Friday, July 23, 2010

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.

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