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Advanced Computer Graphics: Colour James Gain Department of Computer Science University of Cape Town [email protected] Objectives To describe the human visual system and our perception of colour To introduce the physics of colour To cover a range of colour models and their relative merits

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advanced computer graphics colour

Advanced Computer Graphics:Colour

James Gain

Department of Computer ScienceUniversity of Cape Town

[email protected]

Advanced Computer GraphicsCollaborative Visual Computing Laboratory

objectives
Objectives
  • To describe the human visual system and our perception of colour
  • To introduce the physics of colour
  • To cover a range of colour models and their relative merits

Advanced Computer Graphics

what is colour
What is Colour?
  • physical description:
    • a spectra of wavelengths.
  • psychological perception:
    • a stimulus sent from the optic system to the brain.
  • computer description:
    • different sets of bases and coordinates, depending on the type of display and application.
  • Problem:
    • How do we ensure that the different representations create the same visual effect?

Advanced Computer Graphics

sight
Sight
  • Arguably our principle modality.
  • An area of considerable research and development.
  • Components:
    • Wetware: The human visual system.
    • Hardware: Visual display systems (e.g. computer monitor).
    • Software: Rendering of 3D scenes (e.g. PSC).
  • Perceptual Terms:
    • Hue: Distinguishes among colours such as red, green, purple and yellow.
    • Saturation: Refers to how far a colour is from a grey of equal intensity. (How intense is the hue)
    • Brightness: the perceived intensity of a self-luminating object. (How much light is emitted). Alternatively, lightness refers to intensity from a reflecting object.

Advanced Computer Graphics

human visual system
Human Visual System
  • The lens of the eye forms an inverted image of the world on the back surface (retina) of the eye.
  • Cones:
    • 150000 per square millimeter in the fovea.
    • High resolution, colour.
  • Rods:
    • Lower resolution
    • monochromatic.
    • Peripheral vision: so we keep the high-res region in context and avoid being hit by passing branches.
  • Information is passed to the visual cortex (which performs extremely complex processing).

Advanced Computer Graphics

visual cortex tristimulus reality
Visual Cortex: Tristimulus Reality?
  • Types of Cones:
    • Low: 560 nm red ?
    • Medium: 530 nm green ?
    • High: 420 nm blue ?
  • Signal to brain:
    • L - M ®red-green
    • H - (L+M) ®blue-yellow
    • L + M ®red+green» overall luminance
  • Red/Green colour blindness means no signal L – M signal.

Advanced Computer Graphics

hardware the ultimate display
Hardware: The Ultimate Display
  • Ivan Sutherland’s “Ultimate Display” [1965] postulated a display which produced images indistinguishable from reality.
  • Requirements of ultimate Head Mounted Display (HMD):
    • Viewing distance: 10cm
    • Human visual acuity: 1’ ( ) of visual arc on average 5” ( ) in the best-case
    • Field of View (FOV): Horizontal = 200 deg Vertical = 100 deg
    • Update Rate: 60Hz
    • Must also match other aspects of Human Visual System.
  • Required Flat Screen Resolution:
    • 1’ visual acuity requires 12000x6000 pixels
    • 5” visual acuity requires 144000x72000 pixels

Advanced Computer Graphics

artists perception of colour
Saturation

Tints

Tones

Brightness

Greys

Shades

Artists’ Perception of Colour
  • Artists mix white and black with pure colours
    • Tint = Pure colour + white
    • Shade = Pure colour + black
    • Tone = Pure colour + black + white

White

Pure

Colour

Black

Advanced Computer Graphics

physics of colour colorimetry
Physics of Colour: Colorimetry
  • Light is electromagnetic energy in the 400-760nm wavelength
  • Perceived as a spectrum of colours: violet, indigo, blue, green, yellow, orange, red.
  • Light energy, present simultaneously at each wavelength, is represented as a spectral energy distribution, P(l).
  • Physics vs. Perception:
    • Hue = dominant wavelength
    • Saturation = excitation purity
    • Brightness (self-luminous objects), lightness (reflecting objects) = luminance (amount of light)
    • Pure colour: a single highly dominant wavelength

Advanced Computer Graphics

spectral distribution
Spectral Distribution
  • One colour = one spectral energy distribution

Energy

P(l)

Wavelength

l

400 nm

Violet

760 nm

Red

Advanced Computer Graphics

hue saturation and brightness
Hue, Saturation and Brightness

Energy

P(l)

Dominant

wavelength

e2

Brightness =

area under

the curve

Saturation

e1

l

400 nm

Violet

760 nm

Red

Hue

Advanced Computer Graphics

retina response
Retina Response
  • Fraction of light absorbed by the three types of cones (R, G, B):

0.2

G

R

Light

Absorbed

B

l

0.0

760 nm

Red

400 nm

Violet

Advanced Computer Graphics

retina luminous efficiency
Retina Luminous Efficiency
  • The eye’s response to light of constant luminence with varying dominant wavelength.
  • Peak sensitivity (ability to resolve detail) is to yellow-green light.

100

Relative

Sensitivity

l

0

760 nm

Red

400 nm

Violet

Yellow-Green

550 nm

Advanced Computer Graphics

colour definition
Colour Definition
  • Define a colour by its spectral distribution:
    • Large memory requirements to create an adequate sampling of the distribution.
    • Dominant wavelength (hue) is not always immediately obvious.
    • Metamers: Different spectra with the same colour response. No uniqueness.
  • Need for simpler bases:
    • describing all colours
    • with a unique set of coordinates

Advanced Computer Graphics

metamers
Metamers

Same orange-like colour

Energy

P(l)

l

400 nm

Violet

760 nm

Red

Advanced Computer Graphics

primary colours
Primary Colours
  • Since our cones are sensitive to red, green and blue why not describe all colours as a linear combination of these primaries?
  • Below: value of three primaries required to match all wavelengths.

Values

V(l)

l

400 nm

Violet

760 nm

Red

Advanced Computer Graphics

ci model
CIÉ Model
  • Commission Internationale de l’Éclairage defined a colour model in 1931.
  • Three standard primary functions:
    • X, Y, Z
    • Defines all visible colours
    • Only positive coefficients
  • Y = retina luminance perception function
  • X and Y = chromaticity

Advanced Computer Graphics

ci basis functions
CIÉ Basis Functions

Values

V(l)

Z

Y

X

l

400 nm

Violet

760 nm

Red

Advanced Computer Graphics

ci chromaticity diagram
CIÉ Chromaticity Diagram
  • Project the CIÉ plane of constant luminosity (X+Y+Z=1) onto the X-Y plane.

Advanced Computer Graphics

ci chromaticity diagram20
CIÉ Chromaticity Diagram
  • Colours on the horseshoe perimeter are fully saturated.
  • Complementary colours are those that can be mixed to produce white light.
  • Diagram factors out luminence so brown (orange-red at very low level luminance relative to its surrounding area) does not appear.
  • Dominant wavelength can be calculated by drawing a line from white through the colour and intersecting the perimeter.
  • Nonspectral colours (purple and magenta) intersecting the base of the horseshoe do not have a dominant wavelength.

Advanced Computer Graphics

ci chromaticity perimeter
CIÉ Chromaticity Perimeter

y

Green

520

540

560

Yellow

500

580

White

600

Cyan

Red

480

700

Purple

x

400

Advanced Computer Graphics

ci chromaticity attributes
CIÉ Chromaticity Attributes

y

Green

B

Yellow

A

D

Cyan

Red

C

E

F

G

Purple

x

Advanced Computer Graphics

mixing colours
Mixing Colours

y

Green

  • All colours on a straight line segment can be created by mixing the endpoints.
  • Similarly, colours within a triangle are a combination of the endpoints.

Yellow

I

Cyan

Red

J

K

Purple

x

Advanced Computer Graphics

ci colour gamuts
CIÉ Colour Gamuts

Monitor RGB Gamut

Film Gamut

x

Advanced Computer Graphics

beyond ci 1931
Beyond CIÉ 1931
  • Equal steps across the Chromaticity Diagram do not equate to equal perceptual distances.
  • CIÉ 1976: perceptually uniform
  • LUV:
    • L for lightness
    • U and V for chromaticity

Advanced Computer Graphics

computer description
Computer description
  • Display device based colour-spaces:
    • RGB (monitor)
    • CMYK (printer)
    • YIQ (television)
  • Perception based colour-spaces:
    • HSV (user interaction)
  • Need to:
    • Correct for different display characteristics
    • Convert between colour models

Advanced Computer Graphics

rgb colour model
RGB Colour Model
  • Red, Green and Blue primaries.
  • Most well known colour space.
  • Used (internally) in every monitor.
  • Additive (colours added to a black background)
  • Black = (0,0,0), White = (1,1,1)

Advanced Computer Graphics

cmy colour model
CMY Colour Model
  • Cyan, Magenta and Yellow Primaries
  • Used (internally) in colour printers
  • Substractive (colours subtracted from a white background)
  • Black = (1,1,1), White = (0,0,0)
  • Complementary to RGB:

Advanced Computer Graphics

the rgb cmy cube
The RGB/CMY cube

Blue

Cyan

Magenta

White

Black

Green

Red

Yellow

Advanced Computer Graphics

cmyk colour model
CMYK Colour Model
  • CMYK (Cyan, Magenta, Yellow, blacK)
    • Mostly for printer use
    • Saves on coloured inks by using black ink as far as possible
    • As a result dark colours dry more quickly
  • Converting from CMY to CMYK
    • Black is used instead of equal amounts of C, M, Y.
    • K = min(C,M,Y)
    • C = C – K
    • M = M – K
    • Y = Y – K

Advanced Computer Graphics

yiq yuv colour model
YIQ, YUV Colour Model
  • U.S. commercial television broadcasting
  • Recoding of RGB for:
    • Transmission efficiency
    • Backward compatibility with Black and White TV (drop I and Q)
  • YIQ = NTSC
    • Y is luminance
    • I and Q are chromaticity
  • YUV=PAL
  • Exploits visual system:
    • More sensitive to changes in luminance (Y) than chromaticity (I and Q) -> more bandwidth for Y
    • Objects covering a small field of view produce limited colour sensation -> either I or Q can have lower bandwidth.
    • Ratio Y:I:Q = 4:1.5:0.6

Advanced Computer Graphics

hsv colour model
HSV Colour Model
  • Hue, Saturation and Value Primaries
  • Cylindrical co-ordinate system:
    • Hue (H = 0 – 360 deg) rotation
    • Saturation (S = 0.0 – 1.0) radius
    • Value (V = 0.0 – 1.0) height
  • User oriented and based on the intuitive appeal of artist’s colours (hue, tint, shade).
  • Represented by a hexcone.

Advanced Computer Graphics

the hsv cone
The HSV cone

Green

Yellow

Cyan

Red

White

Blue

Magenta

Black

Advanced Computer Graphics

hsv conversion
HSV conversion
  • Flatten RGB cube along the diagonal to create HSV hexagon
  • There is an algorithm for converting in both directions
  • RGB to HSV:

max = max(r,g,b); min = min(r,g,b)[

V = max

S = (max-min)/max

H = more complicated

Green

Yellow

Red

Cyan

Blue

Magenta

Advanced Computer Graphics

hsv properties
HSV properties
  • Interpolating Colour:
    • Linear interpolation of the same two colours in RGB, CMY, YIQ and CIE all produce the same result. Appropriate for Gouraud shading
    • Not true for HSV. But interpolating between colours while keeping Hue, Saturation or Value constant is obviously easier.
  • Effective for visualization:
    • change saturation, at constant hue
    • change hue, at constant saturation (maps)

Advanced Computer Graphics

colour fidelity
Colour Fidelity
  • Problem: ensure that colours look the same when changing display devices
    • Sample the RGB phosphors with colorimeters
    • Sometimes device description are available from manufacturers
  • Convert to XYZ space:
  • From XYZ to device dependent RGB uses the inverse.

Advanced Computer Graphics

intensity perception
Intensity Perception
  • Human perception of intensity is logarithmic:
    • Sensitive to ratios of intensity levels not absolute steps
    • I = 0.1 to 0.11 has same as I = 0.5 to 0.55
    • Cause of Mach-Banding
    • Need more steps at lower intensity levels
  • CRT intensity related to voltage:
    • Constants depend on the particular CRT
  • Gamma Correction: lookup table which correct for both hardware and perceptual issues with intensity.
  • Can lead to strange effects if forgotten. Transferring a picture between monitors with different gamma values causes problems.

Advanced Computer Graphics

displaying colours
Displaying colours
  • Colour ability of the display
    • measured in bits:
      • 1 bit=2 levels, 8 bits=256 levels
    • bits per colour primitive:
      • 24 bits=256 levels for each of R,G,B
  • Depends on the medium:
    • TV Screen: 30 dpi, 8bits colour
    • Computer Screen: 70-100 dpi, 24 bits colour
    • Laser Printer: 300-2400 dpi, 3 bits colour (8 colours)
    • Photo: 800 dpi, 36 bits colour

Advanced Computer Graphics

gaining colour resolution
Gaining colour resolution
  • Sometimes, this colour resolution is not enough. How do we display more colours?
  • Basic idea:
    • Sacrifice some of the spatial resolution for intensity resolution
    • Halftoning and dithering
  • Halftoning:
    • For top quality printers
    • Discs of size varying inversely with Intensity
    • Pattern angle (called screen angle)
    • Halftone resolution (different from spatial resolution)
    • 60-80 dpi for newspapers, 120-200 dpi for books

Advanced Computer Graphics

dithering
Dithering
  • Used if halftoning is not possible (because of the wrong type of printer or use of a monitor)
  • Dither patterns
    • Group of n*n pixels = n*n+1 intensity levels
    • 2x2 example:
    • Matrix notation:

0

1

2

3

4

Advanced Computer Graphics

dithering properties
Dithering Properties
  • For level i, display pixels with v < i
  • Requirement of matrix:
    • Don’t produce visual artefacts (e.g. straight lines)
    • Growth sequence (minimizes differences in nearby areas)
    • dispersed dots for CRT, clustered dots for printers

Advanced Computer Graphics

dithering the next step
Dithering: the next step
  • One image pixel = 4 or 9 printer pixels
  • What if I want one image pixel = one printer pixel?
  • Use modulo:
    • i = x modulo n
    • j = y modulo n
    • Light the pixel if value (i, j) in dithering matrix is smaller than I(x, y)
  • Error diffusion:
    • There is an error at each pixel
    • Dithering pattern is sometimes visible
    • Floyd-Steinberg error diffusion spreads the error to neighbouring pixels

Advanced Computer Graphics

using colours in cg
Using Colours in CG
  • Meaningless colours reduce performance by up to one third.
  • Design colour schemes first in monochrome. This does not prejudice the colour blind.
  • Aesthetics: Use even perceptual steps between colours, complementary colours, even intensities.
  • Using colours for codes can have unintended meanings.
  • Perception:
    • Colour of area is affected by surroundings.
    • Colours seem to advance (red) or recede (blue).
    • Blocks of the same size in different colours appear to have different sizes (red > green)

Advanced Computer Graphics

conclusion
Conclusion
  • Several ways to represent colours. Each one suited to a specific task:
  • Conversion between colour models is often required:
    • for colour fidelity (convert to CIE and back to device-space)
    • for displaying the image in a different medium
  • But remember colour is heavily influenced by our perceptions!

Advanced Computer Graphics

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