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Previous methods to estimate the inherent accuracy of deformable image registration (DIR) have typically been performed relative to a known ground truth, such as tracking of anatomic landmarks or known deformations in a physical or virtual phantom. In this study, we propose a new approach to estimate the spatial geometric uncertainty of DIR using statistical sampling techniques that can be applied to the resulting deformation vector fields (DVFs) for a given registration. The proposed DIR performance metric, the distance discordance metric (DDM), is based on the variability in the distance between corresponding voxels from different images, which are co-registered to the same voxel at location (X) in an arbitrarily chosen 'reference' image. The DDM value, at location (X) in the reference image, represents the mean dispersion between voxels, when these images are registered to other images in the image set. The method requires at least four registered images to estimate the uncertainty of the DIRs, both for inter- and intra-patient DIR. To validate the proposed method, we generated an image set by deforming a software phantom with known DVFs. The registration error was computed at each voxel in the 'reference' phantom and then compared to DDM, inverse consistency error (ICE), and transitivity error (TE) over the entire phantom. The DDM showed a higher Pearson correlation (Rp) with the actual error (Rp ranged from 0.6 to 0.9) in comparison with ICE and TE (Rp ranged from 0.2 to 0.8). In the resulting spatial DDM map, regions with distinct intensity gradients had a lower discordance and therefore, less variability relative to regions with uniform intensity. Subsequently, we applied DDM for intra-patient DIR in an image set of ten longitudinal computed tomography (CT) scans of one prostate cancer patient and for inter-patient DIR in an image set of ten planning CT scans of different head and neck cancer patients. For both intra- and inter-patient DIR, the spatial DDM map showed large variation over the volume of interest (the pelvis for the prostate patient and the head for the head and neck patients). The highest discordance was observed in the soft tissues, such as the brain, bladder, and rectum, due to higher variability in the registration. The smallest DDM values were observed in the bony structures in the pelvis and the base of the skull. The proposed metric, DDM, provides a quantitative tool to evaluate the performance of DIR when a set of images is available. Therefore, DDM can be used to estimate and visualize the uncertainty of intra- and/or inter-patient DIR based on the variability of the registration rather than the absolute registration error.

The distance discordance metric—a novel approach to quantifying spatial uncertainties in intra- and inter-patient deformable image registration