Wicksell and scimitars

In an earlier form of the write up the following was stated.

The Corpuscle Problem arises from the fact that not all arbitrary-shaped 3-D objects have the same probability of being sampled by a 2-D sampling probe (knife blade).

This is not true either. The corpuscle problem did not address arbitrary shaped objects. It addressed balls. That’s all. The goal of the corpuscle problem was to count the number of ball shaped objects in tissue knowing only the profiles observed on slices. This is not a trivial problem. The balls can have a size distribution that is unknown.  The probability is not whether or not the blade samples an object, but how the blade samples a population of balls. Wicksell already knew the probability of sampling a ball. That was rather obvious to him. He was working on a much more complicated problem: how is the population sampled?

An experiment was done with potatoes and scimitars … actually scimitars were not available. Potatoes were sliced with a blade to produce a macroscopic data set that was employed in a corpuscle problem.

Since Wicksell’s 1926 paper showed that the problem was intractable for triaxial ellipsoids a number of different methods have been tried that give reasonable results for sections in opaque media. These include rocks, cement, asphalts, and other materials.

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