Fourier transforms mathematically represent complex contours to a high degree of accuracy. Normalization of Fourier coefficients with respect to contour size, starting point from which the contour is traced, and its orientation, make the coefficients invariant to these contour characteristics that do not represent shape. The mean of the normalized Fourier coefficients and the error can be used to reconstruct the average shape and its deviations. Shape averaging of the 2-D contours using normalized Fourier coefficients was implemented on various ceramic particle systems. The averaged shape provides a convenient mode of shape comparison amongst various powder systems. Copyright (C) 1999 Elsevier Science S.A.
