Beware of Mach Bands in Continuous Color Ramps

A recent post of mine on the cross validated statistics site addressed how to make kernel density maps more visually appealing. The answer there was basically just adjust the bandwidth until you get a reasonably smoothed surface (where reasonable means not over-smoothed to one big hill or undersmoothed to a bunch of unconnected hills).

Another problem that frequently comes along with the utlizing the default types of raster gradients is that of mach bands. Here is a replicated image I used in the cross validated site post (made utilizing the spatstat R library).

Even though the color ramp is continous, you see some artifacts around the gradient where the hue changes from what our eyes see as green to blue. To be more precise, approximately where the green hue touches the blue hue the blue color appears to be lighter than the rest of the blue background. This is not the case though, and is just an optical illusion (you can even see the mach bands in the legend if you look close). Mark Monmonier in How to Lie with Maps gives an example of this, and also uses that as a reason to not use continous color ramps (also another reason he gives is it is very difficult to map a color to an exact numerical location on the ramp). To note this isn’t just something that happens with this particular color ramp, this happens even when the hue is the same (the wikipedia page gives an example with varying grey saturation).

So what you say? Well, part of the reason it is a problem is because the artifact reinforces unnatural boundaries or groupings in the data, the exact opposite of what one wants with a continuous color ramp! Also the groupings are largely at the will of the computer, and I would think the analyst wants to define the groupings themselves when disseminating the maps (although this brings up another problem with how to define the color breaks). A general principle with how people interpret such maps is that they tend to form homogenous groupings anyway, so for both exploratory purposes and disseminating maps we should keep this in mind.

This isn’t a problem limited to isopleth maps either, the Color Brewer online app is explicitly made to demonstrate this phenonenom for choropleth maps visualizing irregular polygons. What happens is that one county that is spatially outlying compared to its neighbors appears more extreme on the color gradient than when it is surrounded by colors with the same hue and saturation. Below is a screen shot of what I am talking about, with some of the examples circled in red. They are easy to see that they are spatially outlying, but harder to map to the actual color on the ramp (and it gets harder when you have more bins).

Even with these problems I think the default plots in the spatstat program are perfectly fine for exploratory analysis. I think to disseminate the plots though I would prefer discrete bins in many (perhaps most) situations. I’ll defer discussion on how to choose the bins to another time!

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  1. The leaning tower optical illusion: Is it applicable to statistical graphics? « Andrew Wheeler

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