Rapid detection of sub-scale particle features using invariant harmonic wavelet descriptors

A new algorithm for calculating invariant shape descriptors was developed based on the Harmonic Wavelet technique. The algorithm requires the perimeter information from a shadow graph parameterized by length along the perimeter in Cartesian component, complex format. The algorithm returns a set of parameters which represent the net amplitude of a disturbance from a circular shape for features with length scales that fit in a narrow range of fractions of the total perimeter length relative to the major diameter of the particle. In pragmatic terms, the descriptors represent a quantitative measure of “roughness” on a variety of length scales that are smaller than the maximum measure of the particle. The descriptors are fully invariant to size, translation, rotation, and shift. Unlike other descriptor sets, one cannot reconstruct the original shape from these descriptors. However, the calculation time for these parameters is on the order of calculating Feret diameters and is about 11 times faster than calculating invariant FFT descriptors. The speed and quantitative measure allow for sampling of larger data sets which reduce uncertainty and allow for detection of small changes in bulk particle property with far greater statistical significance. The algorithm is also ideal for parallel processing.

Graphical abstractFlow Diagram of the Invariant Harmonic Wavelet Descriptor AlgorithmFigure optionsDownload full-size imageDownload as PowerPoint slideHighlights► Particles can be quickly analyzed with IHWDs. ► IHWDs represent magnitudes of roughness on length scales less than the major diameter of the object. ► IHWDs are 11 × faster than invariant FFT descriptors. ► IHWDs have many applications in engineering and science.