The use of Fourier descriptors in the classification of particle shape



A new quantitative method for characterizing quartz grain shape is presented. The method employs a harmonic analysis based upon Fourier descriptors which is a distinct variation of the traditional and widely used Fourier series. Quartz grain images from a scanning electron microscope were ‘frame grabbed’and converted to a digitized grey-level image. The image processing techniques of enhancement, segmentation and boundary tracking were applied to remove all features except the image boundary. This boundary was sampled at uniform intervals of are length and represented mathematically on the complex plane. In this way problems associated with the location of particle centroid and re-entrant values were avoided. The resulting data was standardized relative to scale, rotation and starting position. Hence the discrete Fourier transform was applied using modern fast Fourier transform techniques and the modulus of the resulting harmonic amplitude used to characterize the grain shape. The technique was applied to a sample of 0–5-m quartz grains from three distinct populations: desert quartz, beach grains (Fire Island, New York) and Brazilian crushed quartz. Whilst plots of average amplitude vs. harmonic number for each population appeared similar, discriminant analysis applied to each grain sample distinguished characteristic grain shape with an excellent degree of success. The problems of location of the centroid and re-entrant values were eliminated. This allowed the technique to be applied to a much wider group of irregularly shaped sedimentary particles such as loess.