Ranking of risk of injury from glass contaminants using Fourier shape measures of fragment outlines

The inclusion of glass contaminants in a horticultural peat product supplied to the domestic market, where it may be manipulated by hand, exposes customers to the risk of injury, especially if the fragment is encountered at a sharp edge or pointed corner, and at a high enough velocity. Fragment shape is considered the most important factor in the process of accidental injury, and its determination with a reasonable accuracy would be of great benefit. Glass contaminants included in peat were detected using dual-energy X-ray absorptiometry (DXA), and resulting images processed to isolate glass fragment outlines. Four shape measures derived from the Zahn–Roskies Fourier series of fragment outlines were compared to a corresponding visually determined rank of risk of injury. A similar procedure was also carried out on ranks generated from Cartesian distances of fragments based on the shape measures and those based on visual ranking. Comparison of ranks was carried out using Kendallʹs Rank Correlation Test. It was observed that the parameter of the polygonal approximation of fragment outlines and the highest Fourier harmonic considered affected rank correlation. Results show that the individual shape measures performed reasonably well, the best correlation being τ = −0.721 (p < 0.0000005) at the most suitable polygonal approximation and harmonics considered, both of which were low values demanding a lower computational effort compared to other measures. Combination shape measures were also tested for their utility with the best performing two shape–measure combination resulting in a ranking performance of τ = 0.839 (p < 0.0000005) which is a 16.4% improvement over the best single shape measure. It can be concluded that the Zahn–Roskies Fourier based combination shape measures will enable a high-accuracy online injurious shape identification.