course book details

The Science of Digital Media

• Title: The Science of Digital Media• Author: Jennifer Burg• Publisher: Pearson International Edition• Publication Year: 2009

Course Book Details

23 March 2010 1Metropolia University of Applied Sciences, Digital

Media, Erkki Rämö, Principal Lecturer



• Chapter 1: Digital Data Representation and Communication

• Chapter 2: Digital Image Representation• Chapter 3: Digital Image Processing

General Course Contents





• Chapter 2: Digital Image Representation– Bitmaps– Frequency in Digital Images– The Discrete Cosine Transform– Aliasing– Color– Vector Graphics– Algorithmic art and Procedural Modeling

General Course Contents





• Color is both physical and psychological phenomenon• Physically, color is composed of electromagnetic waves• For humans, the wavelength of visible colors fall

between approximately 370 and 780 nanometers (nm), i.e., 1nm = 10-9 meters

• These waves fall upon the color receptors of the eyes, and in a way not completely understood, the human brain translates the interaction between the waves and the eyes as color perception



Color Perception and Representation

2.6 - Color


• It is possible to create pure color composed of a single wavelength, e.g., by means of a laser

• But most colors we see around us are almost always produced by a combination of wavelengths

• Green cover of a book may look pure green to you, but a spectrograph will break it up into its components wavelengths, producing a spectral density function P(λ)

• A spectral density function shows the contribution of the wavelengths λ to a given perceived color as λ varies across the visible spectrum



Color Perception – Spectral Density (1)

2.6 - Color


• Spectral density functions are one mathematical way to represent colors, but not very convenient way for computers

• One problem is that, more than one spectral density curve can represent two colors that look the same

• It is possible to represent a color by means of a simpler spectral density graph (Hue Saturation Value –HSV and Hue Lightness Saturation - HLS color modes uses this color representation)




2.6 - Color


• Each color in the spectrum can be characterised by a unique graph that has a simple shape

• The graph for each color gives the color’s dominant wavelength, equivalent to the hue; its saturation (i.e., color purity) and its luminance.– The dominant wavelength is the wavelength at the spike

in the graph– The area beneath the curve indicates the luminance L– Saturation S is the ratio of the area of the spike to the

total area.




2.6 - Color


• More precisely with regard to Figure 2.43



L

bcefS

bcefeadL

))((

))(()(

Figure 2.43 Spectral density graph showing hue, saturation and lightness


2.6 - Color


• The dimensions of hue, saturation and brightness do not correspond very well to the computer monitors– Cathode Ray Tube (CRT) monitors – display colored light

through a combination of red, green and blue phosphors, which light up at varying intensities when excited by electron bean

– Liquid Crystal Display (LCD) panels – display color with neighboring pixels of red, green and blue that are either lit up or masked by the liquid crystals




2.6 - Color


• So, what is the best way to model color for the computer?

• There is no simple answer since different models have advantages in different situations.




2.6 - Color


• Varying combinations of three primary colors can create a wide range of colors

• Three colors are primary with respect to one another if no one of them can be created as a combination of the other two

• Red, Gree and Blue are good choices as primary colors because the cones of the eyes (color receptors) are especially sensitive to these hues



RGB Color Model (1)

2.6 - Color


• C = rR + gG + bBwhere r, g and b indicate the relative amounts of red,

green and blue energy respectively. Also referred to as the

values of the RGB color components or (color channelsin application programs)

R, G and B are constant values base on the wavelengths

chosen for the red, green and blue components



RGB Color Model (2)

2.6 - Color


• The color space for the RGB color model is easy to depict graphically

• Let R, G and B correspond to three axes in 3D space• The relative amount of red, green and blue are

normalized to vary between 0 and 1• The origin (0,0,0) of the RGB cube correspond to black

and white is the value (1,1,1). • The remaining corners correspond to red, green and

blue and their complementary colors i.e., cyan, magenta and yellow respectively



RGB Color Model (3)

2.6 - Color


• Other colors are created at values between 0 and 1 for each of the components.

• For example (1, 0.65, 0.15) is light orange etc



RGB Color Model (4)

Figure 2.44: RGB Color Cube

2.6 - Color


• Shades of gray have equal proportions of red, green and blue and lie along the line between (0,0,0) and (1,1,1).

• All grayscale values have equal amount of R, G and B• Standard equation is used to convert RGB to grayscale– Let an RGB color pixel be given by (R, G, B), where R, G

and B are red, green and blue color components respectively. The corresponding gray value is given by (L, L, L), where

L = 0.30R + 0.59G + 0.11B



RGB Color Model (5)

2.6 - Color


• Since all three color components are equal in gray pixel, only one of the three values needs to be stored.

• Thus a 24-bit RGB pixel can be stored as an 8-bit grayscale pixel



RGB Color Model (6)

2.6 - Color


• Like the RGB color model, the CMY color model divides a color into three primaries, but using a subtractive rather than additive color creation process

• The CMY color model can be depicted in a unit cube similar to the RGB model

• The difference is that the origin of the cube is white rather than black

• The value of each component indicates how much red, green and blue are subtracted out , effectively combining the color components cyan, magenta and yellow their respective components



CMY Color Model (1)

2.6 - Color


• Assuming that each of the three RGB (or CMY) components is a value between 0 and 1, the corresponding CMY components can be computed as follows:– For a pixel represented in RGB color, the red, green and

blue color components are respectively, R, G, and B. Then the equivalent C, M and Y color components are given by:

C = 1- RM = 1 - GY = 1 - B



CMY Color Model (2)

2.6 - Color


– Similarly, RGB values cab be computed from CMY valuesR = 1- CG= 1 - MB = 1 - Y

• The values can be given in the range of [0 255] or [0 1]

• The CMY model used in professional four-color printed process, indicates how much cyan, magenta and yellow ink should combine to create color



CMY Color Model (3)

2.6 - Color


• Theoretically, the maximum amount of cyan, magenta and yellow ink should combine to produce black, but practically they produce dark muddy brown

• In four-color professional printing a fourth component is added, a pure black ink for greater clarity and contrast



CMY Color Model (4)

2.6 - Color


• The amount of “K” or black, can be taken as the smallest of the C, M and Y components in the original CMY model. Thus the CMY model is define as follows:– For a pixel represented in the CMY color model, the cyan,

magenta and yellow color components are respectively, C, M and Y. Let K be the minimum of C, M and Y. Then the equivalent color components in the CMYK model, Cnew, Mnew, Ynew and K are given by

K = min(C, M, Y) Cnew = C - K Mnew = M - K Ynew = Y - K



CMY Color Model (5)

2.6 - Color


• Instead of representing color by three primary color components, it is possible to speak of color in terms of:– its hue (i.e., the essential color), – its lightness (or value of luminance) and – its saturation (i.e., the purity of the color)

• Both the HSV color model (also called HSB) and the HLS model represent color in this manner

• Geometrically, the HSV color space is a distortion of the RGB space into a kind of three-dimensional diamond called a hexacone



HSV and HLS Color Models (1)

2.6 - Color


• See Figure 2.45, 2.46, 2.46 and 2.47 for the series of distortions




Figure 2.45: RGB color cube viewed from the top

Figure 2.46: RGB color cube ollapsed to 2D

2.6 - Color





Figure 2.47: HSV color space, a hexacone Figure 2.48: HLS Color Space

2.6 - Color


• The distortion of the RGB color space to either HSV or HLS is a non-linear transformation

• In other words to translate from RGB to HSV, you can’t simply multiply each of the R, G and B components by some coefficient




2.6 - Color


• Algorithm 2.3 shows how to translate RGB to HSV• Algorithm 2.4 translates from RGB to HLS




2.6 - Color


• Another way to specify a color is to capture all the luminance information in one value and put the color (i.e., chrominance) information in the other two values.– The YIQ model is one example that takes this approach

• The YIQ is a simple translation of the RGB model, separating out the information in a way that is more efficient for television broadcasting

• In the early days of color televisions, both black and white and color signals had to be transmitted because not all consumers had color television sets



Luminance and Chrominance Color Models (1)

2.6 - Color


• A linear transformation of the values makes this possible. – For a pixel represented in RGB color, le the red, green and

blue color components be respectively R, G and B. Then the equivalent Y, I and Q color components in the YIQ color model are given by

– The values in the transformation matrix depend upon the particular choice of primaries for the RGB model

– Y is the luminance component, I and Q are chrominance



B

G

R

Q

I

Y

311.0523.0212.0

321.0275.0596.0

114.0587.0299.0


2.6 - Color


• The coefficients in the matrix are based on primary colors of red, green and blue that are appropriate for the standard National Television System Committee (NTSC) RGB phosphor

• One more advantage of isolating luminance is that human vision is more sensitive to differences in luminance that differences in color




2.6 - Color


• In practical terms, this means that we don’t need as many bits and therefore as much bandwidth for the transmission of the I and Q components relative to the Y component

• The inverse of the matrix (previous slide) is used to convert from YIQ to RGB

• The YUV color model, originally used in the Europian PAL analog video standard, is also based on luminance and chrominance




2.6 - Color


• The YCbCr model is closely related to the YUV with its chrominance values scaled and shifted

• The YCbCr is used in JPEG and MPEG compression• Using YCbCr compression technique some

chrominance is can be sacrificed during compression without visible loss of quality in photographic images i.e., chroma sampling




2.6 - Color


• Disadvantage of RGB is that there exists visible colors that cannot be represented with positive values for each of the red, green and blue components

• There are 256 evenly-spaced increments of varying color intensities for red, green and blue component (i.e., 256 x 256 x 256 = 16, 777, 216 colors), but this is wrong!

• There exists colors outside the range of those we can create in RGB, colors that we cannot capture with any combination of red, green and blue

• We can know these colors by an experiment called color matching



CIE XYZ and Color Gamuts

2.6 - Color


• Human subjects are asked to compare pure colors projected onto one side of the screen to composite colors projected beside them

• The pure colors are created by single wavelength light• The composite colors are created by a combination of

red, green and blue light, and the amount of the three components are called the tristimulus values

• There are pure pure colors in the visible spectrum that cannot be reproduced by positive amounts of red, green and blue light



CIE XYZ and Color Gamuts – Color Matching (1)

2.6 - Color


• In some cases it is necessary to “subtract out” some of the red, green or blue in the combined beam to match the pure color

• The implication of this experiment is that no computer that bases its color display on combinations of red, green and blue light can display all visible colors

• The range of colors that a given monitor can display is called color gamuts



CIE XYZ and Color Gamuts - Color Matching (2)

2.6 - Color


• Computer monitors may vary in their choices of basic R, G and B primaries, then two monitors can have different gamuts

• By similar reasoning, the gamut of CMYK model will vary from one based on on RGB




2.6 - Color


• In practical terms, there are colors that you can represent on the computer monitor but cannot print, and vice versa

• CIE XYZ was the first color model that represents all visible colors, was devised in 1931 by the Commission Internationale de I’Eclairage.




2.6 - Color


• Note that in some cases , red has to be “subtracted” from the composite light (i.e., added to the pure sample) in order to achieve a match



CIE XYZ and Color Gamuts - Color Matching (5)• r(λ), g(λ) and b(λ) are the light energy need

to create the perceived pure spectral red at wavelength λ

• Let C(λ) be the color the average observer perceives at wavelength λ, then

C(λ) = r(λ)R + g(λ)G + b(λ)B• R, G and B are pure spectral at a fixed

wavelengthFigure 2.49: Color matching functions

2.6 - Color


• There are no three visible primary colors that can be combined in positive amounts to create all colors in the visible spectrum

• The CIE model based on observation uses three “virtual” primaries called X, Y and Z to do so

• X, Y and Z are purely theoretical primaries rather than physical entities

• While they do not correspond to wavelengths of visible light, they provide a mathematical way to describe colors that exist in the visible spectrum




2.6 - Color


• Expressing the color matching function in terms of X, Y and Z produces the graph in Figure 2.50

– X, Y and Z are chosen so that all three functions remain positive over the wavelengths of the visible spectrum




The equation to represent all visible colors becomes:

C(λ) = x(λ)X + y(λ)Y + z(λ)Z

Figure 2.50: XYZ color matching functions

2.6 - Color


• CIE color model makes it possible to graphically compare the color gamuts

• To simplify things further, it is convenient to normalize the values of x(λ), y(λ) and z(λ) so that they sum to 1

• That is, the three colors combine to unit energy




2.6 - Color


• The normalized values show each component’s fractional contribution to the color’s overall energy

• In this way any two of the color components give us the third one. For example,x’(λ), y’(λ) and z’(λ) are called the Chromaticity values



)()()(

)()(',

)()()(

)()(',

)()()(

)()('

zyx

zz

zyx

yy

zyx

xx

)(')('1)(' zyx

Chromaticity Values

2.6 - Color


• Figure 2.51 shows where the chromaticity values fall within the CIE three-dimensional space.



Chromaticity Values Space

Solid triangle represents positiveoctant (unit energy), the curves on the plane shows the values of s’(λ), i.e., pure spectral colors in the visible spectrum

Figure 2.51: X + Y + Z = 1 plane

2.6 - Color


• The dotted line in Figure 2.52 graphs the values of x, y and z for all perceived colors C(λ) as λ varies across the visible spectrum



Visible Color into X + Y + Z = 1 Plane

s(λ)is the finely dotted line, X+Y+Z=1 plane is a triangle drawn with solid lines and the projection of s(λ) is s’(λ) the horse-shaped coarsely dotted line

Figure 2.52: Visible color spectrum projected onto the X + Y + Z = 1 plane

2.6 - Color




CIE Visible Color Space

Figure 2.53: Visible colors in CIE color space

• The horseshoe-shaped coarsely dotted line, form the perimeter of the cone seen in Figure 2.53

2.6 - Color




CIE Chromaticity Diagram• The 2D projection on the XY

plane (Figure 2.54) is called the CIE Chromaticity Diagram

• In this 2D diagram we have a space to compare the gamuts of varying color models

• Color is a 3D phenomenon, therefore requires three values for its specification, the dropped information in this 2D projection is Energy.

Figure 2.54: CIE chromaticity diagram

2.6 - Color


• CIE diagram is helpful in illustrating color concepts and relationships



RGB versus CMYK Gamuts

• The gamut for RGB color is larger than the CMYK gamut• However, neither color space is

entirely contained within the other• Therefore, there are colors that

you can display on the computer screen that cannot be printed, and vice versa

Figure 2.55: RGB vs. CMYK gamuts

2.6 - Color


• Also CIE Chromaticity Diagram gives us a way to standardize color representation

• The conversion from CIE-XYZ to RGB is a simple linear transformation– For a pixel represented in XYZ color, let the values for

the three color components be X, Y and Z. Then the equivalent R, G and B color components in the RGB color model are given by:



Z

Y

X

B

G

R

06.120.006.0

04.088.197.0

50.054.124.3

Conversion from RGB to CIE-XYZ usesthe inverse of the matrix

CIE XYZ to RGB Linear Transformation

2.6 - Color


• Summary advantages of CIE XYZ model– It is device-independent– It provides a way to present all colors visible to humans– And the representation is based upon

spectrophotometric measurements of colors

• Disadvantages of the RGB and CMYK models– They are not device-independent i.e., different

computer monitors and printers can use different values for R, G and B, gamuts are not identical

– They are not comprehensive, some visible colors to human will exist which cannot be presented



CIE XYZ and Color Gamuts

2.6 - Color


• One disadvantage of CIE XYZ model is that– It is not perceptually uniform– In a perceptually uniform color space, the distance

between two points is directly proportional to the perceived difference between the two colors

– It is possible for a color model to be perceptually uniform in one dimension but not perceptually uniform in its three dimensions taken together



CIE L*a*b*, CIE L*U*V*, and Perceptual Uniformity (1)

2.6 - Color


• In 1976 the Commission Internationale de I’Eclairage refined its color models and produced CIE L*a*b* and CIE L*U*V* modeles– The CIE L*a*b* is a subtractive color model in which L*

axis gives brightness values varying from 0 to 100, the a axis moves from red(positive values) to green(negative values) and the b axis moves from yellow(positive values) to blue(negative values)

– The CIE L*U*V* is additive color model that was similarly constructed to achieve perceptual uniformity, but that was less convenient in practical usage



CIE L*a*b*, CIE L*U*V*, and Perceptual Uniformity (2)

2.6 - Color


• Color management system communicates the assumptions about color space, settings for primary colors and the mapping from color values to pysical representations in pixel and ink from one device to another

• Using CIE color space as a universal, device-independent language, a color management system serves as a translator that communicates color settings from one device or software program to another



Color Management Systems

2.6 - Color


• Color management involves five steps– Calibrating your monitor – Characterizing your monitor’s color profile– Creating an individual image’s color profile that

includes choices for color model and rendering intent– Saving the color profile with the image and– Reproducing the image’s color on another device or

application program on the basis of the source and destination profiles



Steps in Color Management Systems

2.6 - Color


• This can be done with specialized hardware or software• Some operating systems of your computer or image

processing program probably have a color management system or you can use more precise hardware-based systems

• Calibration should be done before the monitor is characterized

• Calibration should be done in typical lighting conditions, on a monitor that has been warmed up, and with a background screen of neutral gray for good results



Monitor calibration and Characterization (1)

2.6 - Color


• Calibration steps – Choice of ICC (International Color Consortium) profile

to which changes can be made– Setting the monitor’s white point– Gamma correction or the adjustment of the midtone

brightness– When the adjustment has been made the new monitor

profile is saved– For precise color reproduction, it is necessary to

recalibrate your monitor periodically as image specification or working environments change



Monitor calibration and Characterization (2)

2.6 - Color


• Once your monitor is properly calibrated, a color management policy can be created and saved with each individual image

• The policy is based upon the monitor profile, to which special settings are added for a particular image or group of images that determine how color is translated from one space to another

• In additional to these standard policies, it is possible to create a profile that customizes the settings for rendering intent, dot gain, and the color management engine to be used



Saving a Color Management Policy

2.6 - Color


• The color management engine determines how pixel values in the image file convert to the voltage values applied to and thus the colors of the pixels on the computer screen

• The rendering intent determines how a color in one color space will be adjusted when it is out of the gamut of color space to which it is being converted i.e., from RGB to CMYK for example

• Dot gain is a matter of the way in which we ink spreads as it is applied to paper, and how this may affect the appearance of an image



Color Management Systems Common Terms

2.6 - Color

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