A technique is described for characterizing arbitrary, simply connected plane figures by a set of numbers derived from the shape of their outlines. The basis of the description is taken to be the slope of the contour as a function of distance along the contour. This function is expanded in Fourier series, and the series coefficients are taken as a set of descriptors. Topics discussed are the effects of distortion and approximation of contours, reconstruction of figures from their descriptors, and application of the descriptors to pattern recognition. Alternates to the Fourier series expansion of the slope function are also considered.