1. 1 Chapter 4 Color in Image and Video 4.1 Color Science 4.2 Color Models in Images 4.3 Color Models in Video 4.4 Further Exploration

2. 2 Chapter 4 Color in Image and Video 4.1 Color Science 4.2 Color Models in Images 4.3 Color Models in Video 4.4 Further Exploration

3. 3 Light and Spectra Light is an electromagnetic wave. Its color is characterized by the wavelength content of the light. Laser light: consists of a single wavelength: e.g., a ruby laser produces a bright, scarlet-red beam. Most light sources: produce contributions over many wavelengths. Visible wavelengths: humans cannot detect all light, just contributions that fall in the “ visible wavelengths". From Blue to Red: Short wavelengths produce a blue sensation, long wavelengths produce a red one.

4. 4 E( ) White light contains all the colors of a rainbow. Visible light is an electromagnetic wave in the range 400 nm to 700 nm “nm” stands for nanometer (10 −9 meters) Daylight (white light) E( ): Spectral Power Distribution (SPD) or spectrum. c.f. Human ear can hear 20 to 20K Hz. https://www.youtube.com/watch?v=qNf9nzvnd1k

5. 5 Electromagnetic Wave

6. 6 Spectrophotometer device used to measure visible light, by reflecting light from a diffraction grating (a ruled surface) that spreads out the different wavelengths.

7. 7 Human Vision Lens ( 水晶體 ) and Retina ( 視網膜 ) The eye works like a camera. Lens focus an image onto the retina (upside- down and left-right reversed). Rods ( 柱狀體 ) and Cones ( 錐狀體 ) Rods: “ all cats are gray at night! “ Three kinds of cones: most sensitive to red (R), green (G), and blue (B) light. 6 millions of cones proportion of R:G:B ~ 40:20:1

8. 8 Spectral Sensitivity Functions q R ( ), q G ( ) and q B ( ) Spectral Sensitivity Curves(1)

9. 9 Fig 4.3 R, G, B cones, and Luminous Efficiency Curve V( ) Spectral Sensitivity Curves (2)

10. 10 Luminous Efficiency Function V ( ) sum of the response curves for R, G, and B. The rod sensitivity curve: looks like the luminous-efficiency function V ( ) but is shifted to the red end of the spectrum. Eye-Brain System The brain is good at algebra. Luminous Efficiency Function

11. 11 These spectral sensitivity functions q ( ) = (q R ( ), q G ( ), q B ( )) T (4.1) The response in each color channel in the eye is proportional to the number of neurons firing. R =  E( ) q R ( ) d G =  E( ) q G ( ) d B =  E( ) q B ( ) d (4.2) Spectral Sensitivity of the Eye

12. 12 Surface Reflectance S( ): reflectance function

13. 13 The equations that take into account the image formation model are: R =  E( ) S( ) q R ( ) d G =  E ( ) S( ) q G ( ) d B =  E( ) S( ) q B ( ) d (4.3) Image formation

14. 14 (break)

15. 15 Color-Matching Functions A technique evolved in psychology Matching a combination of basic R, G, and B lights to a given shade (even without knowing the eye-sensitivity curves of Fig.4.3) Color Primaries 700, 546, 436 – nm (700, 546.1, 435.8) 580, 545, 440 – nm  Error / mistake? 課本這段是錯的， Google “CIE 1931” INTERNATIONAL COMMISSION ON ILLUMINATION

16. 16 Fig 4.8 Colorimeter experiments 700 nm 546 nm 436 nm Colorimeter

17. 17 Fig 4.9 CIE RGB color matching functions CIE 1931 2° Matching Func. 700 nm 546 nm 436 nm Radiant power 72 : 1.3791 : 1

18. 18 Spectral Sensitivity Functions q R ( ), q G ( ) and q B ( ) Recall: Spectral Sensitivity =560, for example

19. 19 Fig 4.9 CIE RGB color matching functions Recall: CIE 1931 2° 700 nm 546 nm 436 nm =560, for example

20. 20 單光源 刺激度 加乘轉換矩陣 (M) 三色光轉換成各別 刺激度再加總 指定  波長 對應  之配色比 單位能量 M [ E(  ) E(  ) E(  ) ] T =436  r(436)=0, g(436)=0, b(436)>0 =546  r(546)=0, g(546)>0, b(546)=0 =700  r(700)>0, g(700)=0, b(700)=0 =560 ... =560 ?

21. 21 [R G B] Stimulus (1) RGB 單一色彩的刺激 也是暫定三原色的組合 ( 紅色的刺激不能只靠暫定紅光模擬 )

22. 22 645 nm 526 nm 444 nm Normalized by Radiant power to 1 : 1 : 1 CIE 1964 10° Matching Func. (2) 另取「暫定三原色」亦無法改變紅光的負值

23. 23 Grassman's Law Additive color results from self-luminous sources lights projected on a white screen phosphors glowing on the monitor glass Additive color matching is linear. color1  a linear combinations of lights color2  another set of weights, then combined color: color1+color2  the sum of the two sets of weights. (3) 配色函數無法呈現色光的加法定理

24. 24 Grassman's Law (Example) Example color1  0.2 X + 0.6 Y + 1.2 Z color2  1.8 X + 0.9 Y + 0.3 Z color1+color2  2 X + 1.5 Y + 1.5 Z Example 2 ( 線性內插 : 假設色彩有坐標 ) color1  (0.2 X + 0.6 Y + 1.2 Z) /2 color2  (1.8 X + 0.9 Y + 0.3 Z) /3 (1/2) color1+ (1/2) color2  0.35 X + 0.3 Y + 0.35 Z

25. 25 Drawback of the RGB Color Matching Functions RGB stimuli are dependent on linear combinations of r( ), g( ), b( ), but not purely respective values of them. r( ) color-matching curve has a negative lobe Thus we cannot conveniently indicate a combined color following Grassman’s law q R (575)!= q R (550)/2+q R 600)/2

26. 26 Fig 4.10 CIE standard XYZ color matching Functions x( ), y( ), z( ). CIE-RGB to CIE-XYZ 下一頁：改用「坐標軸」來看待「調色」

27. 27 Linear Transform (RGB-XYZ) 由「暫定三原色」經線性轉換， 定義出「虛擬三原色」。

28. 28 Fictitious Primaries A 3 x 3 matrix away from r, g, b curves, and are denoted x( ), y( ), z( ), as shown in Fig. 4.10 XYZ color-matching functions with only positives values The middle standard color- matching function y( ) exactly equals the luminous-efficiency curve V ( ) shown in Fig. 4.3. The area under Each curve is the same.

29. 29 Orthogonal XYZ Color Space Original Coordinate before Normalization Pure Colors without Combination

30. 30 CIE Chromaticity Diagram z = 1 – x – y (4.7) (4.8) (4.6) (4.9) (4.10)

31. 31 Fig 4.11 Spectrum Locus horseshoe Line of purples Recall: Grassman’s Law A B C (x,y) Chromaticities 色光皆有座標 混色符合加法 及內插公式

32. 32 Chromaticities and White points of Monitor Specification Table 4.1 4.1.9

33. 33 Out-of-Gamut Colors Fig. 4.13: Approximating an out-of-gamut color 4.1.10

34. 34 (break)

35. 35 Out-of-Gamut Colors Fig. 4.13: Approximating an out-of-gamut color 4.1.10

36. 36 More Color Models YUV system (additive) YUV, YIQ, YCbCr color Models Munsell system (additive) L*a*b* (CIELAB), Munsell color naming system HSI -- Hue, Saturation and Intensity; HSI, HSL, HSV, HSD, HCI color models Lightness/Value/Darkness/Chroma CMY system CMY, CMYK color models Cyan/Magenta/Yellow/blacK

37. 37 More Color Models YUV system (additive) YUV, YIQ, YCbCr color Models Munsell system (additive) L*a*b* (CIELAB), Munsell color naming system HSI -- Hue, Saturation and Intensity; HSI, HSL, HSV, HSD, HCI color models Lightness/Value/Darkness/Chroma CMY system CMY, CMYK color models Cyan/Magenta/Yellow/blacK 傳輸格式

38. 38 RGB  YUV Y= 0.229 R + 0.587 G + 0.114 B U=B-Y V=R-Y

39. 39 YUV Decomposition

40. 40 Y channel (R+G+B)/3

41. 41 YIQ Color Model YIQ is used in NTSC color TV broadcasting “ Y “ in YIQ is the same as in YUV; I and Q are a rotated version (33° ) of U and V. I Q

42. 42 YIQ Transform Matrix

43. 43 YCbCr Color Model ITU Standard (International Telecommunication Unit) ITU-R BT. 601-4 (also known as “Rec. 601”) Closely related to the YUV transform

44. 44 YCbCr Transform Matrix Theoretical: Digital Processing: (16~235/ ± 112+128 )

45. 45 More Color Models YUV system (additive) YUV, YIQ, YCbCr color Models Munsell system (additive) L*a*b* (CIELAB), Munsell color naming system HSI -- Hue, Saturation and Intensity; HSI, HSL, HSV, HSD, HCI color models Lightness/Value/Darkness/Chroma CMY system CMY, CMYK color models Cyan/Magenta/Yellow/blacK 美術命名

46. 46 Fig 4.14 CIELAB Model Max a* Red Min a* Green Max b* Yellow Min b* Blue Outside solid More colorful (saturate) L*a*b* (CIELAB) Color Model

47. 47 Munsell Color Naming System

48. 48 More Color Models YUV system (additive) YUV, YIQ, YCbCr color Models Munsell system (additive) L*a*b* (CIELAB), Munsell color naming system HSI -- Hue, Saturation and Intensity; HSI, HSL, HSV, HSD, HCI color models Lightness/Value/Darkness/Chroma CMY system CMY, CMYK color models Cyan/Magenta/Yellow/blacK 影像處理

49. 49 Gonzalez. Chapter 6 Color Image Processing Gonzalez. Chapter 6 Color Image Processing

50. 50 Hue ( 穿黑白柱，並由紅色光開始旋轉 )

51. 51 Saturation 底三面 S=1 ( 少一色、在外緣繞 ) 往白點 (1,1,1) 收縮時 S  1..0 ( 逐漸被中和 ) (1) 法平面 R+G+B=k 上的點, 此乘數在標準白時為 1 (2) 法平面乘數相等時, 越邊緣的點, 所處的子方塊 越下面, min(R,G,B) 乘數的值越小, 飽和度變大 法平面乘數 see: 標準白 S=0 邊緣乘數 see: 法平面中央 ( 標準黑 S=0) ( 穿黑白柱，由此軸向外越加飽和 )

52. 52 Hue and Saturation 底三面 S=1 往白點 (1,1,1) 收縮的 Sub-cubes 底面 S  1..0 截面中心點 S=0 往外圍 S 值增加 最大值 S ≦ 1 ( 法平面截面可正規化為六角、三角或圓形 )

53. 53 Saturation and Intensity ( 強度值為所有色光強度之平均 )

54. 54 Gonzalez. Chapter 6 Color Image Processing Gonzalez. Chapter 6 Color Image Processing Hue: 從紅點繞一圈 Saturate: 周圍最大 Intensity: 白點最大

55. 55 H.S.I 彩色轉換 建議以上 RGB 值在實作時應取 Value = min(255, floor(…)) 以避免 overflow 而敗給其他兩色

56. 56 Recall: YUV Decomposition

57. 57 HSI Decomposition (I, S, H)

58. 58 圖 10-13 圖 10-10 之飽和度強化 (Saturation enhancement) 圖 10-10 彩色影像 彩色影像強化 — 增加飽和度

59. 59 More Color Models YUV system (additive) YUV, YIQ, YCbCr color Models Munsell system (additive) L*a*b* (CIELAB), Munsell color naming system HSI -- Hue, Saturation and Intensity; HSI, HSL, HSV, HSD, HCI color models Lightness/Value/Darkness/Chroma CMY system CMY, CMYK color models Cyan/Magenta/Yellow/blacK 彩色印刷

60. 60 (1,0,0) (0,1,0) (1, 1, 0) (0,1,1) (0,1,0) (0, 0, 1) Additive v.s. Subtractive Models (1,0,0) (0, 0, 1)

61. 61 Complementary Color I = 0.5 的平面上 Hue 相差 180 的補色示意環

62. 62 RGB Color Mixing Color 1 : Color 2 = a : b Result e.g. Color 1 = (0.8, 0.4, 0.2) Color 2 = (0.5, 0.6, 0.8) …

63. 63 CMY Color Mixing Definition: Color 1 : Color 2 = a : b 色料混合 = 兩色補色相加之後的補色

64. 64 Fig 4.15 RGB cubeCMY cube RGB and CMY color cubes

65. 65 Undercolor Removal: CMYK Sharper and cheaper printer colors Calculate that part of the CMY mix that would be black, Remove it from the color proportions, and add it back as real black. CMYK Model

66. 66 Printer Gamuts “ Crosstalk" between the color channels make it difficult to predict colors achievable in printing. Fig 4.17 (a) Block Dyes (b) Block Dyes Gamut and NTSC Gamut