An improved exponential filter for fast nonlinear registration of brain magnetic resonance images

A linear elastic convolution filter was derived from the eigenfunctions of the Navier–Stokes differential operator by Bro-Nielsen in order to match images with large deformations. Due to the complexity of constructing the elastic convolution filter, the algorithm’s efficiency reduces rapidly with the increase in the image’s size. In our previous work, a simple two-sided exponential filter with high efficiency was proposed to approximate an elastic filter. However, its poor smoothness may degenerate the performance. In this paper, a new exponential filter was constructed by utilizing a modified nonlinear curve fitting method to approximate the elastic filter. The new filter’s good smoothness makes its performance comparable to an elastic filter. Its simple and separable form makes the algorithm’s speed faster than the elastic filter. Furthermore, our experiments demonstrated that the new filter was suitable for both the elastic and fluid models.