PDE-Based Non-rigid Registration of Breast Surfaces

Abstract

Recent advances in breast cancer imaging have generated new ways to characterize the disease, and many of these novel analysis techniques require the registration of breast surfaces during a non-rigid deformation. In this paper, a semi-automated method to register breast surfaces before and after a non-rigid deformation is presented. This method involves solving the Laplace or diffusion equations over the undeformed and deformed breast surfaces, yielding potential fields and isocontours that are used to establish surface correspondence. The proposed partial differential equation (PDE)-based registration method is compared to a thin-plate spline (TPS) interpolation of surface displacements tracked by fiducial markers. These registration methods are tested on a realistic finite element simulation of a breast compression, a breast phantom, and on a clinical data set. The results indicate that the TPS registration technique is the most accurate; however, if fiducial information is not available, the PDE-based registration methods may be viable alternatives. The PDE-based and TPS registration methods have the potential to be used by analyses requiring the non-rigid registration of breast surfaces before and after compression, and both have been used in Modality-Independent Elastography (MIE) to determine the boundary conditions needed for elasticity imaging.