Wicksell's Problem in Local Stereology

Abstract

Wicksell's classical corpuscle problem deals with the retrieval of the size distribution of spherical particles from planar sections. We discuss the problem in a local stereology framework. Each particle is assumed to contain a reference point and the individual particle is sampled with an isotropic random plane through this reference point. Both the size of the section profile and the position of the reference point inside the profile are recorded and used to recover the distribution of the corresponding particle parameters. Theoretical results concerning the relationship between the profile and particle parameters, unfolding of the arising integral equations, uniqueness issues and domain of attraction relations are discussed. We illustrate the approach by reconstructing from simulated data using numerical unfolding algorithms.