**Abstract.** Non-parametric image registration is still among the most

challenging problems in both computer vision and medical imaging. Here,

one tries to minimize a joint functional that is comprised of a similarity

measure and a regularizer in order to obtain a reasonable displacement

ﬁeld that transforms one image to the other. A common way to solve this

problem is to formulate a necessary condition for an optimizer, which in

turn leads to a system of partial differential equations (PDEs). In gen-

eral, the most time consuming part of the registration task is to ﬁnd a

numerical solution for such a system. In this paper, we present a gener-

alized and efficient numerical scheme for solving such PDEs simply by

applying 1-dimensional recursive ﬁltering to the right hand side of the

system based on the Green’s function of the differential operator that

corresponds to the chosen regularizer. So in the end we come up with a

general linear algorithm. We present the associated Green’s function for

the diffusive and curvature regularizers and show how one may efficiently

implement the whole process by using recursive ﬁlter approximation. Fi-

nally, we demonstrate the capability of the proposed method on realistic

examples.