Diffeomorphic demons: Efficient non-parametric image registration

Abstract

We propose an efficient non-parametric diffeomorphic image registration algorithm based on Thirion's demons algorithm. In the first part of this paper, we show that Thirion's demons algorithm can be seen as an optimization procedure on the entire space of displacement fields. We provide strong theoretical roots to the different variants of Thirion's demons algorithm. This analysis predicts a theoretical advantage for the symmetric forces variant of the demons algorithm. We show on controlled experiments that this advantage is confirmed in practice and yields a faster convergence. In the second part of this paper, we adapt the optimization procedure underlying the demons algorithm to a space of diffeomorphic transformations. In contrast to many diffeomorphic registration algorithms, our solution is computationally efficient since in practice it only replaces an addition of displacement fields by a few compositions. Our experiments show that in addition to being diffeomorphic, our algorithm provides results that are similar to the ones from the demons algorithm but with transformations that are much smoother and closer to the gold standard, available in controlled experiments, in terms of Jacobians.

A measure to evaluate deformable registration fields in clinical settings

“…5a) and (b), with an arrow marking the original tumor location, visible in the pretreatment dataset, but significantly reduced on the aftertreatment scan. Three solutions spanning the trade‐off between smoothness of the deformation field and ability to model small changes are compared for this task: a diffeomorphic demons (44) algorithm with the smoothing displacement field option turned off (left column), the same algorithm with the same option turned on (middle panel), and a B‐Spline algorithm (15) (right panel) using just seven grid nodes per dimension.…”

Evaluation of the ΔV 4D CT ventilation calculation method usingin vivoxenon CT ventilation data and comparison to other methods

“…DM and diffeomorphic demons (DD) (29) DIR methods were evaluated using the 4D CT data of the sheep with manually delineated landmarks in the end‐expiration and end‐inspiration phases in this study. The deformation transformations were used to map the landmarks from the expiration phase to the inspiration phase.…”

Radiographic reconstruction of lower-extremity bone fragments: a first trial

“…Computed tomography (CT) scans of intact tibial and femoral bones were semi-automatically segmented using Amira software (FEI, Hillsboro, USA) and correspondences between the models were determined by non-rigid mesh registration [18]. Thereby, a reference volume was selected and the remaining floating volumes were non-rigidly registered using diffeomorphic demons algorithm [19]. For each resulting deformation field, the reference surface model was accordingly warped to recover the shape of the floating instances.…”

“…To avoid subjective interactive landmark picking on the reconstructed models, these landmarks were defined by non-rigid registration of the ground truth models: Firstly, both cropped surface models are transformed to binary volumes using Amira software. Subsequently, diffeomorphic demons algorithm [19] is used to non-rigidly deform the ground truth volume with respect to the reconstructed volume. The computed displacement vector field is then applied to the ground truth landmarks, which have been updated by the rigid transformation f rag T GT (s. step (6) in Fig.…”