Comments on the shortcomings of predicting the precision of Cavalieri volume estimates based upon assumed measurement functions

Abstract

It is well known that the estimation of an object's volume by means of serial cross-sections, the so-called Cavalieri method, yields an unbiased estimate. But by itself it provides no means by which to estimate how precise this estimate is unless the shape of the volume is fully known beforehand. This knowledge can only be partially determined from the serial section information that is collected. Methods have been developed that claim to surmount this difficulty by using the serial section data to create a mathematical model of the volume's shape properties. The model then is used to estimate (predict) the precision of the volume estimate (its CE) from the single set of data available. Unfortunately, the theory underlying the model is flawed and so the model itself amounts to no more than an unsubstantiated guess about the shape of the volume. Therefore, the precision of the volume estimates that one obtains from the method is only as good as the model and this cannot be ascertained from the single set of acquired data. In this letter I explain the inadequacies of the modelling method. I suggest that it be used only with caution, if at all. Instead I suggest two alternative ways to predict the CE, one that is based upon a rule-of-thumb approach to the object's shape, and another that is based upon spectral analysis of the measurement function and that is easy to implement with available computer software.