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# Color Models

Color Model is a method for explaining the properties or behavior of color within some particular context. No single color model can explain all aspects of color, so we make use of different models to help describe the different perceived characteristics of color.

Color Models

Color Model is a method for explaining the properties or behavior of color within some particular context. No single color model can explain all aspects of color, so we make use of different models to help describe the different perceived characteristics of color.

Properties of Light

Light is a narrow frequency band within the electromagnetic system.

Other frequency bands within this spectrum are called radio waves, micro waves, infrared waves and x-rays. The below fig shows the frequency ranges for some of the electromagnetic bands.

Each frequency value within the visible band corresponds to a distinct color.

At the low frequency end is a red color (4.3*104 Hz) and the highest frequency is a violet color (7.5 *10 14Hz)

Spectral colors range from the reds through orange and yellow at the low frequency end to greens, blues and violet at the high end.

Since light is an electro magnetic wave, the various colors are described in terms of either the frequency for the wave length λ of the wave.

The wave length ad frequency of the monochromatic wave are inversely proportional to each other, with the proportionality constants as the speed of light

C where C = λ f

A light source such as the sun or a light bulb emits all frequencies within the visible range to produce white light. When white light is incident upon an object, some frequencies are reflected and some are absorbed by the object. The combination of frequencies present in the reflected light determines what we perceive as the color of the object.

If low frequencies are predominant in the reflected light, the object is described as red. In this case, the perceived light has the dominant frequency at the red end of the spectrum. The dominant frequency is also called the hue, or simply the color of the light.

Brightness is another property, which in the perceived intensity of the light.

Intensity in the radiant energy emitted per limit time, per unit solid angle, and per unit projected area of the source.

Radiant energy is related to the luminance of the source.

The next property in the purity or saturation of the light.

o  Purity describes how washed out or how pure the color of the light appears.

o  Pastels and Pale colors are described as less pure.

The term chromaticity is used to refer collectively to the two properties, purity and dominant frequency.

Two different color light sources with suitably chosen intensities can be used to produce a range of other colors.

If the 2 color sources combine to produce white light, they are called complementary colors. E.g., Red and Cyan, green and magenta, and blue and yellow.

Color models that are used to describe combinations of light in terms of dominant frequency use 3 colors to obtain a wide range of colors, called the color gamut.

The 2 or 3 colors used to produce other colors in a color model are called primary colors.

Standard Primaries

XYZ Color

The set of primaries is generally referred to as the XYZ or (X,Y,Z) color model

where X,Y and Z represent vectors in a 3D, additive color space.

Any color Cλ is expressed as

 Cλ = XX + YY + ZZ------------- (1)

Where X,Y and Z designates the amounts of the standard primaries needed

to match Cλ.

It is convenient to normalize the amount in equation (1) against luminance (X+ Y+ Z). Normalized amounts are calculated as,

x = X/(X+Y+Z),  y = Y/(X+Y+Z),   z = Z/(X+Y+Z)

with x + y + z = 1

Any color can be represented with just the x and y amounts. The parameters x and y are called the chromaticity values because they depend only on hue and purity.

If we specify colors only with x and y, we cannot obtain the amounts X, Y and Z. so, a complete description of a color in given with the 3 values x, y and Y.

X = (x/y)Y,          Z = (z/y)Y

Where z = 1-x-y.

Intuitive Color Concepts

Color paintings can be created by mixing color pigments with white and black pigments to form the various shades, tints and tones.

Starting with the pigment for a „pure color‟ the color is added to black pigment to produce different shades. The more black pigment produces darker shades.

Different tints of the color are obtained by adding a white pigment to the original color, making it lighter as more white is added.

Tones of the color are produced by adding both black and white pigments.

RGB Color Model

Based on the tristimulus theory of version, our eyes perceive color through the stimulation of three visual pigments in the cones on the retina.

These visual pigments have a peak sensitivity at wavelengths of about 630 nm (red), 530 nm (green) and 450 nm (blue).

By comparing intensities in a light source, we perceive the color of the light.

This is the basis for displaying color output on a video monitor using the 3 color primaries, red, green, and blue referred to as the RGB color model. It is represented in the below figure

Vertices of the cube on the axes represent the primary colors, the remaining vertices represents the complementary color for each of the primary colors.

The RGB color scheme is an additive model. (i.e.,) Intensities of the primary colors are added to produce other colors.

Each color point within the bounds of the cube can be represented as the triple (R,G,B) where values for R, G and B are assigned in the range from 0 to1.

The color Cλ is expressed in RGB component as

Cλ = RR + GG + BB

The magenta vertex is obtained by adding red and blue to produce the triple (1,0,1) and white at (1,1,1) in the sum of the red, green and blue vertices.

Shades of gray are represented along the main diagonal of the cube from the origin (black) to the white vertex.

YIQ Color Model

The National Television System Committee (NTSC) color model for forming the composite video signal in the YIQ model.

In the YIQ color model, luminance (brightness) information in contained in the Y parameter, chromaticity information (hue and purity) is contained into the I and Q parameters.

A combination of red, green and blue intensities are chosen for the Y parameter to yield the standard luminosity curve.

Since Y contains the luminance information, black and white TV monitors use only the Y signal.

Parameter I contain orange-cyan hue information that provides the flash-tone shading and occupies a bandwidth of 1.5 MHz.

Parameter Q carries green-magenta hue information in a bandwidth of about 0.6MHz.

CMY Color Model

A color model defined with the primary colors cyan, magenta, and yellow (CMY) in useful for describing color output to hard copy devices.

It is a subtractive color model (i.e.,) cyan can be formed by adding green and blue light. When white light is reflected from cyan-colored ink, the reflected light must have no red component. i.e., red light is absorbed or subtracted by the link.

Magenta ink subtracts the green component from incident light and yellow subtracts the blue component.

In CMY model, point (1,1,1) represents black because all components of the incident light are subtracted.

The origin represents white light.

Equal amounts of each of the primary colors produce grays along the main diagonal of the cube.

A combination of cyan and magenta ink produces blue light because the red and green components of the incident light are absorbed.

The printing process often used with the CMY model generates a color point with a collection of 4 ink dots; one dot is used for each of the primary colors (cyan, magenta and yellow) and one dot in black.

The conversion from an RGB representation to a CMY representation is expressed as

[ ] [ ] [ ]

Where the white is represented in the RGB system as the unit column vector.

Similarly the conversion of CMY to RGB representation is expressed as [ ] [ ] [ ]

Where black is represented in the CMY system as the unit column vector.

HSV Color Model

The HSV model uses color descriptions that have a more interactive appeal to a user.

Color parameters in this model are hue (H), saturation (S), and value (V). The 3D representation of the HSV model is derived from the RGB cube. The outline of the cube has the hexagon shape.

The boundary of the hexagon represents the various hues, and it is used as the top of the HSV hexcone.

In the hexcone, saturation is measured along a horizontal axis, and value is along a vertical axis through the center of the hexcone.

Hue is represented as an angle about the vertical axis, ranging from 00 at red through 3600. Vertices of the hexagon are separated by 600 intervals. Yellow is at 600, green at 1200 and cyan opposite red at H = 1800. Complementary colors are 1800 apart.

Saturation S varies from 0 to 1. the maximum purity at S = 1, at S = 0.25, the hue is said to be one quarter pure, at S = 0, we have the gray scale.

Value V varies from 0 at the apex to 1 at the top.

the apex representation black.

At the top of the hexcone, colors have their maximum intensity.

When V = 1 and S = 1 we have the „pure‟ hues.

White is the point at V = 1 and S = 0.

HLS Color Model

HLS model is based on intuitive color parameters used by Tektronix.

It has the double cone representation shown in the below figure. The 3 parameters in this model are called Hue (H), lightness (L) and saturation (s).

Hue specifies an angle about the vertical axis that locates a chosen hue.

In this model H = θ0 corresponds to Blue.

The remaining colors are specified around the perimeter of the cone in the same order as in the HSV model.

Magenta is at 600, Red in at 1200, and cyan in at H = 1800.

The vertical axis is called lightness (L). At L = 0, we have black, and white is at  L

= 1 Gray scale in along the L axis and the “purehues” on the L = 0.5 plane.

Saturation parameter S specifies relative purity of a color. S varies from 0 to 1 pure hues are those for which S = 1 and L = 0.

As S decreases, the hues are said to be less pure.

At S= 0, it is said to be gray scale.

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