A Parallel-friendly Normalised Mutual Information Gradient for Free-Form Registration

Non-rigid registration techniques are commonly used in medical image analysis. However these techniques are often time consuming. Graphics Processing Unit (GPU) execution appears to be a good way to decrease computation time significantly. However for an efficient implementation on GPU, an algorithm must be data parallel. In this paper we compare the analytical calculation of the gradient of Normalised Mutual Information with an approximation better suited to parallel implementation. Both gradient approaches have been implemented using a Free-Form Deformation framework based on cubic B-Splines and including a smoothness constraint. We applied this technique to recover realistic deformation fields generated from 65 3D-T1 images. The recovered fields using both gradients and the ground truth were compared. We demonstrated that the approximated gradient performed similarly to the analytical gradient but with a greatly reduced computation time when both approaches are implemented on the CPU. The implementation of the approximated gradient on the GPU leads to a computation time of 3 to 4 minutes when registering 190 x 200 x 124 voxel images with a grid including 57 x 61 x 61 control points.