Accurate Small Deformation Exponential Approximant to Integrate Large Velocity Fields: Application to Image Registration

Sebastiano Ferraris, Marco Lorenzi, Pankaj Daga, Marc Modat, Tom Vercauteren

Abstract: One of the basic components of diffeomorphic image registration algorithms based on velocity fields is the numerical method used to integrate velocity parameters and obtain spatial transformations as displacement fields. When the input velocity field does not depend on the time parameter, the solution is often referred to as the Lie exponential of the velocity field. In this work, we present an integration method for its numerical computation based both on a generalization of the scaling and squaring algorithm and on a class of numerical integrators aimed to solve systems of ordinary differential equations called exponential integrators. This new method led to the introduction of three numerical integrators, and the subsequent validation are performed on synthetic deformations and real medical images.