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How to assess a colourmap

Seismic interpreters use colourmaps to display, among other things, time structure maps and amplitude maps. In both cases the distance between data points is constant, so faithful representation of the data requires colourmaps with constant perceptual distance between points on the scale. However, with the exception of greyscale, the majority of colourmaps are not perceptual in this sense. Typically they are simple linear interpolations between pure hue colours in red–green–blue (RGB) or hue–saturation–lightness (HSL) space, like the red–white–blue often used for seismic amplitude, and the spectrum for structure. Welland et al. (2006) showed that what is linear in HSL space is not linear in psychological space and that remapping the red–white–blue colourmap to psychological space allows the discrimination of more subtle variation in the data. Their paper does not say what psychological colour space is but I suspect it is CIE L*a*b*. In this essay, I analyse the spectrum colourmap by graphing the lightness L* (the quantitative axis of L*a*b* space) associated with each colour.

In this essay x is the sample number and y is lightness. The figure is shown here in greyscale, but you can view it in colour at ageo.co/HLOS3a. In the graph the value of L* varies with the colour of each sample in the spectrum, and the line is coloured accordingly. This plot highlights the many issues with the spectrum colourmap. Firstly, the change in lightness is not monotonic. For example it increases from black (L*= 0) to magenta M then drops from magenta to blue B, then increases again, and so on. This is troublesome if the spectrum is used to map elevation because it will interfere with the correct perception of relief, especially if shading is added. The second problem is that the curve gradient changes many times, indicating a non-uniform perceptual distance between samples. There are also plateaus of nearly flat L*, creating bands of constant tone, for example between cyan C and green G.

Let’s use a spectrum to display the Great Pyramid of Giza as a test surface (the scale is in feet). Because pyramids have almost monotonically increasing elevation there should be no substantial discontinuities in the surface if the colourmap is perceptual. My expectation was that instead the spectrum would introduce artificial discontinuities, and this exercise proved that it does. 

In an effort to provide an alternative I created a number of colourmaps that are more perceptually balanced. I will post all the research details and make the colourmaps available at ageo.co/Jcgqgq. The one used below was generated starting with RGB triplets for magenta, blue, cyan, green, and yellow (no red), which were converted to L*a*b*. I replaced L* with an approximately cube law L* function, shown in the bottom left figure — this is consistent with Stevens’ power law of perception (Stevens 1957). I then adjusted a* and b* values, picking from L*a*b* charts, and reconverted to RGB. The results are very good: using this colourmap the pyramid surface is smoothly coloured, without any perceptual artifact.


References

Stevens, S (1957). On the psychophysical law. Psychological Review 64 (3), 153–181. PubMed 1344/853.

Welland M, N Donnelly (2006). Are we properly using our brains in seismic interpretation? The Leading Edge 25, 142–144. 

 

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