the reason tone curves are the way they are. tone curves in a common imaging chain
TRANSCRIPT
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The Reason Tone CurvesAre The Way They Are
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Tone Curves in a common imaging chain.
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An Example Goal: Make the Monitor luminance, L, directly proportional to original scene intensity, I.
Light, I
pixel value, P
Luminance, L
Lmax = 500 lux
L
I00
Lmax
Iw
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Solution #1: The linear camera and monitor
wI
I255P ⋅=
255
PLL max⋅=
w
max
I
LIL ⋅=
L
I00
Lmax
Iw
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Problems: 1. Half the amount of light does not LOOK like half the light. 2. Non-uniform in PERCEPTUAL Sampling of the gray scale. (An 8 bit gray scale allows only 256 samples.)
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Original Linear Transformation
M M2
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0 2000 4000 6000 80000
50%
100%
E(Eye Perceptionof Brightness)
10000
Lux Illumination
WhitePaper
Mid-tonegray card
18% Reflectance
White
Black
bã
wI
I100%E ⎟⎟
⎠
⎞⎜⎜⎝
⎛⋅=
For the eye adapted tobright conditions, b=0.4
Tone response of human vision
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0 2000 4000 6000 80000
128
255
PPixel Value
10000
Lux Illumination
WhitePaper
Mid-tonegray card
18% Reflectance
White
Black
cã
wI
I255P ⎟⎟
⎠
⎞⎜⎜⎝
⎛⋅=
Set camera contrastc=0.4
The Camera TTF
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0 128 2550
200
400
Invert the process in the monitor
PPixel Value
MonitorLuminance
Lmax
c1
max 255P
LL ⎟⎠
⎞⎜⎝
⎛⋅=
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Solution #2: The gamma-corrected camera and monitor
w
max
I
LIL ⋅=
L
I00
Lmax
Iw
c1
max 255P
LL ⎟⎠
⎞⎜⎝
⎛⋅=
cã
wI
I255P ⎟⎟
⎠
⎞⎜⎜⎝
⎛⋅=
The Same linear relationship, but nowsampled evenly in terms of perception.
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Solution #1: The linear camera and monitor
w
max
I
LIL ⋅=
L
I00
Lmax
Iw
c1
max 255P
LL ⎟⎠
⎞⎜⎝
⎛⋅=
cã
wI
I255P ⎟⎟
⎠
⎞⎜⎜⎝
⎛⋅=
This is good enough for most ordinary applications.However, if higher quality color reproduction is required (photographic quality)then better color management is required. Thistypically involves calibrating the monitor to a specific tone curve SUCH AS the one shown above. Then modifications of the pixel values are made before sending them to the monitor.
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We assumed our eyes would work the sameway when viewing a monitor and whenviewing the original scene. This often is not true.
Light, I
pixel value, P
Luminance, L
Iw = 10,000 lux
L
I00
Lmax
Iw
00
Perception ofMonitorBrightness
Perception ofOriginalBrightness
white
white
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0
50%
100%
EBrightnessPerception
10000
Lux IlluminationWhitePaper
0
Mid-tonegray card
18% Reflectance
White
Black0
50%
100%
EBrightnessPerception
500
Lux IlluminationWhitePaper
0
Mid-tonegray card
18% Reflectance
White
Black
We assumed the same response under both conditions.This turns out to be an incorrect assumption.
Original Outdoor Scene Monitor, office viewing
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0
50%
100%
EBrightnessPerception
10000
Lux IlluminationWhitePaper
0
Mid-tonegray card
18% Reflectance
White
Black
Original Outdoor Scene
The gamma of the eye decreases as the surrounding light decreases.
EBrightnessPerception
Lux IlluminationWhitePaper11% Reflectance
White
Black
Monitor, office viewing
0
50%
100%
5000
Mid-tonegray card
eye 0.4 eye 0.32
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Our original goal is NOTwhat we really want.
Light, I
Iw = 10,000 lux
pixel value, P
Luminance, L0
0
Perception ofMonitorBrightness
Perception ofOriginalBrightness
white
white
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A Gamma correction is requiredto adjust for the the adaptationof vision.Light, I
Iw = 10,000 lux
pixel value, P
Luminance, L0
0
Perception ofMonitorBrightness
Perception ofOriginalBrightness
white
white
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Light, I
Iw = 10,000 lux
pixel value, Pc
Luminance, L
pixel value, Pm
00
Perception ofMonitorBrightness
Perception ofOriginalBrightness
white
white
This Gamma correction is typically applied in software.
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The Gamma correction is typically applied in software.
00
Perception ofMonitorBrightness
Perception ofOriginalBrightness
white
white
00
Pm
Pc
255
255ã
cm 255
P255P ⎟
⎠
⎞⎜⎝
⎛⋅=
Light, I
Iw = 10,000 lux
pixel value, Pc
Luminance, L
pixel value, Pm
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The Gamma correction is typically applied in software.
00
Pm
Pc
255
255
Vision adapted toOutdoor Sun LightOffice LightMovie Theater
Use 1.001.251.50
R.W.G. Hunt, "The Reproduction of Colour", Fountain Press, England, p. 56, 1987
ã
cm 255
P255P ⎟
⎠
⎞⎜⎝
⎛⋅=
Light, I
Iw = 10,000 lux
pixel value, Pc
Luminance, L
pixel value, Pm
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ã
cm 255
P255P ⎟
⎠
⎞⎜⎝
⎛⋅=
Summary:
The system requires threebasic tone curves.
c1
mmax 255
PLL ⎟
⎠
⎞⎜⎝
⎛⋅=
cã
wc I
I255P ⎟⎟
⎠
⎞⎜⎜⎝
⎛⋅=Camera
Monitor
Processor
Light, I
Iw = 10,000 lux
pixel value, Pc
Luminance, L
pixel value, Pm
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cã
wc I
I255P ⎟⎟
⎠
⎞⎜⎜⎝
⎛⋅=
Another Parametric Model of the Tone Function
( )⎥⎥⎦
⎤
⎢⎢⎣
⎡⎟⎟⎠
⎞⎜⎜⎝
⎛⋅=
cã
wc I
I255LogPLog
( ) ( )255LogI
ILogãPLog
wcc +⎟⎟
⎠
⎞⎜⎜⎝
⎛⋅=
Gamma as a power
Gamma as a slope
take the log:
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Other Parametric Models of Tone Functions
( ) ( )255LogI
ILogãPLog
wcc +⎟⎟
⎠
⎞⎜⎜⎝
⎛⋅=
Gamma as a slope
By analogy, "gamma" is often defined as the slope of the TTF
( ) ⎟⎠
⎞⎜⎝
⎛=dx
dyxã
Input Variable, x
OutputVariable
y
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For a constant slope:
"gamma" is the Contrast metric,also called the Window metric.
⎟⎠
⎞⎜⎝
⎛ΔΔ
=x
yã
Input Variable, x
OutputVariable
y
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Slope Called Window
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Slope Called Window
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Gamma, or the slope of the TTF, not only controls the perception of contrast, it also influencesresolution and noise
⎟⎠
⎞⎜⎝
⎛ΔΔ
=x
yã
Input Variable, x
OutputVariable
y
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Resolution is influenced by contrast
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Noise is also influenced by contrast
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Summary:
Reasons for Controlling the Tone Transfer Function:
1. Efficient sampling of an 8 bit gray scale
2. Color reproduction
3. Control of resolution
4. Control of noise