# 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.

## 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

#### 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.

## 4. Device Independent

Based on instrumental measurement

## 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.