Topological changes like sliding motion, sources and sinks are a significant challenge in image registration. This work proposes the use of the alternating direction method of multipliers as a general framework for constraining the registration of separate objects with individual deformation fields from overlapping in image registration. This constraint is enforced by introducing a collision detection algorithm from the field of computer graphics which results in a robust divide and conquer optimization strategy using Free-Form Deformations. A series of experiments demonstrate that the proposed framework performs superior with regards to the combination of intersection prevention and image registration including synthetic examples containing complex displacement patterns. The results show compliance with the non-intersection constraints while simultaneously preventing a decrease in registration accuracy. Furthermore, the application of the proposed algorithm to the DIR-Lab data set demonstrates that the framework generalizes to real data by validating it on a lung registration problem.