Estimation of the second order spatio-temporal derivatives of deforming image curves

This paper intends to show that the second order spatio-temporal derivatives of de-forming image curves can be computed quite accurately from image sequences. These quantities, related to the second order optical flow parameters, are useful in the computation of the motion and the structure of a 3-D rigid curve from monocular image sequences. We show that they can be estimated directly from the points of the spatio-temporal surface generated by the image curve using polynomial approximation, and that the accuracy is at least comparable and often much better than that obtained using the other standard techniques. We consider particularly the special case of curvature because the estimation of that quantity has been studied before and show the results obtained using different methods. We then propose a "pseudo scale-space" method that should improve further the accuracy of the results.