Landmark Constrained Non-parametric Image Registration with Isotropic Tolerances

The incorporation of additional user knowledge into a nonrigid registration process is a promising topic in modern registration schemes. The combination of intensity based registration and some interactively chosen landmark pairs is a major approach in this direction. There exist different possibilities to incorporate landmark pairs into a variational non-parametric registration framework. As the interactive localization of point landmarks is always prone to errors, a demand for precise landmark matching is bound to fail. Here, the treatment of the distances of corresponding landmarks as penalties within a constrained optimization problem offers the possibility to control the quality of the matching of each landmark pair individually. More precisely, we introduce inequality constraints, which allow for a sphere-like tolerance around each landmark. We illustrate the performance of this new approach for artificial 2D images as well as for the challenging registration of preoperative CT data to intra-operative 3D ultrasound data of the liver.