Reading 9: Bi-Variate Color Mappings

March 8, 2010

in Assignments

(readings for class Tuesday, 3/23)

Everyone must read:

  • Colin Ware, “Quantitative Texton Sequences for Legible Bivariate Maps,” IEEE Transactions on Visualization and Computer Graphics, vol. 15, no. 6, pp. 1523-1530, Nov./Dec. 2009, doi:10.1109/TVCG.2009.175  (ieee page)

Each person will be assigned to read one of the following (you may read more than one). Your initials will be at the end of the citation.

  1. Rheingans, P. Task-based Color Scale Design In Proceedings Applied Image and Pattern Recognition (SPIE), 1999 (citeseer – has PDF) (DH,SH,PK)
  2. Bruce E. Trumbo. A Theory for Coloring Bivariate Statistical Maps. The American Statistician, Vol. 35, No. 4 (Nov., 1981), pp. 220-226 (web version) (JH,FK,LW)
  3. James R. Miller, “Attribute Blocks: Visualizing Multiple Continuously Defined Attributes,” IEEE Computer Graphics and Applications, vol. 27, no. 3, pp. 57-69, May/June 2007, doi:10.1109/MCG.2007.54 (ieee page) (CH,NK,JYM)
  4. Daniel A. Keim, “Designing Pixel-Oriented Visualization Techniques: Theory and Applications,” IEEE Transactions on Visualization and Computer Graphics, vol. 6, no. 1, pp. 59-78, Jan.-Mar. 2000, doi:10.1109/2945.841121 (ieee page) (author’s page) (ET,CSV,JW,YL)
  5. Haleh Hagh-Shenas, Sunghee Kim, Victoria Interrante, Christopher Healey, “Weaving Versus Blending: a quantitative assessment of the information carrying capacities of two alternative methods for conveying multivariate data with color.,” IEEE Transactions on Visualization and Computer Graphics, pp. 1270-1277, November/December, 2007. (ieee page) (healy’s version) (DA,AM,NV)

Please post a comment on what you read, and what you learn from putting the two together.


Nate March 15, 2010 at 8:16 pm

I read Ware (Textons) and Hagh-Shenas (Weaving Versus Blending) — two approaches to displaying multivariate data in on a field such as a map.

First off, I was oddly surprised that people are still developing novel approaches to this task, when the problem has, presumably, been apparent for at least a few hundred years. I’d have expected this space to be quite thoroughly explored. And secondly, I was very interested, as these problems are quite common in imaging experiments — people would love to see, for example, a group mean activation and statistical significance simultaneously.

For me, the weaving approach is the less interesting of the two. It inherently works best (only?) on large, uniform fields of data (such as county- or state-wide data elements), though it scales, apparently, to six variables. My main difficulty with it, though I know it’s petty, is that it makes ugly, ugly maps. I just don’t like looking at these. Did these fields need to be filled with noise? Couldn’t they have used some kind of regular pattern?

Despite the inherent bivariate limitation of Ware’s texton approach, I liked this a lot. I’m most interested that he took advantage of our ability to perceive texture at least somewhat separately from color, and make maps that really encode two variables quite effectively. (And, incidentally, look good printed in black and white.)

Best of all, you get to say “Texton,” which sounds like something the Transformers would have used for data visualization.

Jim Hill March 15, 2010 at 8:18 pm

My readings include the top Colin Ware paper and “A Theory for Coloring Bivariate Statistical Maps” By Bruce E. Trumbo

Both papers attempt to provide a framework for producing bivariate mappings.

Trumbo’s paper was written in 1981 and provides a theory for choosing good color schemes for bivariate maps. He proposes 5 schemes all of which use color to represent both variables in a map. These schemes pretty much boil down to selecting an area from the HSV color solid and mapping it two a unit square with both variables represented on the axis. His schemes provide different methods for making sure that a number of principles are followed. These principles include: preserving ordering using colors that have a perceptual ordering, choosing colors that are separable when their variables are significantly different, choosing colors that do not interact when attempting to preserve univariate relationships, and resolution of data relations in to three categories relative to the main diagonal. Each of the schemes are rated based on how they adhere to the above principles and we find that none of the schemes satisfies all four. The best is the Hue/Brightness scheme.

It is interesting to note that the paper was written partly as a response to criticisms for the visualization method used by the 1980 census which used color to distinguish bivariate data in a map.

Ware’s paper is much more modern and, I believe, relevant. Like Trumbo, Ware provides 4 principles that he believes produces good bivariate mappings. He then goes on to say that color is not a very good way to distinguish data in a bivariate map. I would have to agree with this, I can’t imagine trying to determine what a mix of two colors represents. Ware proposes using color as the encoding of one variable and something called Quantitative Texton Sequences (QTonS) for the other. He proposes additional principles for choosing QTonS which basically boil down to an ability to determine ordering, the ability to distinguish different QTonS, the ability to make them small and the ability to reduce interference.

Several examples of QTonS are shown and I think that they work very well. The rest of the paper discusses two tests that where performed to determine the usefulness of QTonS over simple color methods. The first test was to determine whether a participant could determine the approximate value of a given point in the mapping. The second was to determine at what density the QTonS where most effective.

The tests both concluded that the QTonS had the smallest error in both tests for both separable and integral data.

One thing that bothered me with the QTonS method is that, while both data sets are shown, one is at a significantly higher resolution that the other. A reader of the map will be able to make much better judgements as to the values in the color maping. With the QTonS mapping, the reader will be forced to interpolate. At high QTonS frequencies, this probably isn’t a big issue except for places where there are even higher spacial frequencies.

punkish March 15, 2010 at 10:50 pm

(Note: This reading is not due until next week, but is confusingly the first thing to see on this page. I mistakenly read this, as I see others too have done so. Since I have already read it, I am noting down my comments right away instead of waiting until next week)

Ware proposes the concept of the awkwardly abbreviated QTonS, but in contrast to the gracelessness of its acronym, a quantitative texton sequence is a rather elegant approach to solving the problem of bi or multivariate mapping. By superimposing texture (or a pattern) on a color, one can convey more than one coincident themes on a map. An effective QTonS has the properties of monotonicity, legibility, smallness of size and minimal interference.

Rheingans stresses that being lazy and resorting to the default color scale, while appropriate sometimes, can be an inappropriate choice in other visualizations where a more careful consideration of color might be more effective. Rheingans defines a number of different common color scales — single variable and multivariate scales. She stresses understanding the goals of visualization, the data and the audience, and to be aware of cultural connotations of color, but be prepared to go against them if required.

These two readings pair very well, like wine and cheese. I have a better appreciation of the problem Ware is trying to solve because of the context established by Rheingans.

Nakho Kim March 22, 2010 at 11:32 pm

My readings were Ware’s paper on QTonS and Miller’s on Attribute Blocks. I was surprised at the intuitiveness of the quantitative texture which did not seem very convicing at first when seen as individual units. However when they blended in with the color in the actual visualization, the perceived quantitative difference was easily perceivable as the density of the pattern. Especially, QTS1 reminded me of the ‘cross-hatching technique’ many artists use when drawing with black ink and pen where the density of the lines are easily perceived as specific shades of grey. I think QTS1 has more potential for various resolutions, while there is a legibility issue with QTS2 in smaller maps.

As for Miller’s attribute blocks which fits multiple color encodings into one visualisation by combining them into ‘blocks’, I’m not sure it works well as blocks consisting of separate variables since the colors in the block tend to mix perceptually. Just like three lights with basic colors blend together to make one color pixel unit on a TV screen, as the distance between the blocks in the unit become narrower it tends to blend into a single color. If the viewer is not familiar with processing basic color mixtures cognitively(e.g. red and blue together looks purple), I don’t think it makes a intuitive visualization in higher resolutions or seen from a distance.

Shuang March 22, 2010 at 11:49 pm

I read Rheingans’ “Task-based Color Scale Design In Proceedings Applied Image and Pattern Recognition (SPIE)” and Colin Ware’s “Quantitative Texton Sequences for Legible Bivariate Maps”. Both articles cover the content of presenting bi-variate mappings and Ware’s work uses Rheigans’ suggestion of hue and value.

Rheigans’ paper focuses on the color selection for different tasks. Single-variate task is different from multivariate cases, and bi-variate case is included in the latter. The example used in this article is from Census, with both scales use yellow to map low value, and use dark blue and red respectively to map high value. Critics of the scheme noted the lack of an intuitive progression in colors along the rows and columns. In the conclusion, the answer for design in color scales is still ‘it depends’.

Ware’s paper uses color sequence as a variable in visualization and introduces another variable as Quantitative Texton Sequences (QTonS). In this paper, the usage of QTonS is discussed comparing with other methods of color. Statistical testing proves that QTonS has smallest error for integral data and separable data.

faisal March 23, 2010 at 1:01 am

I read the Colin’s paper on QTons and Trumbo’s paper on bivariate statistical maps.

These readings provides enough motivation for understanding design choices involved in visualizing bivariate data on a map.The multi-dimensional nature of color makes it preferred choice for encoding bi variate data. Trumbo’s paper argues that choice of colors is an important one and should follow a set of principles e.g order, separation etc. The Colin’s paper take the issue of color selection one step further and stress the superiority of small size textures (Texons) as an alternative encoding scheme for one of the dimensions of data in bivariate maps.

Trumbo’s focus was entirely on effective use of colors and offered theoretical methods for picking colors for an overlay color approach. A more systematic evidence for the suitability of a particular color/texture scheme came from Colin’s paper.

The combined take away points from these readings can be (i) Choice of color sequence should following perceptual guidelines related to correctly specifying the order, separation in the data. (ii) The perceptual separation of small size texture is higher than colors (iii) When reading maps both integral and separate view is an important measure for evaluating design.

As a final note, I found one aspect of the 2-D keys, in Colin paper, contradictory to ‘rainbow maps are bad’. Is this particular key an example of bad color map?

lyalex March 23, 2010 at 1:10 am

Colin Ware’s paper presents a study for visualizing bivariate maps. Using a color-texture method for coding seems to be a valid method, and the study they conducted clearly shows results by actual experiments by parcipants. I like the organization of the paper and the experiment design for evaluation. However, my concern about the QTonS is that the coding system for the texture part is kind of limited. The authors only us 10 different kinds of QTons, but how about a bivariate map with large amount of scalar numbers in both dimensions? How about the extensibility of the second variable?

Daniel Keims paper is a very technical paper with the algorithms for basic pixel-oriented technologies, such as color mapping, pixel arrangement, shape design for subwindows, and ordering for dimension. I’m still struggling in the algorithms and might need some more time to digest them and bring out my own idea.

Jeremy White March 23, 2010 at 1:11 am

The Keim paper (Pixel-Oriented Visualization Techniques) and the Ware paper (Texton Sequences) take different approaches to multi-level encoding problems. Ware’s QTonS technique relies on the user’s ability to distinguish diverging colors and patterns across the same surface. This multi-level encoding and decoding process is, according to Ware, an effective means of representing many layers of information without the need for multiple, adjacent maps. Keim chooses to focus on a more granular approach by assigning pixel values based on different characteristics within the data. Hue, arrangement and grouping are combined to create visualizations that can be used to easily compare different multi-dimensional data.

Combing the two articles is like blending art and science. Ware is relying on the viewer’s ability to determine differences in shapes that follow a logical progression. These shapes are not necessarily generated by any kind of scientific process, but rather chosen based aesthetic principles. Kleim, however, takes a very methodical approach toward the end result. His methods provide a framework for standardizing the visualization of complex datasets which potentially allows comparisons to be made more effectively. As with any blending of art and science, experimentation and practice will be needed to determine the best approach for a given problem.

turetsky March 23, 2010 at 7:57 am

I read the Ware paper as well as the paper by Daniel Keim – “Pixel-Oriented Visualization Techniques”. The idea of the Ware paper, mapping the same variable onto two different features and comparing, at first seemed unintuitive to me. It’s hard to imagine that it could be done in a way that is not more confusing than looking between two maps side by side with the same variable. Looking at the maps created, it is still somewhat confusing to look at, but some things can be taken in at a glance.

Pixel oriented visualizations are all about saving space on the computer screen. The idea is to one piece of data into one color of one pixel. This paper focuses on how various things like location relative to other pixels and color can make a difference as well as giving examples of applications.

It seems that both techniques are about saving “space” in a way. Ware is using one map where he could use two in order to prevent users from having to glance back and forth between them. He is trying to make it easier to take in information at a glance, which is what it seems that pixel oriented techniques are about as well. Though that takes maximizing the amount of information to visual space to the extreme within computer screens.

jeeyoung March 23, 2010 at 8:09 am

I skimmed through mainly figures in Colin Ware’s paper and James Miller’s attribute blocks.

It was hard to see blue or purple color spectrum in attributes blocks because blocks interfere with each other. I kinda failed to see some attributes independently and with integration. Nice thing about this visualization is you can choose to zoom-in, choose one attribute, and block sizes. I wonder a space between blocks might help not to mix colors.

Quantitative texton sequences did well showing bivariates. GR and HL spectrum were misleading, DOT is ok but dot sizes do not pop out and hinders color spectrum a bit.

watkins March 23, 2010 at 9:02 am

I read Colin Ware’s “Quantitative Texton Sequences for Legible Bivariate Maps”, and Bruce Trumbo’s “A Theory for Coloring Bivariate Statistical Maps.” Both papers seemed to be solving the same problem in different ways. Trumbo attempted to find an ideal color scheme that would satisfy a set of four principles he thought were important to interpreting bivariate data. Ware took a different approach, and encoded one dimension with texture and the other dimension with color (hue). Ware, in his approach, satisfied all four principles laid out by Trumbo (order, separation, distinguishable rows and columns, and an easily identifiable diagonal), and he did it a more rigorous way. Trumbo did NO testing to verify the effectiveness of his designs.

ChamanSingh March 23, 2010 at 9:10 am

Paper 1: Quantitative Texton Sequence ….
Paper 2: Designing Pixel-Oriented Visualization ….

Both the papers have addressed two different, yet very important and practical problems. for which there are no clear solutions. Interestingly, both these papers don’t give any new idea, but they provide solutions which are although quite intuitive needs some nitty-gritty details.

I wish in the first paper, the author had used a simple vocabulary for Texton which unnecessarily gives an idea of a new concept, which is not the case. My concern with the texture elements is that they have potential to create “Visual Pollution” and therefore extreme care must be taken in designing and implementation. A generalization of this problem is hard and an efficient and successful implementation may depends on the problem and probably having two images side by side may be better in some cases.

If someone doesn’t read the second paper, then sooner or later, he/she will have to address all the problems, which this paper has addressed. Nice thing about this paper is that it provides some formalization of the problems and give mathematical models to solve them., but unfortunately, solutions of some of these problems are NP complete, and therefore, one has to go for approximation or some kind of heuristics.

dalbers March 23, 2010 at 9:59 am

Both Ware’s paper and Shenas’ “Weaving versus Blending” seem to agree on one key principle: overlaying information in a visualization is really hard. The key to determining the best way to approach this problem appears to lie in addressing how to manipulate perceptual mechanisms such that the viewer can easily read either set of information or potentially both at the same time.

Ware’s QTonS idea is novel in that it addresses the issue of overlaying two distinct maps by using two distinct channels. However, it is not clear to me what the best way to encode such textons is. At least in the examples in the paper, the QTonS seem to run the risk of obscuring data hidden behind the pattern. They also could potentially distract the user from the underlying data mapping if an appropriate color scheme is not selected (i.e. one that does not complement the original color scales used in the mapping such that either popout phenomena dominate the user’s attention or that the QTonS are not readily visible in certain regions.)

Shenas’ paper appears to take a slightly different approach by offering an alternative to the traditional color blending approach of overlapping color regions by manipulating both color and pattern to convey multiple sets of information. While I have my reservations on the experimental design, the idea of randomly blending two colors does remove the obscurity concerns of textons and certainly feels more conventional with respect to traditional encoding principles. However, again if the color set selected does not have enough contrast, the “random noise” encoding could potentially be undetectable. Either way, the simplicity of this idea does make it a promising possible solution.

Adrian Mayorga March 23, 2010 at 10:34 am

I read the Ware (QTonS) and Hagh-Shenas(color weaving) papers.

Both of these try to solve the issue of showing multiple scalar maps on top of each such that correlations between the data are easier to appreciate.

Ware’s approach only deals with two of these at a time, and makes use of different visual channels to encode each scalar map. While this has the advantage of minimizing interference, the “resolution” of each visual channel is not the same (color channel has a much higher resolution than the “texton” channel). This means that one has to pick which one of the two fields is more important, which may not be an obvious choice. Additionally, because of this resolution issue, the textons have to be big enough, which may occlude some of the information underneath.

Hagh-Shenas approach is slightly different. The main idea here is to use random textures to illustrate the values of up to six variables across different regions. While this scales better than Ware’s approach, it does so at the cost of having discrete regions, rather than continuous ones. I also agree with Nate on this one, the random dots look extremely ugly, though I should say that the original incarnation of color weaving (used for labeling LIC images) looks a lot better

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