Assignment 1: Monitor Characterization
======================================

Goal 
----

To create a monitor model that predicts 
the monitor RGB values required to display given 
tristimulus values (CIE XYZ).

What to Do 
----------

1. Using a colorimeter, measure and record tristimulus values
(XYZ or Yxy) for ten or more colours along each of three ramps:  
black to red, black to green, black to blue. The luminance (Y) 
is the most important component, as you will use it for gamma 
correction. A few things to note:
   - the monitor should be warmed up for a while
   - the room lights should be off for measurement
   - the central part of the screen is best for measurement
   - a tripod should be used with the colorimeter
   - the line of sight from the colorimeter to the screen
   should be at right angles to the screen
   - make note of the setup (screen brightness, contrast,
   colorimeter distance to the screen, etc.) in case you 
   need to reproduce it later.

2. Also measure and record tristimulus values for
full white. Presumably you have full black, red, green
and blue from (1). On a good monitor you expect that
roughly R+G+B=W for the XYZ values; more precisely, since
the black point (K) is non-zero, representing ambient
light in the room, you expect (R-K)+(G-K)+(B-K)=(W-K).
If this is not true, it is usually a power limitation of
the monitor.

3. Implement a matrix and lookup table (or matrix and 
gamma function) mapping that takes RGB to XYZ. You can
use the Cowan paper method if you like, or something
simpler with a gamma function, or piecewise linear 
or spline interpolation in a table. Check that
your model does indeed behave like the monitor.

4. Invert the mapping in (3) so that you can map XYZ to
RGB at will. Make sure your code does something sensible
(gives an error, or suggests an approximation)
when out-of-gamut XYZ are input.

What to Hand In
---------------

A. Show tables and/or graphs from your measurements in
(1) and (2). Include at least a graph of the luminances
for the R, G, B ramps, as their shape is of interest.

B. Give me a paragraph describing the method you
chose for the monitor model and inverted model.

C. Here are measurements of a Macbeth colour checker,
using the Colortron II spectrophotometer.

Macbeth Colour Checker (Mac2) with Colortron
X	Y	Z
10.323	9.330	6.291
36.984	34.737	25.721
18.085	19.290	35.750
10.068	12.705	6.513	
24.587	23.354	43.841	
31.419	43.126	44.581	
34.284	27.800	6.035	
13.294	11.763	36.868	
26.955	18.424	14.207	
8.388	6.040	15.072	
33.146	43.396	11.291	
44.500	40.698	8.393	
7.919	5.711	28.346	
14.714	23.450	9.580	
18.705	10.744	5.291	
54.890	58.503	9.900	
29.146	19.223	31.981	
14.523	19.684	38.984	
84.712	89.532	94.411	
55.404	58.745	63.144	
33.852	35.752	39.242	
18.204	19.321	21.038	
8.299	8.809	9.917	
2.541	2.661	3.048	

For each of these tristimulus values, apply your
inverse model, display the resulting color on the
screen, measure with the colorimeter, and record
your result. Show me a table with the given 
Yxy versus your measured Yxy. Write a paragraph
rationalizing any discrepancies.
In addition, tell me whether the given Macbeth data
above was measured under illuminant C, D50 or D65.

D. Create a 4-row by 6-column image using your
predictions in (B) and display it on the monitor.
Compare it visually with the Macbeth colour checker 
as best you can in a reasonably-lit environment.
Write a paragraph commenting on the success of 
this visual comparison.

Marking
-------

For anything that does a basic job of modelling the
monitor (based on C above), I'll give 6/10. The
model will be given a mark out of 2 based on 
any bells or whistles like the full Cowan method,
spline interpolation, or whatever. The paragraphs
will also be given a mark out of 2.