Principle of Point Counting Techniques

In the introduction it was argued that the area of a feature in an area of interest (micrograph or polished surface) could be estimated by counting the number of squares in a regular grid that lie predominantly in the feature. To put this concept into efficient practice requires a simpler approach. It would be easier if each square were marked at its centre:
dotted grid

Now counting the squares predominantly within the features of interest can be recast as counting the number of dots at the centre of the squares that lie in the features of interest. This is obviously much easier, as no qualitative decision has to be made about whether a square is predominantly in or out. The dots are mostly going to be in or out. Part of the trick is to ensure the dots are small enough in relation to the boundary that dots "on the line" are a rare event.

Of course, having decided that counting points is easier than counting squares, we can drop the squares!

Now we merely count the points hitting the features of interest. Their area can be approximated by this number multiplied by the area of a square. This is the origin of the terminology Point Counting Morphometry. In the practice of point counting the points used can take many forms, including grids!

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