Large deformation registration of contrast-enhanced images with volume-preserving constraint

We propose a registration method for the alignment of contrast-enhanced CT liver images. It consists of a fluid-based registration algorithm designed to incorporate a volume-preserving constraint. More specifically our objective is to recover an accurate non-rigid transformation in a perfusion study in presence of contrast-enhanced structures which preserves the incompressibility of liver tissues. This transformation is obtained by integrating a smooth divergence-free vector field derived from the gradient of a statistical similarity measure. This gradient is regularized with a fast recursive low-pass filter and is projected onto the space of divergence-free vector fields using a multigrid solver. Both 2D and 3D versions of the algorithm have been implemented. Simulations and experiments show that our approach improves the registration capture range, enforces the incompressibility constraint with a good level of accuracy, and is computationally efficient. On perfusion. studies, this method prevents the shrinkage of contrast-enhanced regions typically observed with standard fluid methods.