Matlab, Python: Fixing colormap to specified values

Question

It is a simple but common task required when trying to fix a colormap according to a 2D matrix of values. To demonstrate consider the problem in Matlab, the solution does not need to be in Matlab (i.e., the code presented here is only for demonstration purpose).

x = [0,1,2; 3,4,5; 6,7,8];
imagesc(x)
axis square
axis off

So the output is as:

when some values change to over the maximum value it happens like:

x = [0,1,2; 3,4,5; 6,7,18];

which looks logical but makes problems when we wish to compare/trace elements in two maps. Since the colormap association is changed it is almost impossible to find an individual cell for comparison/trace etc.
The solution I implemented is to mask the matrix as:

x = [0,1,2; 3,4,5; 6,7,18];
m = 8;
x(x>=m) = m;

which works perfectly.
Since the provided code requires searching/filtering (extra time consuming!) I wonder if there is a general/more efficient way for this job to be implemented in Matlab, Python etc?

One of the cases that this issue occurs is when we have many simulations sequentially and wish to make a sense-making animation of the progress; in this case each color should keep its association fixed.

Answer 1

The indexing is pretty quick so I don't think you need worry.

However, in Matlab, you can pass in the clims argument to imagesc:

imagesc(x,[0 8]);

This maps all values above 8 to the top colour in the colour scale, and all values below 0 to the bottom colour in the colour scale, and then stretches the scale for colours in-between.

imagesc documentation.

Answer 2

f1 = figure;
x = [0,1,2; 3,4,5; 6,7,8];
imagesc(x)
axis square
axis off

limits = get(gca(f1),'CLim');

f2 = figure;
z = [0,1,2; 3,4,5; 6,7,18];
imagesc(z)
axis square
axis off
caxis(limits)

Answer 3

In Python using package MatPlotLib the solution is as follows:

import pylab as pl
x = [[0,1,2],[3,4,5],[6,7,18]]
pl.matshow(x, vmin=0, vmax=8)
pl.axis('image')
pl.axis('off')
show()

So vmin and vmax are boundary limits for the full range of colormap.