Evaluation of three-dimensional particle shape index from projected two-dimensional image

Traditionally, the shape of a three-dimensional (3D) particle is inferred from a single parameter called the aspect ratio (AR) that is evaluated from a collection of projected two-dimensional (2D) images of the 3D particle. While this approach could offer an estimate of the particle shape, it is likely that a single parameter is insufficient to describe the 3D shape characteristics of a particle. Conventionally, the shape of a 3D particle can be described by two parameters: the elongation index (EI) and the flatness index (FI), defined as the length ratios of different principal dimensions. This paper presents a novel approach that can be used to evaluate the EI and FI of 3D particles based on their projected 2D images. The novelty of this proposed method is that the distribution of the AR is considered rather than only the mean value. The performance of the algorithm is examined using numerically generated ellipsoids and real sand particles scanned using microfocus X-ray computed tomography. The results appear promising and the plausible combinations of the EI and FI of the 3D particles can be obtained.