THE USE OF FOURIER DESCRIPTORS IN THE CLASSIFICATION OF PARTICLE-SHAPE

A new quantitative method for characterizing quartz grain shape is pre sented. The method employs a harmonic analysis based upon Fourier desc riptors which is a distinct variation of the traditional and widely us ed Fourier series. Quartz grain images from a scanning electron micros cope were 'frame grabbed' and converted to a digitized grey-level imag e. The image processing techniques of enhancement, segmentation and bo undary tracking were applied to remove all features except the image b oundary. This boundary was sampled at uniform intervals of are length and represented mathematically on the complex plane. In this way probl ems associated with the location of particle centroid and re-entrant v alues were avoided. The resulting data was standardized relative to sc ale, rotation and starting position. Hence the discrete Fourier transf orm 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 g rains from three distinct populations: desert quartz, beach grains (Fi re Island, New York) and Brazilian crushed quartz. Whilst plots of ave rage amplitude vs. harmonic number for each population appeared simila r, discriminant analysis applied to each grain sample distinguished ch aracteristic grain shape with an excellent degree of success. The prob lems of location of the centroid and re-entrant values were eliminated . This allowed the technique to be applied to a much wider group of ir regularly shaped sedimentary particles such as loess.