Harmonic endurance: A new shape descriptor derived from polygonal harmonics

Particle shape affects the behavior of both powders and individual particles, but techniques for characterizing shape are still largely inchoate. It has been shown that the outline of a two-dimensional view of a particle can be shape characterized using polygonal harmonics, which are constructed at various step lengths by using a structured walk around the outline. The endurances of these harmonics prove to be worthy macroscopic shape descriptors. For example, the endurance of the third harmonic, which is a measure of the ease with which a triangle is constructed on the outline, is a strong indicator of equilateral triangularity. Images of several objects have been analyzed and the utility of harmonic endurances as shape descriptors is demonstrated. Data are best presented by ordering the endurances according to their values. A notion of harmonic impurity is also explored.