Symmetric, transitive, geometric deformation and intensity variation invariant nonrigid image registration

Non-rigid registration of medical images is often posed as an algorithmic problem. While algorithms are important, it is equally critical to investigate non-rigid registration axiomatically: what properties should a registration algorithm possess and how do these properties influence the objective functions of the registration algorithms? In this paper, we present four possible properties that a non-rigid registration algorithm may possess: symmetry, transitivity, geometric deformation invariance, and intensity variation invariance. We also investigate the theoretical and practical implications of these properties, and propose a new non-rigid registration algorithm that provably satisfies these properties. We present experimental results of the use of this algorithm on cardiac and brain images to show that it satisfies the above properties with a very small numerical error.