FAST FLUID REGISTRATION WITH DIRICHLET BOUNDARY CONDITIONS: A TRANSFORM-BASED APPROACH

Abstract

Fluid registration is an example of a nonrigid image registration algorithm that uses a deformation field to define the transformation between two images. The velocity of the deformation field is governed by the Navier-Lame equations, which can be discretized and solved numerically via fixed-point iteration. The fixed-point iteration generates a succession of linear PDE systems, which can be solved quickly via discrete Fourier transform (DFT) techniques, as shown in the prior art. The major drawback of this approach is that it is only applicable when the boundary conditions of the velocity field are assumed to be periodic. This paper shows that by considering the adjoint of the Navier-Lame operator, the succession of linear PDE systems can be solved quickly via discrete sine transform (DST) techniques, generating velocity fields that satisfy Dirichlet boundary conditions (where the velocities are zero on the boundaries)