Color Models Color models cont d Different meanings

Color Models

Color models, cont’d Different meanings of color: • painting • wavelength of visible light • human eye perception

Physical properties of light Visible light is part of the electromagnetic radiation (380750 nm) 1 nm (nanometer) = 10 -10 m (=10 -7 cm) 1 Å (angstrom) = 10 nm Radiation can be expressed in wavelength ( ) or frequency (f), c= f, where c=3. 1010 cm/sec

Physical properties of light White light consists of a spectrum of all visible colors V I B G Y O R

Physical properties of light All kinds of light can be described by the energy of each wavelength The distribution showing the relation between energy and wavelength (or frequency) is called energy spectrum

Physical properties of light This distribution may indicate: 1) a dominant wavelength (or frequency) which is the color of the light (hue), ED 2) brightness (luminance), intensity of the light (value), the area A 3) purity (saturation), ED – EW Contributions from other frequencies produce white light of energy density Ew

Physical properties of light Energy spectrum for a light source with a dominant frequency near the red color

Material properties The color of an object depends on the so called spectral curves for transparency and reflection of the material The spectral curves describe how light of different wavelengths are refracted and reflected

Properties of reflected light Incident white light upon an object is for some wavelengths absorbed, for others reflected E. g. if all light is absorbed => black If all wavelengths but one are absorbed => the one color is observed as the color of the object by the reflection

Color definitions Complementary colors - two colors combine to produce white light Primary colors - (two or) three colors used for describing other colors Two main principles for mixing colors: • additive mixing • subtractive mixing

Additive mixing • pure colors are put close to each other => a mix on the retina of the human eye (cp. RGB) • overlapping gives yellow, cyan, magenta and white • the typical technique on color displays

Subtractive mixing • color pigments are mixed directly in some liquid, e. g. ink • each color in the mixture absorbs its specific part of the incident light • the color of the mixture is determined by subtraction of colored light, e. g. yellow absorbs blue => only red and green, i. e. yellow, will reach the eye (yellow because of addition)

Subtractive mixing, cont’d • primary colors: cyan, magenta and yellow, i. e. CMY • the typical technique in printers/plotters • connection between additive and subtractive primary colors (cp. the color models RGB and CMY)

Additive/subtractive mixing

Human color seeing The retina of the human eye consists of cones (7 -8 M), ”tappar”, and rods (100 -120 M), ”stavar”, which are connected with nerve fibres to the brain

Human color seeing, cont’d Theory: the cones consist of various light absorbing material The light sensitivity of the cones and rods varies with the wavelength, and between persons The ”sum” of • the energy spectrum of the light • the reflection spectrum of the object • the response spectrum of the eye decides the color perception for a person

Overview of color models The human eye can perceive about 382000(!) different colors Necessary with some kind of classification system; all using three coordinates as a basis: 1) CIE(commission Internationale de l’Ḗclairage) standard 2) RGB color model 3) CMY color model (also, CMYK) 4) HSV color model 5) HLS color model

CIE standard Commission Internationale de L’Eclairage (1931) • not a computer model • each color = a weighted sum of three imaginary primary colors

XYZ color space • The CIE XYZ color space was derived from a series of experiments done in the late 1920 s by W. David Wright and John Guild. Their experimental results were combined into the specification of the CIE RGB color space, from which the CIE XYZ color space was derived. • Since the human eye has three types of color sensors that respond to different ranges of wavelengths, a full plot of all visible colors is a three-dimensional figure. However, the concept of color can be divided into two parts: brightness and chromaticity. For example, the color white is a bright color, while the color grey is considered to be a less bright version of that same white. In other words, the chromaticity of white and grey are the same while their brightness differs.

• The CIE XYZ color space was deliberately designed so that the Y parameter was a measure of the brightness or luminance of a color. The chromaticity of a color was then specified by the two derived parameters x and y, two of the three normalized values which are functions of all three tristimulus values X, Y, and Z. • Thus color cλ = Xx+Yy+Zz, where x, y, z represent vectors in 3 D additive color space and X, Y, Z designate the amounts of the standard primaries needed to match cλ. • It is convenient to normalize the amounts against luminance (X+Y+Z). Any color can now be represented with the x and y amounts. Since normalization is done against luminance, parameters x & y are called chromaticity values because they depend on only hue and purity.

CIE standard When x and y is plotted in the visible spectrum we obtain the CIE chromaticity diagram. Labelled according to wavelength in nanometers from red end to violet end of spectrum.

RGB model • Our eyes perceive color through stimulation of visual pigments in the cones of 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 light. • This theory of vision is the basis of displaying color on a monitor and is known as thre RGB color model.

RGB model • all colors are generated from the three primaries • various colors are obtained by changing the amount of each primary • additive mixing (r, g, b), 0≤r, g, b≤ 1

RGB model, cont’d • the RGB cube • 1 bit/primary => 8 colors, 8 bits/primary => 16 M colors

CMY model • cyan, magenta and yellow are complementary colors of red, green and blue, respectively • subtractive mixing • the typical printer technique

CMY model, cont’d • almost the same cube as with RGB; only black<-> white • the various colors are obtained by reducing light, e. g. if red is absorbed => green and blue are added, i. e cyan

RGB vs CMY If the intensities are represented as 0≤r, g, b≤ 1 and 0≤c, m, y≤ 1 (also coordinates 0 -255 can be used), then the relation between RGB and CMY can be described as:

CMYK model For printing and graphics art industry, CMY is not enough; a fourth primary, K which stands for black, is added. Conversions between RGB and CMYK are possible, although they require some extra processing.

HSV model • HSV stands for Hue-Saturation-Value • described by a hexcone derived from the RGB cube

HSV model, cont’d • Hue (0 -360°); ”the color”, cp. the dominant wavelength (128) • Saturation (0 -1); ”the amount of white” (130) • Value (0 -1); ”the amount of black” (23)

HSV model, cont’d The numbers given after each ”primary” are estimates of how many levels a human being is capable to distinguish between, which (in theory) gives the total number of color nuances: 128*130*23 = 382720 In Computer Graphics, usually enough with: 128*8*15 = 16384

HLS model Another model similar to HSV L stands for Lightness

RGB to HSI Conversion • First, we convert RGB color space image to HSI space beginning with normalizing RGB values: • Each normalized H, S and I components are then obtained by,

• For convenience, h, s and i values are converted in the ranges of [0, 360], [0, 100], [0, 255], respectively , by:

HSI to RGB Conversion The result r, g and b are normalized values, which are in the ranges of [0, 1], therefore, they should be multiplied by 255 for displaying.

Color models Some more facts about colors: The distance between two colors in the color cube is not a measure of how far apart the colors are perceptionally! Humans are more sensitive to shifts in blue (and green? ) than, for instance, in yellow