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Dequantification in scientific images

-- Edward Tufte

The latest news on space junk raises the issue of the dequantification of evidence. See first Andrew C. Revin, "Wanted: Traffic Cops for Space," New York Times, February 18, 2003: (requires registration)

This report from the Times has some good diagrams, especially a simple chart of the actual sizes of small objects in relation to their kinetic energy (expressed more as metaphors than quantities). Some scaling problems occur in the illustrations showing the earth.

Also there is an excellent photograph from NASA showing a crater from a paint chip striking a window in the shuttle--except there is no scale on the image nor an object of known size in the common visual field! The image is probably a few inches wide although it looks like a galaxy. The lack of scale here is a reminder of the lack of scale, despite a 22.5-fold vertical exaggeration, on the Venus fly-by movie-images constructed by the Jet Propulsion Laboratory and NASA; see my book Visual Explanations, p. 23-24.

Such dequantification also shows up in the amazing images from the Hubble Space Telescope; what is the size, the distance away, and the location in the sky of the objects shown in the Hubble photographs? Scientific images are scientific because they have scales of measurement; the dequantification of images takes astronomy down the road toward astrology. It is especially important to provide scaling in images for public consumption, since the public might not have the contextual feel for scale that the experts do. And without scales, the images start to look like Hollywood sets rather than scientific evidence.

-- Edward Tufte

It ought to be easy to invent a series of icons that could be unobtrusively placed in the corner of images to show their scale-- eg a double-helix, a virus, etc, on up to a person, the Eiffel Tower, Saturn, a galaxy...

Similarly, I'd like to see icons that mean 'false color' or 'computer generated' or 'retouched' or 'montage'...

-- Jorn Barger (email)

This idea was used in one of the Star Trek films: A rock that one of the producers "liked" was placed in a Zeiss digital scanning electron microscope with a motorized automated stage. The SEM was programmed to zoom in, move around, pan across, and focus on the rock to depict a spaceship coming in for a landing or crash. I worked for a company that made imaging equipment that attaches to SEMs at the time and the Zeiss applications specialist and I had a good laugh at the producer's exuberance about "craters", "valleys", and such.

Point of order: The images had to be retouched in Hollywood because the Zeiss SEM (now LEO brand) automatically inserted a scale into every image.

-- Max M. Houck (email)

What a nice story!

-- Edward Tufte

The simple scale bar. Definitely. But then, I am a microscopist...

-- Alexey Merz (email)

I think the hairline with ticks at obvious divisions gives you a simple and uncluttered design and also allows someone to transfer larger or smaller distances to a slip of paper for measurment. For web presentation, and if measuring is anticipated, other 'tools' might also be desirable. For example, in the browser/OS I use (Safari/Mac OS X), if you click on an image on the page and drag it, you get a slightly transparent image in place of your cursor. So if the photograph were accompanied by a second image file with just the scale bar, I could drag it around over top of the image myself. Using Flash or Java might give you more options, at the risk of reducing accessibility.

Note: A little experimentation reveals that the Safari/OS X trick is useless with larger images, which are scaled down when 'dragged'. This could lead to dangerous errors if not anticipated.

-- John Morse (email)

I prefer the simple bar to give me the quick general size. As I tried to use it as a scale to gauge the width of the river, I found it difficult to rotate it in my mind. So I considered a square:

Or perhaps a simple L shape:

Of course I can also use my thumb, but it leaves prints on the screen.

-- Dave Nash (email)

This photo of Mars adds the North indicator to the scale, but a great deal more information is in the article's text.

An Astronomy Picture of the Day from

-- Dave Nash (email)

How about north to the top?

-- Edward Tufte

"North up" is a quite useful convention; in fact, it's common to assume that north is up unless specifically noted otherwise. When does a useful technique become "too conventional"?

For maps I draft, I find "north up" maps best, unless there is compelling reason, likely driven by the data being displayed and the intended use of the map, that north should NOT be up. I've purposefully observed people with all levels of map-reading skills, and watched as many, at all skill levels, fumble as they get their bearings with "north-not-up" maps.

One of the links( available at the link Dave Nash gives above shows a series of images, all with north to the right- except one (and the last image is a perspective view). I noticed this, but I was looking for it. Asking if the typical reader of that web page would notice this without looking or having it pointed out could be viewed as akin to asking if a NASA engineer for a Mars mission would notice the difference between metric and English units when programming a flight path.

-- Mark Kasinskas (email)

My highschool ecology teacher, Dr. Wendell G. Mohling, had a satellite download station for the LANDSAT, NOAA, and Soviet equivalents. Big lesson learned for my experience in front of that screen: satellites looking down at Earth don't rotate to put north at the top of the CCD. Nor do they always look straight down. If anyone should avoid putting north at the top of the image, it's probably NASA. Last I was at Goddard they had a mindnumbing library of shared algorithms to orient, stitch, and reshape their images.

Side note on Dr. Mohling: he was a finalist for the teacher-in-space program, went on to be a president of the National Science Teacher's Association in 1992, and is now the NSTA's director of professional programs.

-- Niels Olson (email)

A link for Upside-Down (or "Corrected") Maps.

-- John Morse (email)

North is to the left. I believe Space Imaging (who gave us the image) chose this orientation to prevent the appearance of sunlight coming from the bottom of the image (which can tend to cause an optical illusion and invert the topography) and/or to compensate for the oblique angle at which the image was taken.


In general, I prefer north at the top, since it requires less decoding by virue of convention. In this instance I think north to the left is easier to interpret (and lends itself to a horizontal orientation to simultaneously display the arch and Lake Powell.)

Regarding the perspective of satellites, the imagery MUST be geographically corrected for quantitative analysis. As the Earth rotates and a satellite's instruments scan across the curve of the Earth the pixels are skewed and change in shape and size. Look at the 250m/pixel resolution images in this gallery to see examples.

Upside down maps: In my opinion, the distortion in area introduced by the Platte Carre (geographic) projection overwhelm any benefit gained by flipping the map.

-- Rob Simmon (email)

I've found that overlaying a subtle grid on top of the image can often make it easier to judge the sizes of features, without requiring someone to try and guesstimate from an often too-large or too-small scale bar on the other side of the image. An example:

The challenge, of course, is to make the grid noticeable enough to be useful, but not so obtrusive that it detracts from the actual image.

-- Matthew Ericson (email)

A strange anomaly of orientation that occurs in UK and US maps is that where shadowing is shown it is from a light source to the northwest: a rare place for the sun in the northern hemisphere.

-- Martin Ternouth (email)

"The light direction is very important for the design of a shaded relief. Normally the cartographer lets the light "shine" on the terrain from the upper-left. Less popular is illumination from the south, as the relief shading tends to not "look right". In extreme cases, relief inversion occurs where mountains appear as valleys and vice versa." Relief Shading

-- Craig Pickering (email)

Embryology is a great place to add scale bars. This is a sketch I made in class using Illustrator of a slide the professor projected. Minus color this is all the information that was on the slide.

Checking various places in the book I can tell you the top one is the cross section of the spinal cord in a 23-day human embryo (about 3 mm), the middle is from a six-week embryo (8 mm), and the bottom image is a nine-week embryo (50 mm). The reason medical students take embryology is to better understand gross anatomy and disease processes (particularly congenital defects like spina bifida). The challenge for the student is keeping a sense of which cell lines are growing faster relative to other things because these rates dictate which cell lines meet, thus causing further differentiation. Without a scale bar this becomes little more than an exercise in defining completely dequantified topological sets, e.g.

at 23 days the neural tube contains neuroepithelia, the neural crest has bifurcated laterally at the sagittal plane and the central canal contains cerebrospinal fluid. At six weeks the gray matter contains neural cell bodies, macroglia, and microglia; the white matter contains axons and macroglia; the dorsal root contains motor neurons; the ventral root contains sensory neurons; the central canal contains no cells, only cerebrospinal fluid.

This wouldn't be so bad if this was all we talked about, however, with an average of 40 slides an hour and two or three dequantified images per slide, defining sets of cells at various stages doesn't help in understanding the spatiotemporal development of the embryo, which bears directly on understanding the origins of those cell lines, as well as gross anatomic structure and disease processes.

-- Niels Olson (email)

A point that is also important (and not just in graphics -- it applies just as much to tables and other ways of presenting numerical information) is that the units in which the values are given need to be appropriate for the comparisons that are likely to be made.

A classic example in biochemistry concerns the substance 2,3 bisphosphoglycerate, which is now known to be important in red cells because it has a major effect on the affinity of haemoglobin for oxygen. This has been known since the 1960s, but, amazingly, sufficiently accurate information about the amount of 2,3 bisphosphoglycerate in red cells was available in the relevant literature as early as the 1920s. Nonetheless, for 40 years no one paid any attention to it because the amount seemed to be trivially small -- just a trace component of the red cell, it seemed.

The reason it passed unnoticed was that concentrations were traditionally expressed in grams per 100 ml, and as 2,3 bisphosphoglycerate is a very small molecule (compared to haemoglobin) its concentration in grams per 100 ml appeared very small in comparison with the concentration of haemoglobin. It was only when someone (Benesch, I think -- I can check if anyone is interested) thought of expressing all the information in sensible units, i.e. moles per litre (a measure of molecules per litre), that it became obvious that the concentrations of 2,3 bisphosphoglycerate and haemoglobin were essentially the same, and only then did people start asking what 2,3 bisphosphoglycerate might be doing in the red cell in the first place.

-- Athel Cornish-Bowden (email)

What a fine example of an important general point from our Kindly Contributor Athel Cornish-Bowden.

Is there a citable reference that describes the logic here?

-- Edward Tufte

Here's an image of 2,3-bisphosphoglycerate in its hemoglobin binding site. The distance from the center of the upper left blue ball to the center of the lower right blue ball is 9.17 angstroms. This was generated from Protein Data Bank structure 1B86 using Pymol. The prefix deoxy- means that the hemoglobin doesn't have oxygen bound. The red hemoglobin is about as deep as it is tall while every atom of the 2,3-bisphosphoglycerate molecule is visible (chemical formula: C3O10P2). The mass of hemoglobin is 66,980 grams per mole; the mass of 2,3 bisphosphoglycerate is 258 grams per mole.

-- Niels Olson (email)

I think the original reference is probably Reinhold Benesch and Ruth E. Benesch (1967) Biochemical and Biophysical Research Communications 261, 162-167 "The effect of organic phosphates from the human erythrocyte on the allosteric properties of hemoglobin". I say "think" because, maddeningly, the relevant number of the journal is missing from our library. However, the date seems right and the introduction to a later paper by the same authors plus Chi Ing Yu in Biochemistry 8, 2567-2671 (1969) says that that was the first report.

Incidentally, in the older literature 2,3-bisphosphoglycerate was called 2,3-diphosphoglycerate, but it's the same thing. The "2,3-" in the name is essential, because 1,3-bisphosphoglycerate also exists and is far more widely known.

-- Athel Cornish-Bowden (email)

Here is an awful example of a dequantification "near-miss".

When my husband was a graduate student in biochemisty at a large midwestern university with an excellent scientific reputation, one day a fellow graduate student came in really steaming. She had just been to the graduate school office, where the required form-check of thesis hard-copies was performed. The examiner had looked at one of her graphs, and said "this looks awfully busy -- couldn't you take some of the points off?" (!!!) Her reply was "Only if I want to end up in jail!" (it was federal grant supported research).

I am happy to report that the examiner was no longer the same person when I had to go through the same process.

-- Edith Konopka (email)

The reference to the DPG story is (almost) right except that it is in volume 26. The paper doesn't discuss the choice of inappropriate units, but elegantly presents the benefits of getting them right.

-- Jim Reid (email)

The Size Of Our World is a pretty page that could do with a bit of quantification. I like the fact that the shadows on the table top give a sense of how much more voluminous Earth is than Pluto, but wouldn't it have been nicer if the table top had had a light grid of 1,000-kilometre squares? If that was technically challenging, a scale bar would have sufficed.

-- Derek Cotter (email)

Where's the sun? Even just an edge would be good.

-- Edward Tufte

The photograph shown above is one of a series of five in the page I linked to, and the sun makes its first appearance in the third photo in the series, just before the earth becomes too small to see. Jupiter appears in the second photo and becomes invisible after the fourth. The fifth photo shows the giant star Antares, and the sun is a single pixel in that photo.

The presence of common objects in any two adjacent photos helps to maintain the connection as the sizes of the objects increase, but a graduated scale with numbers would still have been nice. For the largest objects a switch from 1000-km to 1-AU scale would have been necessary.

[1 AU=1 astronomical unit, the distance between the earth and the sun, or about 150,000,000 kilometres]

-- Derek Cotter (email)

This is rather a belated comment on Jim Reid's posting of 23rd June, which I missed when it appeared. Sorry about the typo in my citation of the volume number, and thanks to him for correcting it.

I'm not too surprised that Benesch and Benesch don't say too much about the units in the article, as they were probably pressed for space (Biochemical and Biophysical Research Communications is, or at least, it was then, a journal that puts a severe limit on space). My real source was not the paper but a lecture that R. Benesch gave at the FASEB Congress in Atlantic City in 1968, and doubtless he said a lot of chatty things in the lecture that he would not have committed to print.

-- Athel Cornish-Bowden (email)

This has got me interested again...

I regularly teach histologists and biologists how to extract quantitative 3D information from 2D images and the issue of image dequantification is a key part of the program.

There are a number of linked issues;

(1) Often in experimentally derived images the x and y magnifications can be different due to non square CCD pixels, optical distortions etc. This can be overcome by taking images of known gratcules in both directions to check magnification. (2) Using calculated "magnifications" derived from the nominal magnification on the side of the objective is often not accurate. (3) Most histological images are 2D projections of a 3D space (admittedly thin) that has been subjected to considerable tissue processing, shrinkage etc since it was a live piece of tissue. This should be experimentally investigated and accounted for by the scientists. Note that relatively modest linear shrinkage becomes significant 3D volumetric shrinkage. Furthermore not all tissue shrinks the same amount. Famously Herbert Haug a German anatomist found in the 1960's that the brain tissue of young humans shrank more than the brain tissue of old human brains. This led to an apparent "loss" of neurons with age (they had a lower numerical densitry but after correcting for differntial shrinkage the same total number). (4) The act of taking a thin histological (or optical) section leads to an obersved reduction in feature dimension. This is not widely reflected upon and there are no accepted ways to indicate this in standard hsitological images. (5) Often the histology stains used do not stain tissue compartments uniformly.

(6) Histological images are in fact 2D samples (real Flatland stuff) from 3 space and in common with all statistical sampling they suffer from the "Central Paradox of Sampling" = simply by looking at the p[icture you have no idea if it has been randomly sampled or carefully selected (i.e. it is an unbiased or a biased sample).

(7) The short advice I give for all quantitative image analysis tasks is always is to think Outside-In not Inside-Out. i.e. Think about what was done to obtain the image you have in front of you and whether this is appropriate for the scientific task at hand NOT get obsessed by the image details some of which are misleading.

Happy Quantifying

PS for more on this see here (

-- Matt R (email)

Dear ET,

Here is a small clever thing. A paper by J. Adler (2008) called "The unitary scale bar: human and machine readable" which appeared in Journal of Microscopy, 230 No 1. 163-166.


A format is described for a scale bar that encodes the length represented within the structure of the bar itself, thereby removing the need for any supporting text. Although the 'unitary' scale bar has a conventional appearance it is also machine readable and therefore retains information about the scale even when the file format is changed. The format is based on the metre and is suitable for all terrestrial applications.

Best wishes


PS I personally would always also include the text for humans.

-- Matt R (email)

Comparing different editions of a book

Different versions of important books sometimes appear in variorum editions, which combine all the the editions into a single text, with footnotes to indication what was added or deleted (or just corrected) in each one.

P. Z. Myers in his blog Pharyngula today draws attention to a site at that uses a more computer-based application of the same idea to the six editions of The Origin of Species. The six editions are all loaded simultaneously (so it takes several minutes to load) and then presented as a colour-coded graphic -- grey for the 1st edition, orange for the 2nd, etc. (illustrating, incidentally, ET's principle that there is no natural sequence of colours, but in this case I doubt whether a grey scale would work, though it might if it went from the lightest readable grey to full black). Mousing over any region, such as the large red block representing Chapter VII, which appeared only in the 6th edition, causes readable text to pop up corresponding to the position of the mouse.

I found this an interesting idea, but very fatiguing -- I can't imagine anyone having the patience to read the whole book in this way, whereas a conventional variorum edition can be read like any other book. So, I wonder how other contributors to this forum will respond to this: does it work? Could it be done better?

-- Athel Cornish-Bowden (email)

I need to give an explanation, as my posting of yesterday has nothing to do with dequantification in scientific images. The problem is that I wasn't able to work out how to ask a new question -- maybe this is obvious and simple, but I failed to find the answer. Then I thought maybe I could just add a "response" to an existing thread but give it a new subject -- I now see that that was not the way to do it. Sorry.

-- Athel Cornish-Bowden (email)

While visiting St. Joseph, MO, recently, we came upon an impressive church. I told my son to get a good picture of the "twin spires" to show the height of the church. He came back and said, "I included the house on the side, so you can tell how tall it is!" (he's 10!)

Proud papa moment!

<html> <img src=""> </html>

-- Mike Round (email)

I wanted to post some images of the rare three dimensionally preserved trilobite fossils that Harry Whittington discovered in Virginia - and I have below. Then I realised that they were a good example of dequantification. The text indicates the magnification (x4 etc) - but this is ambiguous - are these the magnifications inscribed on the objective lens of the microscope or are they actual magnifications i.e. that the image at final printed size shows a 4x linear magnification of the physical object? The problem is that when you see these images on your computer screen the physical link between the magnification and final printed size on paper has been lost. A simple scale bar would do the trick.

The image is taken from an article that Harry Whittington wrote in 1960, Unique Fossils from Virginia, for the magazine Virginia Minerals ( The article describes trilobite fossils that were incredibly well preserved. As the Obituary for Harry Whittington in the Guardian (July 8th 2010 ) explains;

"Trilobites had hard carapaces made of the mineral calcite, which meant that extraction of the fossil from the rocky matrix could take many hours. But in the late 1940s, Harry and his colleague Bill Evitt discovered a locality in Virginia (in rocks 460m years old) where the "shells" of the trilobite had been replaced by insoluble silica. By throwing samples into acid, they could recover perfect trilobites by the thousand, without hours of digging. They were perfect replicas, effectively made of glass."

These fossils are fully three-dimensional - the acid used in their preparation dissolves the surrounding rocks and leaves exquisite, microscopic, details of the 460 million year old animal.

Stephen Jay Gould makes the point in Wonderful Life that Whittington's exposure to these three dimensional fossils helped prepare him for the task of re-animating the very flattened soft bodied animals of the Burgess Shale.

Best wishes


-- Matt R (email)

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