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Theoretical and Practical Limits to Wide Color Gamut Imaging in Objects, Reproducers, and Cameras

Theoretical and Practical Limits to Wide Color Gamut Imaging in Objects, Reproducers, and Cameras. Wayne Bretl Presented at SMPTE Fall Conference October 2011. Gamut Limitations. Object surface-color limits Covered in textbooks and the paper accompanying this presentation

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Theoretical and Practical Limits to Wide Color Gamut Imaging in Objects, Reproducers, and Cameras

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  1. Theoretical and Practical Limits to Wide Color Gamut Imaging in Objects, Reproducers, and Cameras Wayne Bretl Presented at SMPTE Fall Conference October 2011

  2. GamutLimitations • 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

  3. 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

  4. 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

  5. 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?

  6. A Perfect Camera Camera = sensor + transformation Perfect Camera 3X3 LINEAR MATRIX Camera = Perfect Camera if: sensor + transformation = Standard Observer

  7. 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 Gaussian Spectrum +/- 40 nm GaussianSpectrum +/- 40 nm Gaussian and single wavelength cannot be distinguished single wavelength Gaussian test spectra with various widths and center wavelengths , as seen / differentiated by a perfect camera. Can practical cameras differentiate these object spectra? Note: Wide L-cone response also explains cyan limits in 3-color additive reproductionandlack of highly saturated cyan surface colors

  8. How Are the Spectral Responses and the Spectral Locus Related ? Example – Standard Observer (Wide L Response) High L response pulls the locus toward red Single WavelengthInput LINEAR TRANSFORM Simultaneously decreasing L and increasing S make the spectral locus curved, even though the transform is linear

  9. How Are the Spectral Responses and the Spectral Locus Related ? Example – Narrow L Response Hypothetical narrow L response Spectral locus straight line as L and M vary Spectral locus straight line as M and S vary LINEAR TRANSFORM L and S do not overlap The reported spectral locus is triangular because only two sensor outputs vary at once

  10. How Are the Spectral Responses and the Spectral Locus Related ? Example – Narrow L Response Hypothetical 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)

  11. Consequences for Saturated Cyan Colors Example – Narrow L Response Eyeball single wavelength Hypothetical narrow L response Eyeball Gaussian spectrum LINEAR TRANSFORM Camera single wavelength or Gaussian Spectra that look different to the eye cannot be distinguished by this camera

  12. Before Going Further: Does Camera Gamut Exist? (Yes!) MIXTURE REPORTED HERE REPORTED HERE CAMERA GAMUT (LIMIT OF REPORTABLE COLORS) = CONVEX ENVELOPE ENCLOSING THE SPECTRAL LOCUS HOLM’S* EXAMPLE: (solid green line)SPECTRAL LOCUS REPORTED BY A PRACTICAL SENSOR/TRANSFORM PAIR INPUT HERE 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 *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

  13. 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

  14. Four Imperfect Cameras Digital still camera with narrow responses Transparency film with very narrow responses Digital still camera with overlapping responses Prismatic optics(TV) camera

  15. 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)

  16. 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

  17. Digital Still Camera with Narrow Responses Spectral Responses Result A Camera reported spectral locus B Matrix Cyan edge is straight line in region of constant R response. C Eyeball spectral locus C B A Points A, B, C show how the spectral gamut is related to the spectral responses. Color chart results Eye Camera Pointer’s surface colors limit Test chart is reasonably accurate, but spectrum is not.

  18. Digital Still Camera with Narrow Responses The linear matrix scales and/or rotates everything in the chromaticity plot A A Camera reported spectral locus Camera reported spectral locus B B Matrix Greater coverage of the visual gamut, but all colors are distorted C C C B A Points A, B, C show how the spectral gamut is related to the spectral responses. Color chart results Eye Camera Color chart results Eye Camera

  19. Digital Still Camera with Narrow Responses Net effect on camera gamut: Real colors that never can be reported Unreal colors that may be reported

  20. Transparency Film Sensitivities Transparency Film Sensitivities - Combined with Hypothetical Linear Matrix Many wavelengths are reported as the same color IT-8 Test Chart Gamut Reported spectral locus is triangular due to non-overlapping R and B responses. 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 Note: Camera gamut includes gamut of IT8 test chart produced on this material.

  21. What’s Going On? Why Is the Film Gamut Apparently So Limited in Green and Cyan? • 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.

  22. 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

  23. TV Camera with Linear Matrix (Display is assumed not to limit the gamut) 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.

  24. 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 spectra • Variable bandwidth, with fixed center wavelength • Variable center wavelength, with fixed bandwidth • Variable bandwidth and center wavelength

  25. 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

  26. Narrow-Response Camera Variable Bandwidth (Saturation) Series Colors outside the camera gamut 510 nm Must be reported somewhere inside the camera gamut Poor candidate for expansion by non-linear transform, because highly-saturated colors compress up against the spectral locus. 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

  27. Transparency Film Saturation/Hue Compression Variable Bandwidth (Saturation) Series: Sigma = 10, 25, 35, 45, 60, 80, 120 nmAnimation: Center = 510 to 570 nm in 10 nm steps 510 nm Multiple center wavelengths are compressed strongly toward the corners of the reported gamut. Multiple saturation levels are compressed strongly onto the reported spectral locus 570 nm Poor candidate for non-linear correction

  28. Overlapping Response Camera Compression Variable Bandwidth (Saturation) Series: Sigma = 10, 25, 35, 45, 60, 80, 120 nmAnimation: Center = 510 to 570 nm in 10 nm steps Different wavelengths reported as different points 510 nm 570 nm Different wavelengths are not compressed as strongly towards the “corners” of the reported gamut as with non-overlapping responses; however, some saturation compression is present Some non-linear correction may be possible.

  29. Prism Optics Camera Variable Bandwidth (Saturation) Series 510 nm 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

  30. 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

  31. Narrow-Response Camera Good hue discrimination, poor saturation discrimination –not a good candidate for non-linear saturation correction; hue correction is possible Difference between single wavelength and Gaussian spectrum (eyeball) Gaussian spectra with different center wavelengths are separated from each other 40 nm colors (eyeball) Reported Difference between single wavelength and Gaussian spectrum (camera) Reported 40 nm colors (camera)

  32. Transparency Film Difference (eyeball) Strong compression onto spectral locus, plus compression of colors towards corners. Poor candidate for expansion by non-linear transform Reported difference (camera)

  33. Overlapping Response Camera Difference (eyeball) Some expansion by non-linear transform may be possible due to distance between reported 40 nm locus and reported spectral locus. Reported difference (camera)

  34. Prism Optics Camera Difference (eyeball) 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. Reported difference (camera)

  35. Variable Wavelength and Bandwidth • Over-all indication of compression of colors to the inside of the camera gamut Chromaticities ofGaussian Spectra with Standard Observer

  36. Narrow-Response Camera Strong compression onto spectral locus - poor candidate for expansion by non-linear transform. StandardObserver

  37. Transparency Film Strong compression onto spectral locus - poor candidate for expansion by non-linear transform. StandardObserver

  38. 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. StandardObserver

  39. 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. StandardObserver

  40. Thoughts About Camera Gamut - Consider: How Big a Gamut is Needed? • Object colors and reproducer gamuts are somewhat limited Three-Color AdditiveReproduction Three-Color SubtractiveReproduction 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

  41. 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?

  42. 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

  43. 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

  44. Thank You wayne.bretl@ieee.org

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