Stereological estimation for layered structures based on slabs perpendicular to a surface

This paper deals with the characterization of layered structures sampled with respect to a reference surface. A scheme where thick slabs are sampled perpendicular to a curved surface is considered, resulting in a non-uniform sampling of the structure. We present an estimation procedure based on the Horvitz-Thompson principle. An approximation of the sampling probability is proposed, which depends on the local surface curvatures, on the slab dimensions and on the intensity function of slab anchors. The practical determination of local parameters is detailed for the case of a revolution surface. The procedure is applied to the estimation of surface area density of cell walls in tomato pericarp.