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Theoretical and Practical Limits to Wide Color Gamut Imaging in Objects,
Reproducers, and Cameras
Wayne BretlPresented at SMPTE Fall Conference October 2011
Gamut Limitations
• Object surface-color limits– Covered in textbooks and the paper accompanying this presentation
• Reproducer gamut limits– Covered thoroughly in textbooks
• Camera Limits– Less understood – Focus of this presentation
Can Imperfect Cameras be Perfected?
• Questions:– Do practical cameras cover the full visual gamut?
• Can they cover the full visual gamut?• Should they cover the full visual gamut?
• Explore with Gaussian test spectra
Approach to the Question
• Compare the eye/perfect camera to practical cameras• Explore the color space with Gaussian spectra of varying bandwidth and center wavelength that the eye
can readily distinguishand compare practical camera responses to the ideal
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Wavelength, nm
40 nm Gaussian Spectra
40 nm
Visible Spectrum
What the Perfect Camera Does
• Reports the same color (X, Y, Z) as the Standard Observer for any object spectrum
• This happens if the camera spectral sensitivities are linear transforms of the Standard Observer
– but what if they aren’t?
A Perfect Camera
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Cone Responses
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Wavelength, nm
Standard Observer
xbar
ybar
zbar
3X3 LINEAR MATRIX
Camera = sensor + transformation
Camera = Perfect Camera if: sensor + transformation = Standard Observer
Perfect Camera
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Cone Responses
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A Perfect Camera Viewing Gaussian Test Spectra
• Chromaticities of Gaussian Spectra:– The spectral locus is the extreme case of infinitesimal bandwidth– For a finite bandwidth, saturation reduced in cyan due to wide L-cone response
Note: Wide L-cone response also explains cyan limits in 3-color additive reproduction and lack of highly saturated cyan surface colors
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Chromaticities of Gaussian Spectra
10 nm20 nm30 nm40 nm50 nm70 nm110 nm
GaussianSpectrum+/- 40 nm
Gaussian test spectra with various widths and center wavelengths , as seen / differentiated by a perfect camera. Can practical cameras differentiate these object spectra?
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Wavelength, nm
40 nm Gaussian Spectra
40 nm
Visible Spectrum
Gaussian Spectrum+/- 40 nm
Gaussian and single wavelength
cannot be distinguishedsingle wavelength
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Cone Responses
L
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How Are the Spectral Responses and the Spectral Locus Related ?
High L response pulls the locus toward red
Simultaneously decreasing L and increasing S make the spectral locus curved, even though the transform is linear
Single WavelengthInput
Example – Standard Observer (Wide L Response)
LINEAR TRANSFORM
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Wavelength, nm
Cone Responses
M S
L and S do not overlap
Hypothetical narrow L response
How Are the Spectral Responses and the Spectral Locus Related ?
Example – Narrow L Response
LINEAR TRANSFORM
The reported spectral locus is triangular because only two sensor outputs vary at once
Spectral locus straight line as L and M vary
Spectral locus straight line as M
and S vary
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Wavelength, nm
Cone Responses
M S
Hypothetical narrow L response
How Are the Spectral Responses and the Spectral Locus Related ?
Example – Narrow L Response
LINEAR TRANSFORM
Note that evenly-spaced wavelengths produce unevenly spaced chromaticities due to the shapes of the response curves (even though the transform process is linear)
Note that evenly-spaced wavelengths produce unevenly spaced chromaticities due to the shapes of the response curves (even though the transform process is linear)
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Wavelength, nm
Cone Responses
M S
Hypothetical narrow L response
Consequences for Saturated Cyan Colors
Example – Narrow L Response
LINEAR TRANSFORM
Spectra that look different to the eye cannot be distinguished by this camera
Eyeball single wavelength
Eyeball Gaussian spectrum
Camera single wavelength or
Gaussian
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Canon 20D
Before Going Further: Does Camera Gamut Exist? (Yes!)
*Jack Holm, “Capture Color Analysis Gamuts,” Fourteenth Color Imaging Conference: Color Science and Engineering Systems, Technologies, Applications, Scottsdale, Arizona; November 2006; p. 108-113; ISBN / ISSN: 0-89208-291-7 http://www.color.org/documents/CaptureColorAnalysisGamuts.pdfhttp://www.color.org/documents/CaptureColorAnalysisGamuts_ppt.pdf
HOLM’S* EXAMPLE:(solid green line)SPECTRAL LOCUS REPORTED BY A PRACTICAL SENSOR/TRANSFORM PAIR
CAMERA GAMUT (LIMIT OF REPORTABLE COLORS) = CONVEX ENVELOPE ENCLOSING THE SPECTRAL LOCUS
Note: the TRANSFORM used is linear, and determined by best fit to important object colors and/or most pleasing results
EXAMPLE:MIX TWO WAVELENGTHS
INPUT HERE REPORTED HERE
MIXTURE REPORTED HERE
INPUT HERE
REPORTED HERE
Comparisons of Four Imperfect Cameras
• Spectral responses of practical devices – narrower responses than the Standard Observer (especially, narrow Red response)
• Different linear 3x3 matrix transform for each sensor – optimized for best fit to SMPTE 303 color test chart
Four Imperfect Cameras
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Canon 20d Spectral Response
R G B
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K200 Spectral Response
R G
B
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Canon 50d Spectral Response
R G B
Digital still camera with narrow responses
Transparency film with very narrow responses
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Prismatic Optics Spectral Response
R G B
Prismatic optics(TV) camera
Digital still camera with overlapping responses
Outline of Discussion
• Results for SMPTE 303 color test chart and the reported spectral locus
• Results for Gaussian spectra– Discussion: possibilities for using non-linear transforms
(a camera “profile”, look-up table, or non-linear matrix)
Test Chart and Spectral Locus
• Results for the test chart and the reported spectral locus (i.e., locus for single wavelengths), when optimized for the test chart
• Also: Relationship between the camera spectral response and the reported spectral locus
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Canon 20d Reported Spectral Locus and Pointer's Surface Color Gamut
Color chart
camera
Spectral locus
Pointer's surface colors
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Canon 20d Spectral Response
R G B
Digital Still Camera with Narrow Responses
AB
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B
Points A, B, C show how the spectral gamut is related to the spectral responses.
Cyan edge is straight line in region of constant R response.
Color chart resultsEye Camera
Eyeballspectral locus
Camera reportedspectral locus
Pointer’s surface colors limit
Test chart is reasonably accurate, but spectrum is not.
C
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R G B (D65)X= 0.68 0.24 0.04 0.95Y= 0.32 0.85 -0.17 1.00Z= 0.08 -0.20 1.21 1.09
Spectral Responses
Matrix
Result
R G B (D65)X= 0.68 0.24 0.04 0.95Y= 0.32 0.85 -0.17 1.00Z= 0.08 -0.20 1.21 1.09
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Canon 20d Reported Spectral Locus and Pointer's Surface Color Gamut
Color chart
camera
Spectral locus
Pointer's surface colors
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Canon 20d Spectral Response
R G B
Digital Still Camera with Narrow Responses
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Points A, B, C show how the spectral gamut is related to the spectral responses.
Camera reportedspectral locus
C
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Matrix
Color chart resultsEye Camera
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Canon 20d Reported Spectral Locus and Pointer's Surface Color Gamut
Color chart
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Spectral locus
Pointer's surface colors
Camera reportedspectral locus
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Color chart resultsEye Camera
R G B (D65)X= 0.95 0.00 0.00 0.95Y= 0.27 0.91 -0.18 1.00Z= -0.12 0.00 1.21 1.09
The linear matrix scales and/or rotates everything in the chromaticity plot
Greater coverage of the visual gamut, but all colors are distorted
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Canon 20d Reported Spectral Locus and Pointer's Surface Color Gamut
Color chart
camera
Spectral locus
Pointer's surface colors
Digital Still Camera with Narrow Responses
Real colors that never can be reported
Unreal colors that may be
reported
Net effect on camera gamut:
Transparency Film Sensitivities
Note: Camera gamut includes gamut of IT8 test chart produced on this material.
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K200 Spectral Response
R G
B
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K200 Camera Reported Spectral Locus and Pointer's Surface Color Gamut
Color chart
camera
Spectral locus
Pointer's surface colors
Kodachrome IT-8
Transparency Film Sensitivities - Combined with Hypothetical Linear Matrix
IT-8 Test Chart Gamut
R G B (D65)X= 0.46 0.44 0.05 0.95Y= 0.21 0.82 -0.03 1.00Z= -0.04 0.10 1.04 1.09
Many wavelengths are reported as the same color
Full analysis would include non-linearities, interlayer effects and the effects of the reproducing dyes – producing an effective matrix different from the optimum linear matrix
Reported spectral locus is triangular due to non-overlapping R and B responses.
What’s Going On?
• Traditional imaging (film, lithography) does not offer an accessible transform matrix• Narrow spectral sensitivities are used deliberately, to increase the reported saturation of
ordinary test objects with relatively broad spectra. – This compensates for the limited saturation of the dyes/inks (which are equivalent to a built-in
transform matrix with small coefficients)
• The result (not usually noted in the past): the system cannot distinguish between medium-high-saturation and very-high-saturation blue-greens. – (But the latter are uncommon in objects anyway.)
• This study assumes colorimetric accuracy for the test chart is desired. – Complete film systems are designed for increased contrast and saturation
• Compensates color appearance effects, provides preferred reproduction
• The limitations on sensing the differences between highly saturated object colors still exist when the output contrast and saturation are increased.
Why Is the Film Gamut Apparently So Limited in Green and Cyan?
Digital Still Camera with Wider, Overlapping Responses
Nose of the reported spectral curve is rounded due to overlap of R and B responses.
Cyan and yellow edges are slightly curved
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Canon 50d Spectral Response
R G B
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Canon 50d Reported Spectral Locus and Pointer's Surface Color Gamut
Color chart
camera
Spectral locus
Pointer's surface colors
R G B (D65)X= 0.88 -0.07 0.14 0.95Y= 0.38 0.86 -0.24 1.00Z= 0.01 -0.43 1.51 1.09
TV Camera with Linear Matrix
Reported spectral locus is triangular due to non-overlapping R and B responses.
Similar to film, but requires larger matrix coefficients and therefore covers a larger gamut.
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Prismatic Optics Spectral Response
R G B
(Display is assumed not to limit the gamut)
R G B (D65)X= 0.58 0.23 0.14 0.95Y= 0.29 0.73 -0.02 1.00Z= -0.01 0.03 1.07 1.09
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Prismatic Optics Camera Reported Spectral Locus and Pointer's Surface Color Gamut
Color chart
camera
Spectral locus
Pointer's surface colors
Results for Gaussian Spectra
• The preceding slides showed results for color test chart chips (good results due to matrix design) and single-wavelength spectra (results not so good)
• Need to know what happens for intermediate cases – how does a practical camera differentiate among saturated colors:– Hard limiting or gradual distortion? – Can distortions be corrected?
• Use Gaussian spectra1. Variable bandwidth, with fixed center wavelength2. Variable center wavelength, with fixed bandwidth3. Variable bandwidth and center wavelength
1. Variable Spectral Bandwidth (Saturation)
• 510 nm center wavelength with variable bandwidth• Standard deviation (sigma):
1, 10, 25, 35, 45, 60, 80, 120 nm • Look for:
– Saturation distortion– Hue Distortion
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Canon 20d Gaussian Spectra Bandwidth Series
Spectral locus
Gaussian spectra, center = 510 nm
Canon 20d
Narrow-Response Camera
Poor candidate for expansion by non-linear transform, because highly-saturated colors compress up against the spectral locus.
510 nm
How does this linear system produce such non-linear looking results?
It’s due to the varying widths of the object spectra being multiplied by the curved shapes of the spectral responses
Variable Bandwidth (Saturation) SeriesColors outside the camera
gamut
Must be reported somewhere inside the camera gamut
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K200 Gaussian Spectra Bandwidth Series
Spectral gamut
Gaussian spectra
K200
Transparency Film Saturation/Hue Compression
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K200 Gaussian Spectra Bandwidth Series
Spectral gamut
Gaussian spectra
K200
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K200 Gaussian Spectra Bandwidth Series
Spectral gamut
Gaussian spectra
K200
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K200 Gaussian Spectra Bandwidth Series
Spectral gamut
Gaussian spectra
K200
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K200 Gaussian Spectra Bandwidth Series
Spectral gamut
Gaussian spectra
K200
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K200 Gaussian Spectra Bandwidth Series
Spectral gamut
Gaussian spectra
K200
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K200 Gaussian Spectra Bandwidth Series
Spectral gamut
Gaussian spectra
K200510 nm
570 nm
Multiple saturation levels are compressed strongly onto the reported spectral locus
Variable Bandwidth (Saturation) Series: Sigma = 10, 25, 35, 45, 60, 80, 120 nmAnimation: Center = 510 to 570 nm in 10 nm steps
Multiple center wavelengths are compressed strongly toward the corners of the reported gamut.
Poor candidate for non-linear correction
Overlapping Response Camera Compression
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Canon 50d Gaussian Spectra Bandwidth Series
Spectral gamut
Gaussian spectra
Canon 50d
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Canon 50d Gaussian Spectra Bandwidth Series
Spectral gamut
Gaussian spectra
Canon 50d
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Canon 50d Gaussian Spectra Bandwidth Series
Spectral gamut
Gaussian spectra
Canon 50d
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Canon 50d Gaussian Spectra Bandwidth Series
Spectral gamut
Gaussian spectra
Canon 50d
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Canon 50d Gaussian Spectra Bandwidth Series
Spectral gamut
Gaussian spectra
Canon 50d
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Canon 50d Gaussian Spectra Bandwidth Series
Spectral gamut
Gaussian spectra
Canon 50d
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Canon 50d Gaussian Spectra Bandwidth Series
Spectral gamut
Gaussian spectra
Canon 50d510 nm
570 nmDifferent wavelengths are not compressed as strongly towards the “corners” of the reported gamut as with non-overlapping responses; however, some saturation compression is present
Variable Bandwidth (Saturation) Series: Sigma = 10, 25, 35, 45, 60, 80, 120 nmAnimation: Center = 510 to 570 nm in 10 nm steps
Some non-linear correction may be possible.
Different wavelengths reported as
different points
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Prismatic Optics Camera Gaussian Spectra Bandwidth Series
Spectral locus
Gaussian spectra, center = 510 nm, sigma = 1 nm to 110 nm
Prismatic camera
Prism Optics Camera
Poor candidate for expansion by non-linear transform, because more saturated colors show strong hue shift and concentration towards the corners of the triangular reported gamut
510 nm
Variable Bandwidth (Saturation) Series
2. Variable Center Wavelength
• Sigma = 40 nm with variable center wavelength• 40 nm series encloses the Pointer colors• Observe:
– Compression onto the reported spectral locus– Distance between 40-nm locus and spectral locus indicates variation
available for non-linear gamut expansion
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Canon 20d 40 nm Gaussian Spectra
Spectral locus
40nm
40 nm reported
Narrow-Response Camera
Difference between
single wavelength
and Gaussian spectrum (eyeball)
40 nm colors (eyeball) Reported
Difference between single wavelength and
Gaussian spectrum (camera)
Reported 40 nm colors (camera)
Gaussian spectra with different center wavelengths are separated from each other
Good hue discrimination, poor saturation discrimination –not a good candidate for non-linear saturation correction; hue correction is possible
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0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
y
x
K200 40 nm Gaussian Spectra
Spectral locus
40nm
40 nm reported
Transparency Film
Strong compression onto spectral locus, plus compression of colors towards corners. Poor candidate for expansion by non-linear transform
Difference (eyeball)
Reported difference (camera)
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
y
x
Canon 50d 40 nm Gaussian Spectra
Spectral locus
40nm
40 nm reported
Overlapping Response Camera
Some expansion by non-linear transform may be possible due to distance between reported 40 nm locus and reported spectral locus.
Difference (eyeball)
Reported difference (camera)
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
y
x
Prismatic Optics Camera 40 nm Gaussian Spectra
Spectral locus
40nm
40 nm reported
Pointer's surface colors
Prism Optics Camera
Strong hue distortion and/or compression onto spectral locus. Poor candidate for expansion by non-linear transform.Note, however, that most of Pointer’s colors are covered without expansion.
Difference (eyeball)
Reported difference (camera)
3. Variable Wavelength and Bandwidth
• Over-all indication of compression of colors to the inside of the camera gamut
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
y
x
Chromaticities of Gaussian Spectra
10 nm20 nm30 nm40 nm50 nm70 nm110 nmChromaticities of
Gaussian Spectra with Standard Observer
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
y
x
Canon 20dReported Chromaticities of Gaussian Spectra
10 nm
20 nm
30 nm
40 nm
50 nm
70 nm
110 nm
Spectral locus
Narrow-Response Camera
Strong compression onto spectral locus - poor candidate for expansion by non-linear transform.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
y
x
Chromaticities of Gaussian Spectra
10 nm20 nm30 nm40 nm50 nm70 nm110 nm
StandardObserver
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
y
x
K200Reported Chromaticities of Gaussian Spectra
10 nm
20 nm
30 nm
40 nm
50 nm
70 nm
110 nm
Spectral locus
Transparency Film
Strong compression onto spectral locus - poor candidate for expansion by non-linear transform.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
y
x
Chromaticities of Gaussian Spectra
10 nm20 nm30 nm40 nm50 nm70 nm110 nm
StandardObserver
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
y
x
Canon 50dReported Chromaticities of Gaussian Spectra
10 nm
20 nm
30 nm
40 nm
50 nm
70 nm
110 nm
Spectral locus
Overlapping Response Camera
Some compression onto spectral locus - candidate for expansion by non-linear transform down to sigma = approx. 30 nm?Note Pointer’s colors are covered without expansion.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
y
x
Chromaticities of Gaussian Spectra
10 nm20 nm30 nm40 nm50 nm70 nm110 nm
StandardObserver
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
y
x
Prismatic Optics CameraReported Chromaticities of Gaussian Spectra
10 nm
20 nm
30 nm
40 nm
50 nm
70 nm
110 nm
Spectral locus
Prism Optics Camera
Strong compression onto spectral locus - poor candidate for expansion by non-linear transform.
Note: most of Pointer’s colors are covered without expansion.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
y
x
Chromaticities of Gaussian Spectra
10 nm20 nm30 nm40 nm50 nm70 nm110 nm
StandardObserver
Thoughts About Camera Gamut -
Three-Color SubtractiveReproduction
Three-Color AdditiveReproduction
•Object colors and reproducer gamuts are somewhat limited
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
y
x
Additive Gamuts
sRGB
NTSC
P-3
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
y
x
Transparency IT-8 Targets (5500 K Neutral),
Fuji IT-8
Kodachrome IT-8
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
y
x
Pointer's Surface Colors
Pointer's surface colors
Surface Colors
•The camera may not have to be perfect over the full visual gamut•But also consider that archived material might be used with future wide-gamut systems
Consider: How Big a Gamut is Needed?
Conclusions
• A camera (sensor + transform) typically has a color gamut that limits the cyan scene colors that it can report
• Most cameras have a smaller gamut than the human visual system• Sensors with narrow responses increase the reported saturation of test chart colors but also limit the
gamut of saturated colors that can be reported• Many systems developed in the past had a camera gamut that limited green and cyan saturation, and had
a strong distortion of spectral colors, but were subjectively of very high quality, and were highly successful• Cameras with sufficiently wide responses can have a gamut including Pointer’s surface colors, and
excluding only colors seldom or never encountered in natural scenes:– The spectrum– Lasers– LEDs– Gas discharge tubes?– Back-lit stained glass?– Blue-green Jell-O?
Conclusions
• Gamut expansion (actually distinguishing among saturated colors) is impractical when camera spectral responses are too narrow– Requires impractically strong non-linear correction for chromaticities outside the reported
spectral gamut– Danger of distorting colors of important common objects
• Some gamut expansion may be possible when there is sufficient overlap of the camera spectral responses, but:– Overlapping spectral responses require larger conversion coefficients, increasing colored
noise– Expansion much beyond the reported spectral gamut (by non-linear means) may not be
needed if the reported gamut is sufficiently large• Accurately covering (Pointer’s) surface colors and a bit more is a possible practical
compromise – Combination of some sensor spectral response overlap and some non-linear processing
References
• Holm, Jack, “Capture Color Analysis Gamuts,” Fourteenth Color Imaging Conference: Color Science and Engineering Systems, Technologies, Applications, Scottsdale, Arizona; November 2006; p. 108-113; ISBN / ISSN: 0-89208-291-7 http://www.color.org/documents/CaptureColorAnalysisGamuts.pdfhttp://www.color.org/documents/CaptureColorAnalysisGamuts_ppt.pdf
• Buil, Christian, CANON 40D, 50D, 5D, 5D Mark II Comparison, http://astrosurf.com/buil/50d/test.htm• Eastman Kodak Company Publication no. E-88, Technical Data / Color Reversal Film, Kodachrome 64 and 200 Films, June 2009
http://www.kodak.com/global/en/consumer/products/pdf/e88.pdf• Ballard, Jay, TK-41 prism spectral measurements (private communication)• SMPTE, Standard 0303M-2002, Television – Color Reference Pattern• IT8.7/1 - 1993 (Reaffirmed 2008) Graphic technology - Color transmission target for input scanner calibration• Pointer, M.R., “The gamut of real surface colors”, Color Research and Application, 5, pp. 145–155, 1980.• International Telecommunication Union Radiocommunication Sector, Recommendation ITU-R BT.709-5, “Parameter values for the HDTV standards for
production and international programme exchange,” 2002. http://www.itu.int/dms_pubrec/itu-r/rec/bt/R-REC BT.709-5-200204-I!!PDF-E.pdf• Hunt, R.W.G., The Reproduction of Color, Sixth Edition, John Wiley & Sons Ltd, 2004, reprinted March 2006, Chapters 7 and 9• Ibid., sections 9.4 and 9.5, pp. 132-135• Ibid., section 35.4, pp. 598-599• Ibid., section 2.5, pp. 13-16• Ibid., section 9.2, pp. 126-128
