Color | Sahithyan's Notes

Color is a construct in the brain. It doesn’t correspond to a physical phenomenon. Mixing light waves of different wavelengths produces the perception of different colors.

A few narrow wavelength bands are perceived as distinct colors, named primary colors. Primary colors are orthogonal to each other. Mixing primary colors produces the secondary colors we perceive.

Color reaches the eye from an object 2 ways.

Emission Based

The object emits colored light directly. Adding more light gives a brighter color. All primaries together give white, absence of light gives black.

Computer displays are emission based.

Absorption Based

The object absorbs part of the incident white light and reflects the rest. Adding more colorant removes more of the spectrum, giving a darker color. Bare substrate reflects white, full colorant absorbs everything and gives black.

Print is absorption based.

Color Spaces

A color space is a model that represents colors as tuples of numbers.

RGB

RGB is an emission based color space with primaries red, green and blue.

Each cone type is maximally sensitive to a different wavelength.

L cones respond best to ~560 nm, red light
M cones respond best to ~530 nm, green light
S cones respond best to ~420 nm, blue light

Any visible color is the brain’s interpretation of signals from these 3 cone types firing at different intensities. RGB primaries are chosen because they align with cone sensitivity. Each wavelength band stimulates a different cone type, making them orthogonal. Any visible color can be recreated by combining red, green and blue light in the right proportions, without the full spectrum.

Each channel is an 8-bit value in $[0, 255]$ . All channels at $0$ gives black. All channels at $255$ gives white.

CMYK

CMYK is an absorption based color space with colorants cyan, magenta, yellow and key.

$C$ : cyan, absorbs red
$M$ : magenta, absorbs green
$Y$ : yellow, absorbs blue
$K$ : key, black ink added to deepen dark tones and reduce colored ink use

Each component is a fraction in $[0, 1]$ . All components at $0$ gives white, the bare substrate. $K = 1$ gives black.

Cyan, magenta and yellow are the secondary colors of RGB. Each absorbs one RGB primary, so CMY is the subtractive counterpart of the additive RGB primaries.

Conversion Between RGB and CMYK

Normalize each RGB channel to $[0, 1]$ .

R' = \frac{R}{255} \quad G' = \frac{G}{255} \quad B' = \frac{B}{255}

K = 1 - \max(R', G', B')

C = \frac{1 - R' - K}{1 - K} \quad M = \frac{1 - G' - K}{1 - K} \quad Y = \frac{1 - B' - K}{1 - K}

When $K = 1$ , set $C = M = Y = 0$ .

The reverse conversion.

R = 255 (1 - C)(1 - K) \quad G = 255 (1 - M)(1 - K) \quad B = 255 (1 - Y)(1 - K)

The RGB gamut and the CMYK gamut differ, so a round trip is not always exact.

RGB

R G B

CMYK

C M Y K

rgb(62, 40, 184) cmyk(0.66, 0.78, 0.00, 0.28)

Color Representation

A digital color image is stored as a multi-channel structure, one image per attribute.

Channels

RGB
Maintains the intensity of red, green and blue in separate channels.
Luminance and chrominance
Separates brightness (luminance) from color (chrominance) into separate channels.

Y = w_r\,R + w_g\,G + w_b\,B

$Y$ is a weighted sum of the linear RGB components, matching the eye’s differing sensitivity to each. $C_r$ and $C_b$ are the red and blue differences from luminance, scaled so each spans $[-0.5, 0.5]$ .

C_r = \frac{R - Y}{2\,(1 - w_r)} \qquad C_b = \frac{B - Y}{2\,(1 - w_b)}

The weights follow from the RGB primaries and white point fixed by the chosen standard, defined by the ITU Radiocommunication Sector (ITU-R). Different versions define different weights.

ITU-R BT.601 (SD)
$w_r = 0.299$ , $w_g = 0.587$ , $w_b = 0.114$
ITU-R BT.709 (HD)
$w_r = 0.2126$ , $w_g = 0.7152$ , $w_b = 0.0722$
ITU-R BT.2020 (UHD)
$w_r = 0.2627$ , $w_g = 0.6780$ , $w_b = 0.0593$

Discarding $C_r, C_b$ gives a monochrome image directly.

The human visual system is more sensitive to luminance than color, so YCrCb formats often allocate bits in a 4:2:2 ratio. Widely used for this inherent compression capability.

Per-Pixel Storage

How much color each pixel holds, independent of the channel layout.

Binary
1 bit per pixel, black or white.
Grayscale
A single intensity channel, usually 8-bit.
Indexed
Each pixel is an index into a color table. Covered below as palette based representation.
True color
Each pixel stores a full color value.
High color
15 or 16-bit direct color. Largely historical.

True Color

An image that stores a full color value in every pixel. RGB uses 24 bits per pixel, or 3 bytes. CMYK needs 4 bytes per pixel.

Palette Based Representation

Most images use far fewer distinct colors than true color allows. A 1920x1024 image has under 2 million pixels, so at most 2 million distinct colors, against the $2^{24}$ an RGB pixel can encode.

Storing a table of the colors actually used, then storing pointers into that table, is more storage-efficient than true color.

Palette length determines how many distinct colors can be used at once, out of the full $2^{24}$
Bits per pixel in image memory depend on the palette table length
The palette table is usually stored with the image, allowing a custom color set per image