A general approach to nonrigid registration: decoupled optimization

To a great extent, the success or advanced image-guided medical procedures hinges on non-rigid volume registration. For example, non-rigid registration must be applied in interventional approaches where intra-operative information is used to update high-quality preoperative data; in follow-up studies in order to assess time-evolution of development; aging, pathology or treatment; and in many other applications including inter-subject variability and population-based atlas construction. In this paper we examine several computational schemes that warp one volumetric dataset onto another. We also explore the inevitable trade-off between the computational load and the incorporation of sophisticated similarity measures necessary for multimodal volumes. Estimated deformation fields are based on the variational formulation of partial derivative equations (PDEs), which includes a similarity and a regularization term. We compare numerical solutions to this problem using the Euler-Lagrange equations (EL), the finite element discretization (FE), and decoupled optimization over the possible deformations (DO).