cs781 - Colour for Computer Graphics - Winter 2012

Course Notes

Lecture 18 - Calibrating Subtractive Colour

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Continuous Tone Subtractive Devices

Digital

Continuous tone is what you have with most additive devices

• half-tone:
  • only colour or no colour
  • intermediate colours average colour areas with no colour areas, so they are not uniform
  • pseudo-pixels must be bigger than the resolution of the device
• continuous-tone
  • `continuous' range of colours
  • no averaging needed
  • pseudo-pixels need be only as big as the number of colour channels

Examples

• dye sublimation
• ink-jet

Craft

• rotogravure: monochrome, as close as you can get to the subtle tones of B&W photography
• fine art prints: colour, often using many screens each with a different ink.

Photography

How is it different?

• The photosensitive material is disordered, in image capture and in image creation.
• In B&W this is silver grains randomly located on the film or paper.
• Two types of colour:
  1. Technicolor, which is additive
     • split the incoming light into three
     • expose B&W film through three filters.
     • project from three carefully aligned projectors
     • combine in a beam-splitter
  2. Dye-coupled layers, which is subtractive
     • film has three layers with three different photosensitive chemicals
     • Chemicals develop into three B&W images
     • Three dye couplers attach themselves, one to each image
     • Beer's law applied to three filters that differ in density determines the final colour.
• In both cases the grains vary in size and are randomly placed.
• Resampling is done optically.

Nostalgia for Kodachrome

Calibrating Subtractive Colour

Definition. Given

• a standardized source of illumination
• standard paper,
• standard inks, and
• adequate stability in the printing process,

you can create a mapping from CMYK --> XYZ. With a little trouble, and a few workarounds, you can make it invertible. The problem is ensuring that it will be the same tomorrow. Then you can use

• RGB --> XYZ --> CMYK, from an additive device to a subtractive one (e.g., monitor to printer), or
• CMYK --> XYZ --> C'M'Y'K', from one subtractive device to another (e.g., printer to a different printer).

Adobe put something like this into PostScript under the name `colour model'.

Making the Mapping

The stability assumption is the hard one.

• It's not hard to make it work for a print run,
• but a laser printer doing several dozen pages a day is another matter.

Using Brute Force

1. Print a calibration sheet with 8x8x8 (=512) colours using the printer's CMY --> CMYK conversion function
2. Using the standard illumination measure XYZ for each sample.
3. Usually assuming monotonicity, fit the data to something smooth.
4. Rebuild the tabular function.
5. Use trilinear interpolation to interpolate in the table.
6. Use interpolation to build the reverse table.

Using a Model

Think about the actual process of making colour. For example,

1. The CMY you give an ink-jet printer is converted internally to CMYK.
2. Each pass adds some pigment to the paper.
3. Measure how much pigmented ink is added to the paper in each channel
4. Using an ink-mixing model like Kubelka-Munk to find the result. (You can find many recent papers tweaking such models for the properties of inks on paper.)

Note about Mappings

Mappings from input coordinates to amounts of ink, or toner, or coloured wax, etc. are a required feature of every printer, and are an important aspect of creating satisfied customers. Calibration services for any sort of colour device have not been successful outside commercial colour reproduction, where they are usually done in-house.

Gamut Mapping

When the gamuts don't fit,

• maximize brightness, preserving contrast, saturation, and hue.
  • Tone repreduction curve (TRC) may help here.
  • Photographers have for more than a century manipulated TRCs using chemistry.
  • Printers have manipulated TRCs electro-mechanically.
  • Photoshop et al. users have manipulated TRCs using direct manipulation
• maximize contrast, preserving saturation and hue
• maximize saturation, preserving hue
• rotate hue preserving order and colour names
• clip a few colours to make the fit better

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