The Black Box problem

For many people stereology is a black box. Most people do not understand what is required but are able to enter some numbers and then see one or more numbers spit out by the black box.

Consider the follow simple problem. There is a tract of land with trees on it. A question that can be asked of the trees is the mean diameter of the trees. The method selected to determine mean diameter is to wrap a tape around the tree and to read off the length. This is the perimeter of the tree trunk. Divide that by pi to obtain the mean diameter of the tree trunk. Another way to do this is to make a tape measure that is in units of pi. At pi centimeters write 1, at 2pi centimeters write 2, and so forth to make a tape where the measurements taken do not require the additional step of dividing by pi.

This sounds all well and good. There is a problem.

This simple stereological procedure does not provide the mean diameter of the tree trunk.

The value that is measured here is always greater than the mean diameter except in the case of a circle.

If you buy a tape for forestry it is marked as described above. It provides a measure of the tree. Should that tape claim to provide a measure of the mean diameter and you did not know better then you would move forward with the wrong understanding of the measurements being taken.

The same applies to other products that provide stereological results. Do not treat them as a black box. Understand what needs to be done. Use a spreadsheet of your own making to check the results of the product. Check the computed results. Make sure that the inputs are what is required. Do not trust the protocols provided by automated equipment. Independently verify that the protocols are correct.

Failure to understand stereological protocols can be a problem. Articles have been published that had to be withdrawn because the work was done without the researcher having taken the time to learn stereological methods.

Degradation of a bad article

Earlier this month I stumbled upon a short write up that has circulated on the web for a while. It was inaccurate to start with but somehow it is being copied and altered slightly becoming even worse.

Shortly after the initial stereology discussion on the Feldberg, Prof. Elias sent a tiny statement on the trial to the biography Science. Soon thereafter, he received an heated reply from researchers in academia, supervision agencies, and in isolation attention at institutions around the world. They contacted Prof. Elias for data about the next stereology meeting. What Elias suspected had been correct — scientists opposite extended disciplines compulsory right away approaches is to analyses of 3-D objects formed on their look on 2-D sections.

This is from the following link (purposely altered to prevent a link to the site in question).
http://boatsforhelp . com/boat-help/the-history-of-modern-stereology/

The original write up was just plain wrong.

In 1637, Bonaventura Cavalieri, a tyro of Galileo Galilei in Florence during the high Italian Renaissance, showed that the meant volume of a race of non-classically made objects could be estimated fairly from the total of areas on the cut surfaces of the objects (right). The Cavalieri Principle provides the basement is to volume determination of biological structures from their areas on hankie sections.

Cavalieri did not deal with estimations. The principle dealt with showing that 2 objects had the same volume.

[quote]In 1777, Count George Leclerc Buffon presented the Needle Problem to the Royal Academy of Sciences in Paris, France. The Needle Problem reserve the luck theory for stream approaches to guess the aspect area and length of biological objects in an unprejudiced (accurate) manner.[/quote]
Buffon was a nickname. The year was 1733 and he did not show the needle problem to the RAS. The needle problem can be used to derive methods for the estimation of length, but it does not lead to area estimations.

[quote]In 1847, the French mining operative and geologist, Auguste Delesse, demonstrated that the approaching worth is to volume of an intent varies in directly suit to the celebrated area on a pointless division cut by the object. The Delesse Principle provides the basement for precise and effective determination of intent and regions volumes by indicate counting.[/quote]
Delesse's method leads to volume fractions. He was not interested in volumes. Furthermore, the technique he developed was too cumbersome to use. It was neglected after Delesse himself used it for a short while.

Hopefully, such poorly constructed copies of the original incorrect article are not copied more and more about the internet.

A meeting of the ISS, the International Stereology Society, will be held in October of this year in Beijing. The meeting will be held October 19 to October 23, 2011. During that meeting new concepts in stereology will be presented along with studies that discuss the implementation of stereological methods.

The ISS, founded in 1961 and incorporated in 1963,
includes members from the fields of mathematics,
statistics, biology, and materials science. The
purpose of the ISS is to promote the exchange and
dissemination of information on stereology amongst
persons of various scientific disciplines and countries.
Stereology is nominally the science of determining
the spatial structure of materials on the basis of
sections and projections through the materials.
Furthermore, stereology embraces the analysis of
planar images per se, and three-dimensional probes
of materials. A main concern of the ISS is the
practical applications of stereology. The ISS
promotes such practical fields, including Image
Analysis and Processing, Stochastic Geometry,http://www.blogger.com/img/blank.gif
Mathematical Morphology, Pattern Recognition,
and Fractal Geometry.

When information about the papers being presented becomes available I will post it.

For now visit http://www.ics13.beijing.org for more information.

Is this really true?

"Two peer-review journals were established that focused primarily on stereology – Journal of Microscopy and Acta Stereologica (immediately Image Analysis & Stereology)."

That is the quote I saw. Well, I thought that the Journal of Microscopy was the Journal from the Royal Microscopy Society. The journal was renamed. The volume numbers were not changed. Back in the 1975 the volume numbers were 100, 101, and 102. So that's 3 volumes per year and there are 100 volumes. It sure seems that 33 years or more of publication occurred before 1975. That clearly puts the Journal of Microscopy's origin before the early 1960s when the term stereology was coined.

The Journal of Microscopy was not established to disseminate information on stereology.

Apparently, the article being tossed around the internet lately needs a substantial revision. Even the basics are wrong.

Curved lines and Consistent Counting

A typical stereological procedure involves the use of probes. Probes are used to investigate the geometrical properties of the objects being studied. There are two types of probes. One class of probes are placed at random with respect to the objects being studied. The placement of the probes should be done to fulfill the random requirement of the math. Examples of these types of probes are lines, points, and cycloids. The other class of probes are placed with respect to reference points identified for the object of interest. These are called local probes. Examples are the nucleator, planar rotator, and surfactor. In all of these cases, the probe is placed relative to a reference point. The reference point is identified first, and then the probe is placed relative to the reference point. The randomness requirements are fulfilled after the reference point is selected.

Most probes involve straight lines or points. Cycloids and circles are the only curved probes that are frequently used.

It turns out that determining if a probe intersects a curved structure is made substantially more difficult if the probe is not a straight line. People work well with straight lines, but not that well with curved lines. A well known problem that is still being studied is the ability of people to catch a thrown ball. The ball moves in an arc that approximates a parabola. On a windy day the path of the ball can be even more complicated. Despite this people can still catch the ball. A large number of suggestions have been made.

1.The person runs to make the ball approach the person in a straight line.
2.The person runs to maintain a constant angle of the ball to the horizon.

All of these ideas suggest that people need to reduce problems with curves to problems that avoid curves. This lesson should be carried over to stereological work as well. If it is possible to avoid using a curved probe, then do it. There are straight probes to use in place of all of the curved probes. Mistakes and inconsistencies that lead to bias can be avoided by using straight probes.

Snedecor

Snedecor was a statistician that helped lay out the design of many experiments through his book on the subject. Many references to his 1902 book can be found in the stereological literature. His work saw a recent rejuvenation when one of his formulas was inappropriately used to compute the coefficient of error. Some of Snedecor's work was mentioned in a book by Scheaffer et al. This work is based on the notion that the samples are independent, which is clearly not the case.

One of the earliest formulas for the coefficient of error was the binomial distribution formula which was suggested for use in point counting. The geologists and later other scientists realized the inadequacy of the formula for their work. The same was true of the Snedecor formula. In both cases, the problem was linked to the lack of independence between samples. The solutions offered to counter this problem was to take samples far enough away to avoid problems. The same can be seen in Rosiwal's work where it is recommended that no two traversal lines cross the same crystal. One of the early studies that realized that the Snedecor formula was not appropriate studied sugar beets in agriculture.

The problem had been identified by hundreds of researchers across the globe. A solution to the problem was eventually worked out by reexamining the problem from the position of developing a method to calculate the coefficient of error when the samples were known to be related to each other. The pioneering work was done by Matheron. He started with the assumption that the samples were taken in a systematic manner and used this to determine a formula for the measure of dispersion.

For unknown reasons an old formula that was not applicable was resurrected. The lessons of hundreds of researchers from many different scientific fields from metallurgy, to geology, to biology was forgotten. Their incite into the cause of the problem and the success of Matheron to develop a formula which was applicable to systematic sampling was overlooked.

Fortunately, the resurrection of this old and inapplicable method appears to have been just a brief stumble in the advancement of stereological research.

The best means of estimating the coefficient of error today is the extension of the Matheron technique. This technique has been extended to point counting and to counting of objects. Important research continues to be done by Garcia-Finana, Cruz-Orive, Gundersen, and Baddeley.

Failure to understand stereology

A few years back there was a presentation on stereology in which the speaker claimed you could break the rules and still get a "good" answer. The speaker came to this conclusion because they had done an experiment using proper protocols and then did an experiment with sloppy methods. The two answers they decided were good enough and then deiced that being sloppy and being a good scientist were the same thing. Ok. Those are not the words used in the presentation, but that is what the person was saying. So a real stereologist stands up and suggests that the speaker "Didn't look hard enough to find a difference."

This was exchange between sloppy work is no different than using a method known to get a wrong result. There are many reasons given to use methods than are known to be biased.
1. The person running the lab says "Worked for me, it'll work for you"
2. It's simpler to get the wrong answer.
3. Claim it's just as good without knowing the answer.