Dear Bin Jiang,

both classification concpets -natural breaks and head/tail breaks- introduce bias to the representation of your DEM. Therefore I would recommend neither of them but suggest to use an definded interval, particular if you are using the DEM as basis for a map.

For visual interpretation, the result of natural breaks looks much more useful to me because it reveals a lot more details. In my opinion, however, a stretched display, using e.g. a histogram-equalize algorithm, performs much better than any classification for the purpose of visual interpretation.

Best,

David 

Thanks David! Now that you like the defined interval, I have created the outcome together with those by the other classification methods: equal interval, defined interval, quantile, and standard deviation. Which maps or images tell white lies?

Hello,

maybe you can use hillshading, so that the color scale rescaling and classification is not a visual problem anymore.

Personnally, I generally use blue/green colors for the lower plain areas, yellow/brown for the hills, and shades of white for higher hilltops (but, it depends on the heights of the mountains). The hillshading is then used to show natural breaks.

cheers

Many thanks for your comments!

If I understand you correctly, you mean using "stretched" without classification. Based on your suggestion on coloring (blue to brown color scale), I have created the stretched outcome with hillshading. This is shown to the left of the following figure. To the right, you see the outcome of head/tail breaks classification. Any further comments?

Dear Bin Jiang,

the question really is: what do you want to do with your DEM representation?

As you will certainly see, the stretched visualization (with added hillshade) displays surface details best, providing a good base for visual interpretation. However, the color ramp you have chosen does not fit the topic (red-blue gradients are typically used e.g. for temperature). Either do it similar to Michel's suggestion and use a green-brown(-white) gradient or use some ready-made color ramps such as:

http://blogs.esri.com/esri/arcgis/2011/12/17/esri-color-ramps-version-30/

If you are preparing a topographic map, a realistic and quantifiable presentation is most important. In this case, you should avoid "white lies" by using an equal interval classifiication. Additionally, you should consider the type of landscape you want to display in your map. If there are no glaciers on top of your summits, white color for the summits is misleading. If your study area is a desert, don't use a strong green for lowlands. Etc.

Best,

David

Dear David, Herewith the color ramp you suggested - green-brown. What I am concerned here is not so much which color ramp should be used, but what classification is the most appropriate. I am not convinced that the equal interval classification is a best option.

Hi Bin,

I think there are two different issues; the classification method to be applied and the color ramp to adopt.

As for the classification method, in this case is more tan justified to apply an exogenous method. In line with David Loibl question, the key is the purpose of the map. Altitude could be classified following key values that are pertinent to the purpose of your map.

As for the ramp to adopt, we are used to ESRI's and others' ramps and we adopt them without asking much but we should more carefully think about it.  If altitute values are low, then it's not point in adopting a ramp that ranges from blue (wáter) to light pink or white (permanently snow covered mountains).

Hope it helped

Cheers

Dear Francisco,

Many thanks for your insightful comments!

Yes, there are two issues involved: classification methods and color ramps. As you can see from the previous maps, all conventional methods (natural breaks, equal interval, defined interval, quantile, and standard deviation) tend to have more high areas than that of the head/tail breaks.

One of my students has conducted human tests to compare conventional classifications and the head/tail breaks. In order to get rid of color biases, she deliberately used gray scales for all the maps. Surprisingly, many people are in favor of maps by the head/tail breaks rather than maps by the conventional methods.

Wu J. (2015), Examining the New Kind of Beauty Using Human Beings as a Measuring Instrument, Master thesis at the University of Gävle, Sweden: http://hig.diva-portal.org/smash/get/diva2:805296/FULLTEXT01.pdf

Hi Bin,

your student work is most interesting. Thanks for sharing it.

My point is that both the classification method and the colour ramp, when applied to DTM, has to take into account máximum and mínimum values existing in the DTM. If low lands, all colours should rank from dark to light green and never include browns and whites which would denote high altitude. People may find more attractive a map whose colours range from green to white and browns-purples in between but this would distort the message making people think that there are high altitudes in the area depicted.

The DTM shown in your student's work is coloured, not b/w, so I think my comment applies.

Cheers

HI, Francisco,

You are right, since you referred to the USA DTM, which is colored. I was referring to a set of maps of gray scale on pages 27 or 34. Sorry for the misunderstanding. Your comment on color ramps makes perfect sense to me.

Even with the color DTM, there would be little biases involved in the human tests, because each time a person is shown two maps (with a same color ramp, but different classifications), from which he/she chose one that mirrors him/herself.

As for the test result for the DTM, many people chose natural breaks rather than head/tail breaks. This is because this test was mainly done by cartographers or geographers, who are already used to the traditional rendering. If this DEM were used, we would assume many people chose the rendering by the head/tail breaks. Of course, this is just my hypothesis now.

Dear Bin Jiang

If you aim is to create a DEM for cartographic purposes I think none of the classification methods and tools provided by GIS is usefull. Digital cartography has their own tools some of those completely different from geospatial analysis tools. Some of those looks alike but the application and conceptual meaning is different. Please take a look to Tom Paterson work at http://www.shadedrelief.com/. And if you want take a look to my presentation about DEM and cartography (unfortunately is in spanish) http://www.slideshare.net/gasato/el-tratamiento-grfico-de-los-modelos-digitales-de-terreno-fuentes-de-error-la-generalizacin-el-sombreado-y-la-paleta-imhof.

Please see the difference GIS vs Digital Cartography

Dear Gabriel Asato,

Many thanks for your comment that helps to bring the discussion in this thread at a high level. There are two kinds of beauty: one is triggered by surface colors and nice designs that is subjective, and the other exists in deep structure that is objective. I fully agree with you that some people like you are in favor of Tom Paterson's rendering, which looks beautiful and eye-catching. On  the other hand, a majority of people find (consciously or subconsciously) head/tail breaks-induced rendering has positive impacts on human well-being. The second kind of beauty can be effectively revealed by the head/tail breaks rather than conventional classification methods. I made this point clear in this paper:

Jiang B. and Sui D. (2014), A new kind of beauty out of the underlying scaling of geographic space, The Professional Geographer, 66(4), 676–686.

Even though there is no classification involved Tom Paterson's rendering, the color scale is still similar to those by conventional classification methods. Instead, I think the color scale should be similar to one by the head/tail breaks. Note: by color scale, I mean how color should be transitioned from one end to another (linearly, non-linearly, or arbitrarily).

More recently I developed a mathematical model of wholeness, with which one can learn why something is beautiful, but also how much something is beautiful.

Jiang B. (2015), Wholeness as a hierarchical graph to capture the nature of space, International Journal of Geographical Information Science, xx(x), xx-xx, Preprint: http://arxiv.org/abs/1502.03554

Clearly the right pattern is more beautiful than the left one. Benoit Mandelbrot referred to the left as cold and dry, while Christopher Alexander referred to the right as a living structure.

Dear Roger Werner

There are a not well known discussion among cartographers if GIS can produce maps (cartography) in the strict sense of the statement. Cartographers thinks that GIS is not the best tool for creating cartography because results are so far of what they  expect. They are saying that GIS produce a kind of graphics ( a cartogram?) that look like maps but in fact they are not REAL maps. Behind cartography there are a lot of know how about geographic representation, generalization comunication and art. Cartographers thinks that GIS is far behind of what they are thinking what digital cartography must be.

The confusion between what is GIS and what is Digital Cartography in some countries is having strong impact because new GIS "digital maps" have less quality than those produced using the old fashion methods.

In fact the origin of the confusion is a conceptual problem because GIS is good for data management and analysis and results can be seeing quickly. The aim of digital cartographic techniques aims on representation and clarity of very complex geographic reality. Digital cartographic methods doesn't bother too much on digital data preservation.

From my point of view is really important understand why GIS and Digital Cartography are different disciplines. If you think GIS produce maps your organization will probably lost the opportunity to create a good and better product. If you think GIS is for Digital Cartography you are probably introducing in your database a lot of rubbish and artifacts that can be a nuisance for future analysis.

Let me explain with a simple example:

Buffer in GIS

Buffer is a corridor that is produced at constant distance from an spatial object. It is used for corridor and distance analysis.

Buffer in Digital Cartography (Halo)

An Halo is a corridor produced at certain distance of a cartographic object with smooth perimeter  (distance is not conserved). Sharp edges or narrow gulfs are not permitted. The graphical style of the halo can be composed of a color degrade or with a water line texture.

And now tell me what will happen if somebody will  make a geographic analysis using an halo insted of a buffer.

In regards of your question what software I am using, well I am using the same of you but I have to clarify that digital cartographic techniques are about methods not only software. By the way in 2012 I visited the National Geographic Institute of France, they told me that they are working with two separated databases. One for GIS and the other for Digital Cartography and the software they are using for digital cartography is called Merkator.

Best regards

Herewith a set of tutorials on how to do head/tail breaks with your own data:

https://www.dropbox.com/s/imcmomtkpkpgoq6/LabHTBreaks.zip?dl=0