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 

eld 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.