cs781 - Colour for Computer Graphics - Winter 2012

Course Notes

Lecture 20 - Colour Spaces

And Now from our Sponsor

1. Projects
   • April 2: All
2. Tables of useful colour data

Colour Spaces

Suppose you are on the beach.

The four categories below represent increasingly objective/mathematical ways of describing how you have arranged the colours.

1. Based on Substances

2. Based on Samples

These have a variety of different purposes

1. Colour specification: Munsell, OSA
2. Measurement of colour differences: Munsell, OSA
3. Creation of colour harmonies: Goethe, Ostwald, OSA

All colour spaces based on samples have the same strength and weakness

• that you need to have a bunch of colour samples with you
• the strength is that making a match under the same illumination is natural
  • except for surface metamerism
• the weakness is that the colour samples change colour fast if you use them
  • old sample books are better than new ones

Samples

Munsell

Albert H. Munsell

• small samples, 2 degree, are practical for use
• but provide poor colour appearance.
• an interesting mixture of artist, technologist and businessman.

OSA

These samples are bigger, 10 degree, but are not well ordered.

• They appeared at the end of the era of using samples

Artist's Colour Spaces

• Goethe
  • good observations
  • poor explanations
• Ostwald
  • Plochere colour system
• Pantone
  • Used by designers
  • excellent interface to printing

3. Device Dependent

Device dependent means that a point in the colour space provides the input values to a class of devices. Thus, the colour produced, in the sense of colour matching, is only constant for a single device. Nonetheless, there is a little investigated possibility that the appearance of a colour is perceived relative to the gamut of a device on which it appears.

Postscript now has what it calls colour models, a term borrowed from X. When your document tells it, for example, to interpret input colours as encoded as RGB, the driver uses a device model like the one you calibrated with to get device independent colour. The printer then converts it into values appropriate to produce that colour

Additive Devices

RGB

The colour space of computer monitors, broadcast televisions and just about any other kind of additive device..

• Its shape is not exactly what you expect.

HSV, HLS, HSB, HVC, etc.

• All are defined in terms of RGB
• All segregate colour experience by
  • hue (H)
  • saturation, colourfulness (SC)
  • value, lightness, brightness (VLB)
• Promoted as being user-friendly (dread word)

RGYB

Coordinates are r, g & L

• R = rL
• G = gL
• B = (1 - max(r,g))L

R+G+B = (1 + min(r,g))L. Do I believe this?

YIQ

• NTSC colour encoding
  • Y - B&W, 4.2 MHz
  • I - in phase, 1.4 MHz
  • Q - quadrature, 0.4 MHz
• roughly
  • I+Q - Red-green
  • I-Q - Red-yellow
• specifically focussed on minimizing transmission bandwidth.

Subtractive Devices

CMY

This is the device model used for pretty well any kind of subtractive device, usually keyed to particular inks and colouring processes.

CMYK

4. Device Independent

Based on instrumental measurement

Tristimulus Values

Chromaticity Coordinates

5. Colour Difference

The colour spaces above give us

1. increasingly standardized colour identity
2. correct colour topology

They do not give us a measure of colour difference!

• that is, a metric

Lot's of ways to do colour difference experiments

• two colours - report
• two pairs - greater difference
• seven colours - make them all equally distant

Question 1

• How many dimensions are needed to embed the data?
• Is the triangle inequality universally true?

Question 2.

• How should the colour arrangement be stretched or compressed?

Answers to these two questions were provided by the CIE in 1978.

1. The first answer was 3, which is incorrect; the second answer was twins, two uniform colour spaces.
2. Luv
   • L = 116 (Y/Yn)^(1/3) - 16
   • u = 13 L (u' - un):
     • u' = 4 X / (X + 15 Y + 3 Z), un = 4 Xn / (Xn + 15 Yn + 3 Zn)
   • v = 13 L (v' - vn):
     • v' = 9 Y / (X + 15 Y + 3 Z), vn = 9 Yn / (Xn + 15 Yn + 3 Zn)
3. Lab
   • L = 116 (Y/Yn)^(1/3) - 16
   • a = 500 ( (X/Xn)^(1/3) - (Y/Yn)^(1/3) )
   • b = 200 ( (Y/Yn)^(1/3) - (Z/Zn)^(1/3) )

Why are there two?

What does this mean about colour difference?

Comparing Images

Here's three ways that it is done

1. Sum ( (R - R")^2 + (G-G')^2 + (B - B')^2 ) ^(1/2) over pixels
2. Sum ( (X - X")^2 + (Y-Y')^2 + (Z - Z')^2 ) ^(1/2) over pixels
3. Sum ( (L - L")^2 + (u-u')^2 + (v - v')^2 ) ^(1/2) over pixels

Why are neither of these satisfactory?

Suggestions for improvement.

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