3-D Motion parameters from contours using a canonic differential

A method for finding the affine transformation which relates two projections of a planar curve, arbitrarily oriented in 3-space, is presented. The method is based on a canonic parameterization of curves and the decomposition of these curves into component ellipses such that an arbitrary linear transformation applied to the whole scene also applies to the component ellipses. The relationship between the ellipses allows for a simple solution for the affine transformation relating views of a contour without point correspondence information. Experimental results indicated the need for contour smoothing in the presence of noise; hence filtering in the Fourier domain was applied to the contours prior to parameterization. The theoretical development of this technique and experimental results are presented.