Accurate measurement of radius evolution as a function of direction in 3D images

Very often the reason for using of X-Ray tomography in a research project is to measure the evolution of some geometrical characteristic. The sought characteristic may be explained in simple words like size, shape, or distance, but in practice measures based on these notions can have a complex implementation.
We present a simple problem, measuring the evolution of radius in a cylindrical sample (a common shape for sample preparation for tomography) and how this value differs according the direction in which we look, when such evolution is known to be anisotropic.
The solution is not unique, but we show that a naïve manual approach are not accurate enough, and how even a simple geometric notion such as radius needs a thorough definition in relation to its applicability to 3D image analysis. We extend the argument to how a good understanding of the notions and algorithms used in the quantification of geometrical characteristics can directly affect the pertinence and representativity of the results.