Estimate of three-dimensional Wadell roundness of irregular particles using image processing and topographic analysis

Wadell roundness is a general particle shape descriptor used in many fields, such as mining engineering, civil engineering, and geotechnical engineering. Initially, Wadell roundness was defined as two-dimensional, and now it has been generalized to three-dimensional. This study proposes a novel image-based method using topographic analysis to estimate the three-dimensional Wadell roundness of irregular particles. And an alternative strategy to estimate 3D Wadell roundness from other shape descriptors is further proposed. The effect of mesh density on 3D Wadell roundness is quantitatively analyzed. In addition, the relationships between 3D Wadell roundness and eleven shape descriptors, including 2D Wadell roundness and the other ten 1D, 2D, and 3D shape descriptors, are discussed. Finally, the computation time of the 3D Wadell roundness estimation algorithm proposed in this study is recorded to evaluate the algorithm's efficiency. The results show that the 3D Wadell roundness estimation algorithm is robust and can be used for idealized geometries and realistic particles of various shapes. The mesh density of particles significantly influences the 3D Wadell roundness. It proved difficult to predict the 3D Wadell roundness from the eleven shape descriptors mentioned in this study. The 3D Wadell roundness estimation al-gorithm can be finished in a few minutes, potentially using the algorithm in rock shape analysis and mechanics responses investigation.