Consider an opaque medium which contains 3D particles. All particles are convex bodies of the same shape, but they vary in size. The particles are randomly positioned and oriented within the medium and cannot be observed directly. Taking a planar section of the medium we obtain a sample of observed 2D section profile areas of the intersected particles. In this paper the distribution of interest is the underlying 3D particle size distribution for which an identifiability result is obtained. Moreover, a nonparametric estimator is proposed for this size distribution. The estimator is proven to be consistent and its performance is assessed in a simulation study.

翻译：考虑一种含有三维颗粒的不透明介质。所有颗粒均为形状相同的凸体，但尺寸各异。这些颗粒在介质中随机分布且取向随机，无法直接观测。通过对介质进行平面切片，可获得被截切颗粒的二维截面面积样本。本文研究的目标分布是潜在的三维颗粒粒度分布，并获得了该分布的可识别性结果。此外，针对该粒度分布提出了一种非参数估计量。该估计量被证明具有一致性，并通过模拟研究评估了其性能。