Random walker image registration with inverse consistency

One important property of a registration solution is inverse consistency. While often overlooked, this property is critical in many medical applications, including radiation-therapy treatment planning and unbiased atlas-construction. In this paper, we propose a novel extension to the graph-based random walker image registration (RWIR) algorithm to ensure its inverse consistency. In contrast to many existing inverse-consistent algorithms, where two bi-directional transformations are independently sought and subsequently averaged, we calculate both transformations simultaneously by performing a constrained graph labeling in a common domain onto which both images are mapped, and employ a set of coupled labels so that both transformations are computed within a single optimization step. As our results on synthetic and real problems involving cardiac, thigh and brain images demonstrate, our method not only improved inverse consistency of RWIR, but also statistically significantly improved its accuracy. Comparison to another state-of-the-art symmetric algorithm on various datasets also gave highly encouraging results.