Superellipsoid-based study on reproducing 3D particle geometry from 2D projections

The potential of reproducing the 3D geometrical features, e.g., sizes, elongation and flatness, of idealized convex granular particles from their 2D random projections was investigated based on a superellipsoid model. Using the random projection method, the relationships between the geometrical features of monosized superellipsoids and the statistical distributions of the corresponding 2D projected counterparts were examined. The 2D size parameters, e.g., r_1max, r_mean and r_2min, obtained from the projected images were well correlated with the semi-axial principal dimensions of the 3D particles, e.g., R₁, R₂ and R₃. Further studies of randomised superellipsoid particles with various aspherical shapes and limited projection numbers were performed to validate the findings. The capability and reliability of predicting 3D sizes and shapes from 2D projections were statistically analysed and verified. The correlation of prediction accuracy with increasing projection number and varied aspherical shapes was investigated. Based on the results, a particle geometry prediction framework was proposed, and the associated performance was examined using realistic cobble particles obtained from 3D laser scanning. The promising results highlight the potential of this approach in future industrial applications.