Understanding Color: Light, Perception, and Gamma Correction

1. Chapter 2: Color Basics

2. What is light? • EM wave, radiation • Visible light has a spectrum wavelength from 400 – 780 nm. • Light can be composed of radiation of various wavelengths. • Light can be described by a spectral power distribution (SPD). wavelength B G R

3. What is color? • Human retina has • 3 types of color photoreceptor cone cells • rod cells (only effective at extremely low light levels, or night-vision). • When light falls on the retina, the 3 types of cone cells response (at different levels) to create the sensation of color. • CIE (Commission Internationale de L’Eclairage) specifies how an SPD can be transformed into tri-stimulus values that specify a color.

4. What is color? • Given 3 primary lights: red, green, and blue, most colors can be described by a triplet RGB. Each value is (linearly) proportional to the physical power (radiance) of a component light. • We call these linear RGB values. R=0.81 G=0.52 B=0.56 R=0.36 G=0.69 B=0.74 R=0.0 G=0.0 B=0.69 R=0.0 G=0.0 B=0.91 R=0.69 G=0.69 B=0.69 R=0.91 G=0.91 B=0.91

5. Gamma • A color CRT has 3 types of phosphors that emit different-colored (RGB) light. • A typical CRT has a non-linear transfer function. That is, the amount of power (luminance) emitted is approximately proportional to the applied voltage (scaled to the range [0,1]) raised to a constant power, commonly called gamma, . • Luminance  Voltage • Typical CRTs have gamma values close to 2.5.

6. Gamma luminance 1 gamma < 1 gamma = 1 gamma > 1 voltage 0 1

7. Gamma luminance 1 gamma < 1 gamma = 1 0.176 gamma > 1 voltage 0 0.5 1

8. Gamma luminance 1 gamma < 1 gamma = 1 gamma > 1 0.031 voltage 0 0.25 1

9. Gamma correction • A camera records the luminance (i.e., radiance) of an object. If the recorded values are translated into a voltage signal, and applied directly to a CRT, the reproduced image will have a distorted luminance. • A typical camera, therefore, applies a gamma correction transfer function. That is, it applies a 1/gamma power function to the recorded RGB values: • R’ = R1/gamma (likewise for G and B) • Note: the RGB values used in the formula are all normalized to the [0,1] range.

10. Gamma (example) as displayed on a CRT without gamma correction original

11. Gamma correction • The gamma corrected values R’G’B’ are distinguished from the original RGB values by the prime notation. They are called non-linear (or gamma corrected) RGB. • When we are processing digital images, the pixel values we are dealing with are usually the non-linear (R’G’B’) values.

12. Gamma correction eye RGB RGB camera gamma correction R’G’B’ computer R’G’B’ CRT x x1/ (x1/) 

13. Lightness • Human vision has a non-linear perceptual response to luminance • e.g., a source having a luminance (power) of 18% of another source appears about half as bright. • The perceptual response to luminance is called lightness. • The transfer function of human perceptual response to luminance resembles (very roughly) a 0.4 power curve, i.e., • Lightness  Luminance0.4

14. Lightness RGB computer R’G’B’ CRT y y (y)0.4 lightness pixel value intensity

15. Lightness • 0.4 * 2.5 = 1.0. Hence, amazingly, the human transfer function is roughly the inverse of that of a CRT. • Recall that the nonlinear R’G’B’ values are (usually) used in a computer as pixel values. • The nonlinear values are used to drive a CRT’s voltage for controlling the brightness of phosphors. • The luminance emitted by a CRT is a 2.5 power curve. • The human vision system has a transfer function of a 0.4 power curve. • Hence, the nonlinear R’G’B’ values are approximately proportional to lightness (a perceptual value).

17. Luminance efficiency • If one looks at 3 light sources: red, green, and blue, each at the same power, then the green source appears the brightest, followed by the red source and then by the blue source. • Human vision system is more sensitive to luminance than to color. A video system usually encodes RGB as 1 luminance component Y’ (or luma) and 2 chrominance components. • The chrominance components are usually given lower bandwidth (or data capacity) than the luminance component.

18. Color differences • Luma (Y’) can be computed as a weighted sum of non-linear R’G’B’ components: (ITU-R Recommendation BT. 601, formerly known as CCIR 601) • Y’ = 0.299R’ + 0.587G’ + 0.114B’ • Color differences refer to color components where (informally) “brightness” is “removed”. • The standard is to subtract luma from non-linear blue, and from non-linear red: • B’-Y’ and R’-Y’ (these are called chroma).

21. Scaling chroma • Various scaling factors are applied to the chroma (B’-Y’, R’-Y’) for different applications: • Y’PBPR – for component analog video • Y’UV – for composite analog video (PAL) • Y’IQ – ditto (NTSC) • Y’CBCR – for digital images and video

22. Y’CBCR • Rec. 601 specifies a range of [16, 235] for Y’ and [16, 240] for CB and CR. • To obtain Y’CBCR from 8-bit R’G’B’ values (i.e., in the range [0, 255]), use the transformation:

23. Chromatic sub-sampling • The CB, CR chroma components are usually sub-sampled to reduce the data requirement in digital images and video. • 4:2:2 sub-sample chroma horizontally by a factor of 2 (Rec. 601). a row of pixels take these chroma values

31. Perceptual uniformity • Human vision responds to about a hundred-to-one contrast ratio. That is, if the difference in brightness of two dots is less than 1%, our eyes won’t detect the difference. Can you see the circle? decreasing I I+I I

32. Contrast ratio • Contrast ratio refers to the ratio of luminance between the brightest spot and that of the darkest spot of a particular device and environment. • Example: 30:1 (TV, home with mild lighting)

33. Why 8 bits per sample • Let L be the intensity level of the darkest spot. With a contrast ratio of 20, the brightest spot has an intensity of 20L. • We need: • 1 code to represent dark (i.e., L) • 1 code to represent 1.01 dark (i.e., 1.01L) • 1 code to represent (1.01)2 L • … • 1 code to represent 20L • Hence, we need about 300 codes (or quantization levels) • 8 bits are used because they can be conveniently packed into a byte.

34. Perceptual uniformity • If we use an 8-bit linear coding system to represent luminance (i.e., intensity), we may not be making good use of the 256 codes. 25 100 200 Y 0 255 26 101 201

35. Perceptual uniformity • If we use an 8-bit linear coding system to represent luminance (i.e., intensity), we may not be making good use of the 256 codes. 25 100 200 Y 0 255 26 101 201 ? ?

36. Contouring • Luminance codes above 100 suffer no artifacts due to visibility of the jumps between codes. Some codes are not useful. • Also, successive codes that are near black has poor luminance resolution. This leads to contouring. 25 26 27

37. 5 bits 32 gray levels Contouring 8 bits 256 gray levels

38. Perceptual uniformity • If we code the non-linear gamma corrected value (i.e., luma) instead, contouring is ameliorated. 25 100 200 0 255 26 101 201 0.098 0.391 0.781 Y 0 1 0.102 0.395 0.785 0.539 0.394 0.687 0.906 0 1 Y’ 0.401 0.689 0.908 101 232 175 0 255 103 176

39. Gamma Correction • Gamma correction thus helps: • to compensate the non-linearity of a typical CRT; • to allow perceptually uniform coding.

40. True color • A true color system (or a 24-bit system) represents a pixel by its RGB (or R’G’B’) values with 8 bits for each component. • A 24-bit system allows us to describe 224 = 16,777,216 different colors. In many cases, such a high color resolution is not needed. • Example: • How many different colors can you see in • a 640  480 image? • your window desktop?

41. Pseudocolor/indexed color/ colormapped system • To save storage space, we can analyze an image to find out all the distinct colors that are present in the image. • Let n be the number of distinct colors found (usually n << 16.7M). We assign a code to each distinct color. • We keep a Color Lookup Table (CLUT, or colormap, or palette) that translates a code to its corresponding RGB values. • Each color is thus represented by log2n bits.

42. CLUT • Using the CLUT approach, • we waste space for storing the CLUT. • we save space by using fewer bits for each pixel. • Usually the latter factor outweighs the first.

43. 248 distinct colors CLUT