The question of what is the appropriate number of colors to use in an elevation map is an interesting one. Currently I contemplate MARS when thinking about this:
M: What is the resolution of the Map data? Noise results when the color resolution exceeds this.
A: Is the the Absolute elevation important? Tree heights, building heights, hill heights want this.
R: Or are Relative elevation differences more important? Drainage of driveways, parking areas, hills want this.
S: Does the Spatial resolution of the map match the eye?
If the color resolution is greater than the map resolution, the elevation map will display noise. So it is important to understand the map resolution when selecting the size of the color palette.
DroneDeploy can create maps with outstanding elevation resolution. Here is one of the most vivid examples I have come across. It is for a map created from a mission flown at 300' on an overcast day with low wind that resulted in an RMSE of 6.2'.
Over a 100' distance, the DroneDeploy 3D model shows a slope of 0.21-0.24"/ft which is very close to the design spec of 0.25"/ft. On-site measurements showed that both the absolute and relative elevation values were correct within 2" over the 100' distance. It should be noted that the good absolute elevation accuracy of this map is due to the fact that the absolute elevation at the takeoff location (165' distance from this region) was calibrated to within 1" using ACT (Auto-Calibration Technique) which I have described in prior posts on the DD Forum. Be sure to notice the very low noise on the profile plots at the left, about 1 line-width or 0.75". This map demonstrates that the DroneDeploy absolute and relative map elevation resolution can be well below 1"/ft. Thus with a 70 color pallet, the map elevation range should be 6' or larger for low noise. Thus almost all DD elevation maps should have low noise.
If reading the absolute elevation of the map is important, then a smaller color pallet is appropriate. This will make for crisper color differences on the map and allow easier translation to absolute elevation using the map key. Below is an example. Click on map to see details
If the absolute elevation is not critical and the relative elevation differences are important in regions with a slowly changing elevation, then a map with a larger color pallet is needed. For example, when grading for pavement that is to have a 1/4"/ft drainage slope, it is critical to be able to see small changes over a wide area which calls for a large color pallet. Below is a map with focus on the driveway of a 17 acres site. This is an extreme case with only a 6.9' elevation range and a small 0.1'/color. It is trying to tease out the 1/4"/ft slope of the driveway which it does reasonably well (it would look much better inside DroneDeploy as the exported 3D model has only a fraction of the resolution of the full 3D model within DD). Here identification of the absolute elevation is not very important. It is the relative elevation differences that provide an understanding of the drainage over this paved area. And the map does shows good drainage away from the building for all the paved surfaces.
In the map above, the color for regions with elevation data outside the region of interest (989' to 996') was set to a neutral grey color. This eliminates distracting extreme colors from the large, unimportant regions of the map and allows better focus on the areas of interest. This should be a standard option in all map color designers.
With 20/20 vision, the eye can resolve the 1 arc-minute gaps in the 5 arc-minute size of characters on line 8 of a Snellen eye chart when viewed at 20'. If we treat colors more like letters and not gaps, then a map's color spatial-resolution (CSR) need not be better than 5 arc-minutes at the viewing distance. To cover a wider range of viewers, let's add a 40% margin so this makes it 7 arc-minutes. Matching the CSR of the map to the eye maximizes the amount of information that can be displayed. So what should be the size of the color palette for a match? The answer:
N = Y/(CSR x D) x 360/(2 x pi) x 60
N is the number of colors in the Palette
Y is the size available in inches for display of all the colors in the palette
CSR is the color spatial-resolution = 7 arc-minutes
D is the viewing distance in inches
360/(2 x pi) converts radians to degrees
60 converts degrees to arc-minutes
or you can use the simplified formula:
N = 491.1 x Y/D
and if your viewing distance is 24", this can be further simplified to:
N = 20.5 x Y
So what does this mean? For your setup almost all of the numbers are fixed except for Y, the size available for display of all the colors in the palette. More colors can be used when there is more area available for their display. For example, a 3D elevation map provides more area for the display of each color which encourages the use of a wider color pallet. Similarly, a 2D map with gradual slopes also provides a generous area for the exploitation of a wide color pallet. A wide color pallet is also interesting on a map with large elevation differences.
To explore this equation, I went back and took a closer look at the map with the smallest elevation range of 143', the conformal elevation map of the entire 17 acres site with 70 colors at a color resolution of 2.1'/color. Click on map to see details.
On my 42" 4K monitor, this map provides 3.5" of vertical space for the display of the 70 colors or 0.05"/color. At a 24" viewing distance, the CSR is 7.2 arc-minutes which is a good match to the eye. To investigate this, I re-did the map with a 3X worse CSR of 21 arc-min which resulted in a 24-color pallet and 6.6'/color. Now, on my display, I can clearly see the color steps. Click on map to see details.
So the full 70-color pallet used on the original map is about right for maximizing the information content when viewed full screen. For smaller displays, the number of colors should be scaled proportionally. This experiment confirms that the color spatial-resolution of the eye is about 7 arc-min.
As a further conformation, I re-did an elevation map with 221' range using the 24-color pallet. The larger elevation range makes this map look noticeably worse; its color resolution of 9.6'/color is about 50% poorer. The map provides 5.25" for display of the 24 colors which gives a CSR of 31 arc-min, far short of the eye's 7 arc-min. Click on map to see details.
Even with the full 70-color pallet, this map exhibits noticeable steps in the flatter regions. Here the CSR is 11 arc-min, a bit short of the eye's 7 arc-min. Click on map to see details.
There is one more possibility for maximizing the information content of this map: instead of stepped colors, a continuous gradient can be used with the difference between colors being interpolated. This results in a map with a CSR that more closely matches the eye. Click on map to see details.
Here is the same map with a different hillside shading options. Click on map to see details.
It is not required to match the color spatial-resolution of the map to the eye. Fewer colors with noticeable color steps can be an advantage in many applications. But more colors are clearly wasted when the CSR of the map is better than 7 arc-minutes at the viewing distance for your monitor.
To compute the color spatial-resolution of a map for your monitor at your viewing distance use:
CSR = Y/(N x D) x 360/(2 x pi) x 60
CSR is the color spatial-resolution in arc-minutes
Y is the length in inches on your display used to display the full color range of the color palette
N is the number of colors in the palette
D is the viewing distance in inches from the screen to your eye
x 360/(2 x pi) converts radians to degrees
x 60 converts degrees to arc-minutes
The simplified formula is:
CSR = 3437.75 x Y/(N x D)
and for a 24" viewing distance it becomes:
CSR = 143.2 x Y/N
Example: Y = 3.5" to display N = 70 colors at D = 24" viewing distance
CSR = 143.2 x 3.5/70 = 7.2 arc-minutes
Different people have different vision and so the examples above are not optimum for everyone. But with a flexible color designer that incorporates the 7 options I mentioned in my 2nd post to this topic, the coloring can be quickly adapted to suite a wide range of visions.