Collision Constraints & 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. While ensuring discontinuous movement with a piecewise registration approach, inter-domain boundary interactions as well as intra-domain deformation smoothness need to be regulated. The LDDMM registration method coupled with collision detection enforces the required constraints and is evaluated on synthetic and medical data. 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 lung-by-lung registration permitting lobar sliding and preventing self-intersection, discontinuities around the fissures are examined in a medical setting.