Symmetric Interleaved Geodesic Shooting in Diffeomorphisms - Niethammer, Marc (Information Processing in Medical Imaging, 2017)
Many nonlinear registration algorithms are subject to an asymmetry with respect to the order of image inputs. Often, one image is considered the moving image while the other is fixed. Hence, the moving image is subject to additional interpolation relative to the fixed image. Further, the fixed image is in a way represented by the deformed moving image; any noise or artifacts present in the moving image are thus retained in this representation. This asymmetry has even been shown to result in bias in various forms of registration derived measurements. These problems are particularly evident in the geodesic shooting in diffeomorphisms context, where a continuous time geodesic model of image deformation is on the orbit of the moving image. Were the images input in the opposite order, the model would lie on the orbit of the other image. This paper presents a symmetrical formulation of the geodesic shooting in diffeomorphisms model with an accompanying algorithm that treats the intensity and gradient information in both images in nearly an equal way. After formulating the algorithm, we validate in a set of longitudinal 3D brain MRI pairs that the transformations the symmetrical algorithm produces are indeed significantly more robust to switching the order of image inputs than traditional geodesic shooting.