3D non-rigid image registration with inverse consistency constraint on elastodynamics wave equation

Abstract

In this work, a new inverse consistent non-rigid image registration method is presented. The inter-subject deformations are modeled as elastic waves which tend to propagate over the image domain while recovering the nonlinear discrepancies between the two images. An inverse consistency constraint is introduced into the inertial force that is part of the elastodynamics wave equation which governs the underlying non-rigid deformations. The proposed registration method was analyzed over 3D MR brain scans both quantitatively and qualitatively. Normalized cross-correlation (NCC) was utilized to check the registration accuracy, and it revealed that the performance of proposed registration method with and without inverse consistency constraint is comparable in terms of NCC which increased by $$13\%$$ from its initial value. Moreover, Dice coefficient for segmented structures was computed and compared against state-of-the-art symmetric image normalization method, free form deformation and diffeomorphic demons registration methods. The extent to which the proposed registration scheme enforced inverse consistency was analyzed through inverse consistency error. The results showed that the inverse consistency error reduced by $$99\%$$ with the proposed inverse consistent registration method as compared to the inverse inconsistent counterpart.