Collision Constraints and Diffeomorphisms: Dealing With Physics in Deformable Image Registration

Discontinuous displacements pose a substantial challenge to image registration algorithms, which generally assume smooth deformations. Two prominent cases occur in 4DCT lung scans. The first instance exists at the lung-thorax-boundary, where due to high elasticities and expansion properties, lungs exhibit higher displacements than the surrounding thoracic cavity, leading to sliding motions along their interface. Discontinuous motion is facilitated through a piecewise registration framework, in which inter-domain boundary interactions are constrained via collision detection, and intra-domain deformation smoothness is governed by the Large Deformation Diffeomorphic Metric Mapping (LDDMM) model. The second case with discontinuous displacements is found between lung lobes along the separating lung fissures. A fissure reconstruction algorithm for sparse segmentation is presented, improving geometric lung representation. Utilizing a refined Free-Form Deformation model for lobe-on-lobe registration that permits lobar sliding and prevents self-intersection, this approach examines discontinuities around the pulmonary fissures. Both cases are evaluated on synthetic and medical data, with boundary inconsistency results and average registration metrics on the DIRLAB dataset comparable to other approaches addressing sliding motion.