## Basics of Color

### Light and Spectra

• Visible light is an electromagnetic wave in the 400 nm - 700 nm range.

• Most light we see is not one wavelength, it's a combination of many wavelengths. • The profile above is called a spectral power distribution or spectrum.

### The Human Retina

• The eye is basically just a camera

• Each neuron is either a rod or a cone. Rods are not sensitive to color.

### Cones and Perception

• Cones come in 3 types: red, green and blue. Each responds differently to various frequencies of light. The following figure shows the spectral sensitivity functions of the cones and the luminous-efficiency function of the human eye.

• • The color signal to the brain comes from the response of the 3 cones to the spectra being observed. That is, the signal consists of 3 numbers:

•  where E is the light (spectral power distribution) and S are the spectral sensitivity functions.

• A color can be specified as the sum of three colors. So colors form a 3 dimensional vector space.
• The following figure shows the amounts of three primaries needed to match all the wavelengths of the visible spectrum.

• • The negative value indicates that some colors cannot be exactly produced by adding up the primaries.

### CIE Chromaticity Diagram

• Q: Does a set of primaries exist that span the space with only positive coefficients?
• A: Yes, but no pure colors.

• In 1931, the CIE (Commission Internationale de L'Eclairage, or International Commission on Illumination) defined three standard primaries (X, Y, Z). The Y primary was intentionally chosen to be identical to the luminous-efficiency function of human eyes. • The above figure shows the amounts of X, Y, Z needed to exactly reproduce any visible color.

•

• All visible colors are in a "horseshoe" shaped cone in the X-Y-Z space. Consider the plane X+Y+Z=1 and project it onto the X-Y plane, we get the CIE chromaticity diagram as below.

• • The edges represent the "pure" colors (sine waves at the appropriate frequency)
• White (a blackbody radiating at 6447 kelvin) is at the "dot"
• When added, any two colors (points on the CIE diagram) produce a point on the line between them.
• Q: how can we find a color's complement on the CIE diagram?

### L*a*b (Lab) Color Model • A refined CIE model, named CIE L*a*b in 1976
• Luminance: L

• Chrominance: a -- ranges from green to red, b -- ranges from blue to yellow
• Used by Photoshop

•

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## Color Models in Images

• A color image is a 2-D array of (R,G,B) integer triplets. These triplets encode how much the corresponding phosphor should be excited in devices such as a monitor.

### RGB Color Model for CRT Displays

• CRT displays have three phosphors (RGB) which produce a combination of wavelengths when excited with electrons. ### CMY Color Model

• Cyan, Magenta, and Yellow (CMY) are complementary colors of RGB. They can be used as Subtractive Primaries.
• CMY model is mostly used in printing devices where the color pigments on the paper absorb certain colors (e.g., no red light reflected from cyan ink). ### Conversion between RGB and CMY:

-- e.g., convert White from (1, 1, 1) in RGB to (0, 0, 0) in CMY.  • Sometimes, an alternative CMYK model (K stands for Black) is used in color printing (e.g., to produce darker black than simply mixing CMY).
• K := min (C, M, Y), C := C - K, M := M - K, Y := Y - K.

### Comparison of Three Color Gamuts • The gamut of colors is all colors that can be reproduced using the three primaries
• The Lab gamut covers all colors in visible spectrum
• The RGB gamut is smaller, hence certain visible colors (e.g. pure yellow, pure cyan) cannot be seen on monitors
• The CMYK gamut is the smallest (but not a straight subset of the RGB gamut)
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## Color Models in Video

• YIQ and YUV are the two commonly used color models in video

### YUV Color Model

• Initially, for PAL analog video, it is now also used in CCIR 601 standard for digital video
• Y (luminance) is the CIE Y primary.

• Y = 0.299R + 0.587G + 0.114B

• Chrominance is defined as the difference between a color and a reference white at the same luminance. It can be represented by U and V -- the color differences.

• U = B - Y
V = R - Y

• If b/w image, then U = V = 0. --> No chrominance!
• ** In actual PAL implementation:

• U = 0.492 (B - Y)
V = 0.877 (R - Y)

• Sample YUV Decomposition:

• Y U V   • Eye is most sensitive to Y. In PAL, 5 (or 5.5) MHz is allocated to Y, 1.3 MHz to U and V.

### YCbCr Color Model

• The YCbCr model is closely related to the YUV, it is a scaled and shifted YUV.

• Cb = (B - Y) / 1.772 + 0.5
Cr = (R - Y) / 1.402 + 0.5

• The chrominance values in YCbCr are always in the range of 0 to 1.
• YCbCr is used in JPEG and MPEG.

### YIQ Color Model

• YIQ is used in NTSC color TV broadcasting, it is downward compatible with B/W TV where only Y is used.
• Although U and V nicely define the color differences, they do not align with the desired human perceptual color sensitivities. In NTSC, I and Q are used instead.

• I is the orange-blue axis, Q is the purple-green axis.
I and Q axes are scaled and rotated R - Y and B - Y (by 33 degrees clockwise).

I = 0.877(R - Y) cos 33 - 0.492(B - Y) sin 33
Q = 0.877(R - Y) sin 33 + 0.492(B - Y) cos 33

Namely,

I = 0.736(R - Y) - 0.268(B - Y) = 0.596R - 0.275G - 0.321B
Q = 0.478(R - Y) + 0.413(B - Y) = 0.212R - 0.523G + 0.311B

• The YIQ transform:

• • Eye is most sensitive to Y, next to I, next to Q.

• In NTSC broadcast TV, 4.2 MHz is allocated to Y, 1.5 MHz to I and 0.55 MHz to Q. For VCR, Y is cut down to 3.2 MHz and I to 0.63 MHz.

### Summary

• Color images are encoded as triplets of values.
• RGB is an additive color model that is used for light-emitting devices, e.g., CRT displays

• CMY is a subtractive model that is used often for printers
• Two common color models in imaging are RGB and CMY, two common color models in video are YUV and YIQ.
• YUV uses properties of the human eye to prioritize information. Y is the black and white (luminance) image, U and V are the color difference (chrominance) images. YIQ uses similar idea.
• Besides the hardware-oriented color models (i.e., RGB, CMY, YUV, YIQ), HSB (Hue, Saturation, and Brightness) and HLS (Hue, Lightness, and Saturation) are also commonly used.

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