Symmetric non-rigid image registration via an adaptive quasi-volume-preserving constraint

The standard implementation of non-rigid image registration is asymmetric, even though symmetry might be an intrinsic attribute of the particular application, e.g., pairwise image alignment. Current approaches to restore symmetry to non-rigid registration, although successful in achieving inverse-consistency, generally alter the objective function through implicit inclusion of a nonuniform weight in the integral that is computed on the native space of an input image. This inhomogeneous integral measure, which varies through the course of the registration, results in regional biases by allowing image regions to contribute differently to the objective function. In this work, instead of symmetrizing the objective function, we address the root of the problem: the nonuniformity of the integral in both the asymmetric and the symmetrized implementations. We introduce a new quasi-volume-preserving constraint that keeps the forward and backward objective functions arbitrarily close to each other - hence the registration symmetry - without compromising the uniformity of the integrals. We show the advantages of our method through experiments on synthetic images and real X-ray and MRI data.