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Chapter 2: Color Basics

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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).

wavelengthB G R

power

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Spectrum

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SPD

Taken fromAdobe

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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 respond (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 (XYZ) that specify a color.

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Sensitivity

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For your interest

Mantis shrimps have 16 photoreceptors, about 4 of them are in the ultraviolet region

While human beings can distinguish some 10,000 colors, mantis shrimps can distinguish 110,000 colors.

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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=0.81G=0.52B=0.56

R=0.36G=0.69B=0.74

R=0.0G=0.0B=0.69

R=0.0G=0.0B=0.91

R=0.91G=0.91B=0.91

R=0.69G=0.69B=0.69

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Gamma

A color CRT has 3 types of phosphors that emit different-colored (RGB) light.

Intensity measures the power of a radiating light source. A typical CRT has a non-linear transfer function. That is,

the amount of power (intensity) emitted is approximately proportional to the applied voltage (scaled to the range [0,1]) raised to a constant power, commonly called gamma, .

Intensity Voltage

Typical CRTs have gamma values close to 2.5.

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Gamma

gamma = 1

gamma > 1

gamma < 1

voltage

intensity

0 1

1

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Gamma

gamma = 1

gamma > 1

voltage

intensity

01

1

0.5

0.176

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Gamma

gamma = 1

gamma > 1

voltage

intensity

01

1

0.25

0.031

0.9

0.77

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Gamma correction

A camera records the intensity (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 intensity.

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.

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Gamma correction

1.0 0.5 1.0 0.176

Gamma (example)

original as displayed on a CRTwithout gamma correction

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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.

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Gamma correction

cameraRGB

gammacorrection

computerR’G’B’ CRTR’G’B’RGB

eye

x x1/ (x1/)

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Lightness

Human vision system has a non-linear perceptual response to intensity e.g., a source having a luminance (power) of 18% of

another source appears about half as bright. The perceptual response to intensity is called

lightness. The transfer function of human perceptual response

to intensity resembles (very roughly) a 0.4 power curve, i.e., Lightness Intensity0.4

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Lightness

computer CRTR’G’B’RGB

y y (y)0.4

lightnessintensitypixelvalue

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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 intensity 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).

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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 (or chroma).

The chrominance components are usually given lower bandwidth (or data capacity) than the luminance component.

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Spectral sensitivity

TakenfromAdobe

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Cone cell distribution

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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).

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Scaling chroma

Various scaling factors are applied to the chroma values (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

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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

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Perceptual uniformity

Human vision responds to about a hundred-to-one contrast ratio. That is, if the difference in intensity of two light sources is less than 1%, our eyes won’t detect the difference.

I I+I

decreasing I Can yousee the circle?

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Contrast ratio

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

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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.

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Why 8 bits per sample

intensity

L1.01L

Intensities within this region areindistinguishable from L

Intensities within this region areindistinguishable from 1.01L

(1.01)2L

(1.01)3L

30L

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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.

0

25

26

100 200

255101 201

Y

0000000000000001 ….11111111

256codes

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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.

0

25

26

100 200

255101 201

Y

? ?

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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.

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Contouring

A B

Intensity

25

26

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A B

Intensity

25

26

27

B

25

2627

A

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Contouring

8 bits256graylevels

5 bits32 graylevels

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Perceptual uniformity

If we code the non-linear gamma corrected value (i.e., luma) instead, contouring is ameliorated.

025

26

100 200255

101 201

Y 0 10.098

0.102

0.391

0.395 0.785

0.781

0 10.394

0.401

0.687 0.906

0.689

0.539

Y’

0 255101

103

175

176

232

0.908

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Gamma Correction

Gamma correction thus helps: to compensate the non-linearity of a typical

CRT; to allow a more perceptually uniform coding.

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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?

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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.

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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.

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CLUT

248distinctcolors

640 x 238

How much storage space is neededfor a true color system? For a CLUT system?

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