Tone mapping
Digital Visual Effects Yung-Yu Chuang
with slides by Fredo Durand, Lin-Yu Tseng, and Alexei Efros
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
-610
610
-610
6Real world radiance
Display intensity
dynamic range
Pixel value 0 to 255
CRT has 300:1 dynamic range
The ultimate goal is a visual match
We do not need to reproduce the true radiance as long as it gives us a visual match.
visual adaption
Eye is not a photometer!
• Dynamic range along the visual pathway is only around 32:1.
• The key is adaptation
Eye is not a photometer!
Are the headlights different in two images? Physically, they are the same, but perceptually different.
We are more sensitive to contrast
• Weber’s law
% 1
~
b b
I
I
background intensity
Just-noticeable Difference (JND)
flash
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
Preliminaries
• For color images
• Log domain is usually preferred.
w w d
w w d
w w d
d d d
L L B
L L G
L L R
B G R
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 DLP
800:1
LCD 300:1
diffuser Theoretically, 240,000:1.
Due to imperfect optical depth,
54,000:1 measured
Sunnybrook HDR display
Slide from the 2005 Siggraph course on HDR
How it works
Slide from the 2005 Siggraph course on HDR
Brightside HDR display
37”
200000:1 Acquired by Dolby
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
Photographic Tone Reproduction for Digital Images
Erik Reinhard Mike Stark Peter Shirley Jim Ferwerda
SIGGRAPH 2002
Global v.s. local
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
Zone system
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
The Zones
The Zone system
• You decide to put part of the system in a given zone
• Decision: exposure, development, print
Dodging and burning
• During the print
• Hide part of the print during exposure
– Makes it brighter
From The Master Printing Course, Rudman
Dodging and burning
From Photography by London et al.
dodging burning
Dodging and burning
• Must be done for every single print!
Straight print After dodging and burning
Global operator
y x
w
w L x y
L N
,
)) ,
( 1 log(
exp
) , ( )
,
( L x y
L y a
x
L w
w
m
Approximation of scene’s key (how light or dark it is).
Map to 18% of display range for average-key scene
User-specified; high key or low key
) , ( 1
) , ) (
,
( L x y
y x y L
x L
m m
d
transfer function to compress high luminances
Global operator
) , ( 1
) , (
) , 1 (
) , ( )
, (
2
y x L
y x L
y x y L
x L
y x L
m
white m m
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
low key (0.18) high key (0.5)
Dodging and burning (local operators)
• Area receiving a different exposure is often bounded by sharp contrast
• Find largest surrounding area without any sharp contrast
) , ( )
, ( )
,
(x y L x y G x y
Lblurs m s
blur s blur
s blur
s
s a s L
y x L
y x y L
x
V
2 1
2
) , ( )
, ) (
,
(
y) (x, : max
max Vs
s
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
) , ) (
, (
max x y
L
y x y L
x
L blur
s m
d
Dodging and burning
Frequency domain
• First proposed by Oppenheim in 1968!
• Under simplified assumptions,
image = illuminance * reflectance
low-frequency
attenuate more high-frequency attenuate less
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
kf c kf
c f
s
) 1 1
( )
(
Fast Bilateral Filtering for the
Display of High-Dynamic-Range Images
Frédo Durand & Julie Dorsey SIGGRAPH 2002
A typical photo
• Sun is overexposed
• Foreground is underexposed
Gamma compression
• X X
• Colors are washed-out
Input Gamma
Gamma compression on intensity
• Colors are OK, but details (intensity high- frequency) are blurred
Gamma on intensity Intensity
Color
Chiu et al. 1993
• Reduce contrast of low-frequencies
• Keep high frequencies
Reduce low frequency Low-freq.
High-freq.
Color
The halo nightmare
• For strong edges
• Because they contain high frequency
Reduce low frequency Low-freq.
High-freq.
Color
Durand and Dorsey
• Do not blur across edges
• Non-linear filtering
Output Large-scale
Detail
Color
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-preserving Gaussian blur
Input
Contrast reduction
Input HDR image
Contrast too high!
Contrast reduction
Color
Input HDR image
Intensity
Contrast reduction
Color
Intensity Large scale
Fast
Bilateral Filter
Input HDR image
Contrast reduction
Detail
Color
Intensity Large scale
Fast
Bilateral Filter
Input HDR image
Contrast reduction
Detail
Color
Intensity Large scale
Fast
Bilateral Filter
Reduce contrast
Large scale
Input HDR image
Scale in log domain
Contrast reduction
Detail
Color
Intensity Large scale
Fast
Bilateral Filter
Reduce contrast
Detail
Large scale
Preserve!
Input HDR image
Contrast reduction
Detail
Color
Intensity Large scale
Fast
Bilateral Filter
Reduce contrast
Detail
Large scale
Color
Preserve!
Input HDR image Output
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.
Oppenheim bilateral
Gradient Domain High Dynamic Range Compression
Raanan Fattal Dani Lischinski Michael Werman SIGGRAPH 2002
Log domain
• Logorithm is a crude approximation to the perceived brightness
• Gradients in log domain correspond to ratios (local contrast) in the luminance domain
The method in 1D
log derivative
attenuate
integrate exp
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
H
y x
H y
x
G ( , ) ( , )
Solution
• Look for image
I
with gradient closest toG
in the least squares sense.• I
minimizes the integral: ,
2 2
2
xG
yy G I
x G I
I G
I F
F I , G dxdy
y G x
G y
I x
I
x y
2 2 2
2 Poisson
equation
Solve
y G x
G y
I x
I
x y
2 2 2
2
) 1 ,
( )
, ( )
, 1 (
) ,
( x y G x y G x y G x y
G
x x y y) , ( 4 )
1 ,
( )
1 ,
( )
, 1 (
) , 1
( x y I x y I x y I x y I x y
I
.. 1 … 1 -4 1 … 1 ..
I
Solving Poisson equation
• No analytical solution
• Multigrid method
• Conjugate gradient method
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
Attenuation
gradient magnitude
log(Luminance) attenuation map
) 1
, ) (
, (
k x y Hkx y
H
10. 8 . 0
~
Multiscale gradient attenuation
interpolate
interpolate
X =
X =
Final gradient attenuation map
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
Bilateral
[Durand et al.]
Photographic [Reinhard et al.]
Gradient domain [Fattal et al.]
Informal comparison
Informal comparison
Bilateral
[Durand et al.]
Photographic [Reinhard et al.]
Gradient domain [Fattal et al.]
Bilateral
[Durand et al.]
Photographic [Reinhard et al.]
Gradient domain [Fattal et al.]
Informal comparison
Evaluation of Tone Mapping
Operators using a High Dynamic Range Display
Patrick Ledda Alan Chalmers Tom Troscinko Helge Seetzen
SIGGRAPH 2005
Six operators
• H: histogram adjustment
• B: bilateral filter
• P: photographic reproduction
• I: iCAM
• L: logarithm mapping
• A: local eye adaption
23 scenes
Experiment setting
HDR display tonemapping
result tonemapping
result
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)
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.
Overall similarity
• Scene 8
Summary
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.
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.