Stereology applies geometry and statistics to the problem of measuring things that cannot be directly perceived because they exist in a higher dimensional space than that in which the measurement takes place. Typically this refers to 3 or 4-dimensional entities represented though 2-dimensional pictures. Because these methods are statistical, attention has been focused on bias in sampling and calculation as well as on efficiency, the relation between sample size and expected accuracy of estimate. There is often a tradeoff. For instance, Horvitz-Thompson ratio estimators are unbiased. Yet, John Hilliard and his school tended to dismiss methods based on this approach as iinefficient; the accuracy gained through zero-bias might be small compared to the inaccuracy resulting from the measurement variance for samples of practical size. What may be surprising is that usually the greatest source of error lies in something totally apart from stereology itself, in idealizing the image as a geometric construction before any stereological or mathematical morphological method is applied. Perhaps the most obvious example (among many) of this idealization is in the application of thresholding. Thresholding is used to differentiate features from background.

A current problem in stereology: Void outlines obtained from level sets are often used to measure surface area per volume. The value measured depends strongly on the threshold chosen, and that is somewhat arbitrary. THe method of level sets is by itself often an inadequate approach. Analogous problems exist in all types of image segmentation.