Re: [matplotlib-devel] Matplotlib's new default colormap

[Maximilian A. <max...@gm...>]

Hi all,

I had a discussion with Phil Elson about this last weekend during the
Bloomberg Open Source Day. I don't consider myself an expert on colormaps
by any means, but I started digging into them a while ago when I was
looking for a way of generating a perceptually linear *cyclic* colormap in
order to represent phase angle values. (I've been meaning to discuss this
issue on this list for a while but will do so in a different thread once I
get around to tidying up my results so far.) Phil encouraged me to reply to
this thread because he said that even non-expert views would be very
welcome, so here you go.

Basically, I agree with most of what Nathaniel Smith suggested in his email
from November 21. I'm going to comment on some of his points inline below
and will finally suggest a way of designing a new colormap at the end.


Nathaniel Smith wrote:

> it should be a sequential colormap [...]

Agreed.

> it should be perceptually uniform

Agreed.

> There's lots of research on how to measure perceptual distance --
> a colleague and I happen to have recently implemented a
> state-of-the-art model of this for another project, in case anyone
> wants to play with it [3].

I haven't had time to check this out in detail yet, but it looks pretty
interesting and will certainly be very useful to assess the quality of any
suggestions. However, can this help to actually *design* a new colormap?
The answer might be hidden in the referenced paper [Luo2006], but I haven't
read it yet.

> or just using good-old-L*a*b* is a reasonable quick-and-dirty
approximation.

Can you elaborate how "dirty" you think using L*a*b* would be? (See my
suggestion for finding a new colormap below.)

>- it should have a perceptually uniform luminance ramp, i.e. if you
> convert to greyscale it should still be uniform.

Agreed. What's unclear to me is how large this luminance ramp should be. We
certainly can't go all the way to full luminance because this won't be
visible on a white background. This probably needs experimenting (again see
below).

> - it should also have some kind of variation in hue, because
> hue variation is a really helpful additional cue to perception,
> having two cues is better than one, and there's no reason
> not to do it.

Agreed.

> - the hue variation should be chosen to produce reasonable results
> even for viewers with the more common types of colorblindness.
> (Which rules out things like red-to-green.)

Agreed. Are you aware of any simple ways of avoiding the most common
issues? Are there any blog posts or papers on designing colormaps that are
suitable for colorblind people?

> And, for bonus points, it would be nice to choose a hue ramp that
> still works if you throw away the luminance variation, because then we
> could use the version with varying luminance for 2d plots, and the
> version with just hue variation for 3d plots. (In 3d plots you really
> want to reserve the luminance channel for lighting/shading, because
> your brain is *really* good at extracting 3d shape from luminance
> variation. If the 3d surface itself has massively varying luminance
> then this screws up the ability to see shape.)

Just out of interest, is there currently an easy way in matplotlib of
producing a 3d plot where luminance is used for lighting/shading as you
suggest?


Now the question is: how do we actually *design* a colormap with these
requirements? Leon Krischer's notebook [1] looks totally awesome, but if I
understand correctly the optimisation he uses "only" takes care of
linearising the luminance value, but this does not necessarily guarantee
that the hue values are also linear, right? It also feels somewhat clumsy
to me to start out with a colormap that's "wrong" (w.r.t. our requirements
above) and then "fix" it. However, the notebook looks like a great guidance
for finding suitable candidates and assessing their quality.

It appears to me that a simple yet effective way of coming up with a good
colormap would be to pick two points in the L*a*b* color space that can be
represented by RGB values, connect them by a line and use the interpolated
values for the resulting colormap. Since L*a*b* space is (close to)
perceptually linear, this would pretty much guarantee all the requirements
above.

What's missing is an easy way of doing this. I'm envisaging a simply GUI
which allows the user to easily pick two points in L*a*b* space, generates
a colormap from them as described above and also generates a few sample
plots to evaluate the quality of the colormap (along the lines of [1] or
the numerous blog posts linked to in the discussion). I am close to having
a prototype for such a GUI which should allow to do this relatively
painlessly. I'll try to finish it up over the weekend and will post here
once it's ready. Btw, if anyone has suggestions for sample datasets that
can help in assessing the quality of colormaps they would be much
appreciated.

Any comments or clarifications of points that I misunderstood are very
welcome.

Best wishes,
Max

[1] http://nbviewer.ipython.org/gist/krischer/d35096a9d3b6da5846a5