo4)
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Statistical measurements
• Statistical measurements are used to evaluate:– Agreement: whether most agree on the ranking
between two tone mapping operators.– Consistency: no cycle in ranking. If all are confused
in ranking some pairs, it means they are hard to compare. If someone is inconsistent alone, his ranking could be droped.
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Overall similarity
• Scene 8
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Summary
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Not settled yet!
• Some other experiment said bilateral are better than others.
• For your reference, photographic reproduction performs well in both reports.
• There are parameters to tune and the space could be huge.
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References• Raanan Fattal, Dani Lischinski, Michael Werman,
Gradient Domain High Dynamic Range Compression, SIGGRAPH 2002.
• Fredo Durand, Julie Dorsey, Fast Bilateral Filtering for the Display of High Dynamic Range Images, SIGGRAPH 2002.
• Erik Reinhard, Michael Stark, Peter Shirley, Jim Ferwerda, Photographics Tone Reproduction for Digital Images, SIGGRAPH 2002.
• Patrick Ledda, Alan Chalmers, Tom Troscianko, Helge Seetzen, Evaluation of Tone Mapping Operators using a High Dynamic Range Display, SIGGRAPH 2005.
• Jiangtao Kuang, Hiroshi Yamaguchi, Changmeng Liu, Garrett Johnson, Mark Fairchild, Evaluating HDR Rendering Algorithms, ACM Transactions on Applied Perception, 2007.