Abstract

A method for computing the circularity of any closed two-dimensional trajectory of arbitrary shape is described. The core of this technique is the derivation of moments of area for each closed contour defined by perimeter coordinates. The method can be used to analyze two-dimensional data of any form, and provides output information including the number of closed contours within the data set, the area of each contour, the position of the centroid of each contour, the orientation of each contour, and the parameters of the ellipse that best fits each contour. A number of applications are discussed, including the comparison of kinematic trajectories, the calculation of cross-sectional areas from digitized MRI scans, and the analysis of phase portraits.