Default Color Map

While at lunch recently I was flipping through a recent edition of IEEE Computer Graphics and Applications and came across the following article by David Borland and Russell M. Taylor II: "Rainbow Color Map (Still) Considered Harmful." The article iterates over all the well known ways that the rainbow color map fouls up visualization. What really caught my eye, though, was that ParaView was specifically mentioned.

Inspection or documentation indicated that ParaView, Matlab, VisAD, Ensight, Iris Explorer, and AVS Express all use the rainbow color map by default. Supplied tutorials indicated that SCIRun and OpenDX use the rainbow color map by default. Amira is the only program reviewed that does not use the rainbow color map by default.

It is a little bit embarrassing to be pointed out in a national article as a bad example for visualization. Still, we are also lumped into the same category as Ensight, AVS, and SCIRun (and VisIt was never even mentioned). Nonetheless, as a world leader in visualization it would be nice to do something better or, if we can't, have a pretty good reason why not. Thus, I started my quest to find that elusive "best" color map.

The rest of this Wiki page visits each color map in consideration and lists the pros and cons of each. It then shows image examples of the color map in use on three data sets. The first set is a spatial contrast sensitivity function. You will see frequency increasing to the right and contrast increasing to the bottom. This data set demonstrates the ability of the color map to show minimal contrast field changes. The second data set is a torus with the elevation filter applied to it. This data set can highlight banding caused by a color map. The third data set is a skull with a scalar field synthesized by summing the sine of the coordinates. I choose the scalar field in a way that would most interfere with the shading cues used to discern the shape of the object.

Rainbow Color Map

We all know and love (or hate) the rainbow color map. Adopted early on by physicists (who knew much more about electromagnetic radiation than human visual perception), it has become the rather unfortunate de-facto standard for visualization.

Pros

It is pretty. Although you will probably never see this mentioned as a factor in the literature, it can be pretty important in practice. Users will never choose ParaView if they feel our images are less "slick" than others.
It has high ordinality. The rainbow passes through 5 distinct colors (blue, cyan, green, yellow, and red) and we could increase that to 6 if we chose to go down to violet. The colors visually separate the field into regions. Although the region boundaries are arbitrary and uneven, it nonetheless can simplify comparing regions.

Cons

The ordering is based on a physical phenomenon far removed from the visual perception of color. Experiments show that when human subjects are asked to order these colors, the results vary.
Uneven perceptual changes. Equal increments in RGB or HSV space do not necessarily lead to equal perceptual increments. This leads to variation in widths of colors and occasional sharp transitions between colors, which leads to uneven bands in the color map. This can be actively misleading as there will be sharp transitions where there is none. It can also hide transitions that happen to fall within a band perceptually equivalent color. This is demonstrated in the spatial contrast sensitivity function below.
Erratic luminance. The visual system perceives high spatial frequencies through changes in luminance, and luminance is often the best cue to ordering. However, the rainbow map is neither isoluminant nor ordered luminance. It goes from low luminance (blue) to high (cyan) to moderate (green) to high (yellow) to moderate (red).

That said, the rainbow color map is probably not as bad as indicated by the literature. The ordering is probably already ingrained in our users. We learn it pretty quickly. For example, my 6-year-old knows the colors of the rainbow in the proper order, consistently draws rainbows correctly, and has pointed out to me (without prompting) mistakes in other drawings. The perceptual problems introduced by the color map do not seem to bother many users either. I don't recall ever hearing a single complaint from users who go ballistic whenever data is inappropriately modified or misrepresented. In fact, one user told me that he was using rainbow pseudocoloring rather than grayscale on height field images knowing the perceptual problems involved with no explanation other than he simply "liked the colors". Perhaps the examples of bad mapping that we can easily construct do not often come to play in real-world problems.

Grayscale and Black-Body Radiation Color Maps

The visual system is most sensitive to changes in luminance, so it comes as no surprise that a popular color map in literature is simply a grayscale that goes from black to white. This map is also popular in the medical field, although it may simply be an artifact of classical x-ray imagery being grayscale.

Pros

Clear perceptual ordering.
High spatial contrast sensitivity.

Cons

Bad absolute resolution. The visual system interprets the luminance of a location relative to that its surroundings. Thus, it is difficult to get the absolute value represented by the color map. Experiments show that users produce errors of up to 20 percent (see Colin Ware's Information Visualization: Perception for Design).
Inappropriate for 3D surfaces. Both this color map and 3D shading use changes in luminance. Thus, the two used together will interfere with each other. That makes this color map ineligible as a default for ParaView.

A similar color map is the black-body radiation color map, which mimics the visible color of a physical object as it is heated. At about 600 C, the object begins to glow a dull red. The color gets brighter as the object gets hotter, and the color moves from red to orange to yellow to white.

Pros

About all of the same pros as the grayscale.
The colors add some information about the absolute value in the map.
The images can look pretty slick.

Cons

The coloring ordering is opposite that of the rainbow color map that many people are used to, although the luminance should give enough indication of ordering.
The black still interferes with shading, making it still inappropriate for 3D surfaces.

Isoluminant Color Maps

The fourth and last color map presented by the CG&A article was an isoluminant color map. The one given in the paper was a green-to-red isoluminant map which I have mimicked here. (Note: I was lazy and just did an RGB interpolation from <1,0,0> to <0,0,1>. It's not totally isoluminant --- specially at the ends --- but it is pretty close.) I also tried the "CIELab" isoluminant color map that has been with ParaView for many years now. I'm not sure on its origins, but it looks to be one of the better isoluminant color maps I have seen.

Pros

Does not interfere with shading.
Relative comparisons are consistent.
Visibly retrieving the values is relatively accurate.

Cons

They are butt ugly.
They tend to look too dark.
The visual system is not great as picking up small changes in hue. Thus, the effective resolution is low.

In short, I think these color maps would be quickly rejected by users.

Brewer Color Maps

The CG&A article left me a little flat. Having no better suggestion, it recommends an isoluminant color map for 3D surfaces. However, the isoluminant color maps have a fairly low perceptual resolution and, quite frankly, look like crap.

It did have another suggestion, though (one I have heard before), and that is to go to the ColorBrewer, which is basically a collection of color maps designed by color expert Cindy Brewer. The color maps are designed to be both aesthetically pleasing and contain changes that are perceptually consistent. Although the maps are designed to be used on a finite number of classes, I get around that by simply interpolating between colors (which may or may not be a good thing).

I picked divergent color maps (maps that go from color to neutral to color which separates values with a median point) mostly to maximize the range of colors. I went through three iterations. The first one looks good, but has a bit of a sickly yellow color in the middle. I then chose a similar map but with white in the middle. I think it looks nicer but may not be quite as smooth as the first. I was a little worried about how dark the ends were and how they effect shading, so I made a third version that goes to lighter colors. It reduces the luminance changes but also decreases the perceptual resolution. Like with all things it is a tradeoff.

Pros

Perceptual ordering is fairly intuitive. It goes from cool (blue) to neutral (white) to warm (red).
It is similar to the rainbow color map. It is fairly similar to the current ParaView rainbow color map default except that we have swapped out the green for white. Users probably will not get upset by the change.
It is aesthetically pleasing.
It does not interfere too much with shading.
It does not hide data in bands as much as the rainbow. Compare the images of the spatial contrast sensitivity function.

Cons

Lots of control points. Each one has 9 to 11 control points, which can be a hassle to users if they want to edit the color map. We may get around that some by doing interpolation in a perceptually linear space like CIE.
It is not quite as sensitive to change as the grayscale map and interferes a little more with shading than the isoluminant maps. It also has less color separation than the rainbow. However, these are all conflicting requirements, and I think these color maps make a good compromise.

Table of Color Maps

For reference and comparison, here is a table comparing all the color maps with three different data sets. From left to right, the data sets are: a spatial contrast sensitivity function, a torus with an elevation field, and a skull with a distracting scalar field. From top to bottom, the color maps are: rainbow, grayscale, black-body radiation, isoluminant red-green, isoluminant CIE lab, and three maps derived from the ColorBrewer.