Transitive nonrigid image registration: application to cardiac MR image sequences

Abstract

A method for constructing transitive nonrigid image registration algorithms is presented. Although transitivity is a desirable property of nonrigid image registration algorithms, the algorithms available in the literature are not transitive. The proposed approach can be applied to any nonrigid image registration algorithm and it generalizes to any-dimensional case. The transitivity property is achieved exactly up to the error of numerical implementation, which can be arbitrary small. To the best of our knowledge, this is the first time that transitivity of image registration algorithms has been achieved. An existing 2D nonrigid image registration algorithm was made transitive using the presented method. The algorithm was tested on two sequences of cardiac short axis MR images. The maximal transitivity error (defined in the paper) for several triples of images randomly selected from the two sequences of cardiac images was on the order of a millionth of a pixel.