1. The Reason Tone Curves Are The Way They Are

2. Tone Curves in a common imaging chain.

3. An Example Goal: Make the Monitor luminance, L, directly proportional to original scene intensity, I. Light, I pixel value, P Luminance, L L max = 500 lux L I 0 0 L max IwIw

4. Solution #1: The linear camera and monitor L I 0 0 L max IwIw

5. 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.)

6. OriginalLinear Transformation

7. 02000400060008000 0 50% 100% E (Eye Perception of Brightness) 10000 Lux Illumination White Paper Mid-tone gray card 18% Reflectance White Black For the eye adapted to bright conditions,  b =0.4 Tone response of human vision

8. 02000400060008000 0 128 255 P Pixel Value 10000 Lux Illumination White Paper Mid-tone gray card 18% Reflectance White Black Set camera contrast  c =0.4 The Camera TTF

9. 0 128255 0 200 400 Invert the process in the monitor P Pixel Value Monitor Luminance L max

10. Solution #2: The gamma-corrected camera and monitor L I 0 0 L max IwIw The Same linear relationship, but now sampled evenly in terms of perception.

11. Solution #1: The linear camera and monitor L I 0 0 L max IwIw This is good enough for most ordinary applications. However, if higher quality color reproduction is required (photographic quality) then better color management is required. This typically 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.

12. We assumed our eyes would work the same way when viewing a monitor and when viewing the original scene. This often is not true. Light, I pixel value, P Luminance, L I w = 10,000 lux L I 0 0 L max IwIw 0 0 Perception of Monitor Brightness Perception of Original Brightness white

13. 0 50% 100% E Brightness Perception 10000 Lux Illumination White Paper 0 Mid-tone gray card 18% Reflectance White Black 0 50% 100% E Brightness Perception 500 Lux Illumination White Paper 0 Mid-tone gray card 18% Reflectance White Black We assumed the same response under both conditions. This turns out to be an incorrect assumption. Original Outdoor SceneMonitor, office viewing

14. 0 50% 100% E Brightness Perception 10000 Lux Illumination White Paper 0 Mid-tone gray card 18% Reflectance White Black Original Outdoor Scene The gamma of the eye decreases as the surrounding light decreases. E Brightness Perception Lux Illumination White Paper 11% Reflectance White Black Monitor, office viewing 0 50% 100% 500 0 Mid-tone gray card eye  0.4 eye  0.32

15. Our original goal is NOT what we really want. Light, I I w = 10,000 lux pixel value, P Luminance, L 0 0 Perception of Monitor Brightness Perception of Original Brightness white

16. A Gamma correction is required to adjust for the the adaptation of vision. Light, I I w = 10,000 lux pixel value, P Luminance, L 0 0 Perception of Monitor Brightness Perception of Original Brightness white

17. Light, I I w = 10,000 lux pixel value, P c Luminance, L pixel value, P m 0 0 Perception of Monitor Brightness Perception of Original Brightness white This Gamma correction is typically applied in software.

18. The Gamma correction is typically applied in software. 0 0 Perception of Monitor Brightness Perception of Original Brightness white 0 0 PmPm PcPc 255 Light, I I w = 10,000 lux pixel value, P c Luminance, L pixel value, P m

19. The Gamma correction is typically applied in software. 0 0 PmPm PcPc 255 Vision adapted to Outdoor Sun Light Office Light Movie Theater Use  1.00 1.25 1.50 R.W.G. Hunt, "The Reproduction of Colour", Fountain Press, England, p. 56, 1987 Light, I I w = 10,000 lux pixel value, P c Luminance, L pixel value, P m

20. Summary: The system requires three basic tone curves. Camera Monitor Processor Light, I I w = 10,000 lux pixel value, P c Luminance, L pixel value, P m

21. Another Parametric Model of the Tone Function Gamma as a power Gamma as a slope take the log:

22. Other Parametric Models of Tone Functions Gamma as a slope By analogy, "gamma" is often defined as the slope of the TTF Input Variable, x Output Variable y

23. For a constant slope: "gamma" is the Contrast metric, also called the Window metric. Input Variable, x Output Variable y

24. Slope Called Window

26. Gamma, or the slope of the TTF, not only controls the perception of contrast, it also influences resolution and noise Input Variable, x Output Variable y

27. Resolution is influenced by contrast

28. Noise is also influenced by contrast

29. 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