Motion synthesis through 1D affine matching

We present the study of a data-driven motion synthesis approach based on a 1D affine image-matching equation. We start by deriving the relevant properties of the exact matching operator, such as the existence of a singular point. Next, we approximate such operator by the Green’s function of a second-order differential equation, finding that it leads to a more compelling motion impression, due to the incorporation of blur. We then proceed to show that, by judicious choice of the matching parameters, the 1D affine Green’s filter allows the simulation of a broad class of effects, such as zoom-in and zoom-out, and of complex nonrigid motions such as that of a pulsating heart.