Determining the shape of agricultural materials using spherical harmonics

Abstract

Determining the shape of agricultural products is important in many areas of the food industry, such as for classification or quality inspection. The characterization methods used to describe the behaviour of particulate systems during handling may also benefit from an accurate description of the particle shapes. Several methods for particle shape representation have been proposed, including those using super-quadric equations, polygon formulations, or composite particles. However, it has been proved that these methods are not accurate enough to represent complex-shaped particles. The use of spherical harmonics has recently received increasing attention for this purpose. In this paper, spherical harmonics are used to obtain the shapes of three agricultural grains, namely bean, chickpea, and maize, which differ in complexity. Once it has been proved that spherical harmonics can accurately describe the shapes of agricultural grains, the advantages and disadvantages of this technique are discussed. Furthermore, the relationship between spherical harmonics and the discrete element method for the simulation of particle systems is also discussed.