Inferring 3D ellipsoids based on cross-sectional images with applications to porosity control of additive manufacturing

This article develops a series of statistical approaches that can be used to infer size distribution, volume number density, and volume fraction of three-dimensional (3D) ellipsoidal particles based on two-dimensional (2D) cross-sectional images. Specifically, this article first establishes an explicit linkage between the size of the ellipsoidal particles and the size of cross-sectional elliptical contours. Then an efficient Quasi-Monte Carlo EM algorithm is developed to overcome the challenge of 3D size distribution estimation based on the established complex linkage. The relationship between the 3D and 2D particle number densities is also identified to estimate the volume number density and volume fraction. The effectiveness of the proposed method is demonstrated through simulation and case studies.