A fast inverse consistent deformable image registration method based on symmetric optical flow computation

Deformable image registration is widely used in various radiation therapy applications including 4D-CT and treatment planning adaptation. In this work, a simple and efficient inverse consistency deformable registration method is proposed with aims of higher registration accuracy and faster convergence speed. Instead of registering image I to the second image J, two images are symmetrically deformed toward one another in multiple passes, until both deformed images are registered. In every pass, a delta motion field is computed by minimizing a symmetric optical flow system cost function using the modified optical flow algorithms. The images are then further deformed with the delta motion field in positive and negative directions, respectively, and then used for the next pass. The magnitude of the delta motion field is forced to be less than 0.4 voxel for every pass in order to guarantee the smoothness and invertibility of the two overall motion fields which are accumulating the delta motion fields in positive and negative directions, respectively. The final motion fields to register the original images I and J, in either direction, are calculated by inverting one overall motion field and composing the inversion result with the other overall motion field. The final motion fields are inversely consistent and this is ensured by the symmetric way that registration is carried out. Results suggest that the method is able to improve the overall accuracy by 30% or more, reduce the inverse consistency error, and increase the convergence rate. The computation speed may slightly decrease, or increase in some cases because the new method converges faster. Comparing to previously published inverse consistency algorithms, the proposed method is simpler in theory, easier to implement, and faster.