A total variation based nonrigid image registration by combining parametric and non-parametric transformation models

To overcome the conflict between the global robustness and the local accuracy of dense nonrigid image registration, we propose a union registration approach by combining parametric and non-parametric transformation models. On one hand, to guarantee the robustness, we constrain the displacement field φ using a mapping difference metric between the B-spline parametric space Ψ and the non-parametric transformation space Φ. On the other hand, to correct the densely and highly localized geometrical distortions, we introduce a total variation (TV) regularization term for the displacement field φ. Accounting for the effect of spatially varying intensity distortions, the residual complexity (RC) is used as the similarity metric. Moreover, to solve the proposed union nonrigid registration, which is a composite convex optimization problem by the smooth ℓ₂ term and the non-smooth ℓ₁ term (TV), we design a two-stage algorithm using split Bregman iteration. Experiments with both synthetic and real images from different domains illustrate that this approach can capture the local details of transformation accurately and effectively while being robust to the spatially varying intensity distortions.