Deformable Registration with Discontinuity Preservation using Multi-Scale MRF

Deformable (2D or 3D) medical image registration is a challenging problem. Existing approaches assume that the underlying deformation is smooth. This smoothness assumption allows for solving the deformable registration at a coarse resolution and interpolate for finer resolutions. However, sliding of organs and breathing motion, exhibit discontinuities. We propose a discrete optimization approach to preserve these discontinuities. Solving continuous deformations using discrete optimization requires a fine distribution of the discrete labels. Coupled with the typical size of medical image datasets, his poses challenges to compute solutions efficiently. In this paper we present a practical, multi-scale formulation. We describe how discontinuities can e preserved, and how the optimization problem is solved. Results on synthetic 2D, and real 3D data show that we can well approximate the smoothness of continuous optimization, while accurately maintaining discontinuities.