Objective fitting of ellipses in the centre-to-centre (Fry) method of strain analysis

Centre-to-centre measurements are used in the Fry method of estimating fabric ellipses for strain analysis. Despite the usefulness of the method, estimation of the elliptical shape of the central vacancy field in a Fry plot is typically subjective. Two new methods can provide more objective estimates of the fabric ellipse by locating the locus of maximum point-density gradient. The point-count density method compares the number of points in a central elliptical area with the number in a surrounding annulus having the same area. By varying the dimensions of the ellipse it is possible to maximize the point-density contrast between the inner ellipse and the surrounding annulus, providing an estimate of the shape of the fabric ellipse. The continuous function method uses an exponential function to measure the fit of points in the Fry plot to a trial ellipse. By varying the dimensions of the trial ellipse, it is possible to maximize the value of this function, providing a second estimate of the shape of the fabric ellipse. Both methods use the image processing software ImageJ, although the search for the optimum ellipse in the continuous function method is more rapidly executed using the Solver program in Microsoft Excel.