A TV-l ₁ based nonrigid image registration by coupling parametric and non-parametric transformation

To overcome the conflict between the global robustness and the local accuracy in the dense nonrigid image registration, we propose a union registration approach using a l₁-norm based term to couple the parametric transformation and the non-parametric transformation. On one hand, we take the parametric deformation field as a constraint for the non-parametric registration, which is a strong constraint that guarantees the robustness of the non-parametric registration result. On the other hand, the non-parametric deformation field is taken as a force to improve the accuracy of the parametric registration. Then, an alternating optimization scheme is carried out to improve the accuracy of both the parametric registration and the non-parametric registration. Moreover, accounting for the effect of spatially-varying intensity distortions and the sparse gradient prior of the deformation field, we adopt the residual complexity (RC) as the similarity metric and the total variation (TV) as the regularization. Because of the TV-l₁-l₂ composite property of the objective function in our union image registration, we resort to the split Bregman iteration for the complex problem solving. Experiments with both synthetic and real images in different domains illustrate that this approach outperforms the separately performed parametric registration or non-parametric registration.