Persistence of Polygonal Harmonics as Shape Descriptors

Characterization of the overall (lage scale) shape of rugged particles poses a problem which is not readily solved by existing shape analysis techniques. Recent research on the divider stepping method used in factal analysis has led to the examination of polygonal harmonics which can be constructed in both smooth and rugged particle silhouettes. The persistence of these harmonics is defined as the ratio of the longest step length to shortest step length which can be used to create that harmonic. It is proposed that the persistences of the first three harmonics provide useful descriptors for particle shape. Variation of these persistences within several geometric figures is explored, protocols for the analysis are adopted and some preliminary work on rugged silhouettes is discussed. Characterization by this technique holds great promise in the development of a general approach to particle shape description.