Membrane Nonrigid Image Registration

We introduce a novel nonrigid 2D image registration method that establishes dense and accurate correspondences across images without the need of any manual intervention. Our key insight is to model the image as a membrane, i.e., a thin 3D surface, and to constrain its deformation based on its geometric properties. To do so, we derive a novel Bayesian formulation. We impose priors on the moving membrane which act to preserve its shape as it deforms to meet the target. We derive these as curvature weighted first and second order derivatives that correspond to the changes in stretching and bending potential energies of the membrane and estimate the registration as the maximum a posteriori. Experimental results on real data demonstrate the effectiveness of our method, in particular, its robustness to local minima and its ability to establish accurate correspondences across the entire image. The results clearly show that our method overcomes the shortcomings of previous intensity-based and feature-based approaches with conventional uniform smoothing or diffeomorphic constraints that suffer from large errors in textureless regions and in areas in-between specified features.