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Background:  Commonly used methods of assessing the accuracy of deformable image registration (DIR) rely on image segmentation or landmark selection. These methods are very labor intensive and thus limited to relatively small number of image pairs. The direct voxel-by-voxel comparison can be automated to examine fluctuations in DIR quality on a long series of image pairs.   Methods:  A voxel-by-voxel comparison of three DIR algorithms applied to lung patients is presented. Registrations are compared by comparing volume histograms formed both with individual DIR maps and with a voxel-by-voxel subtraction of the two maps. When two DIR maps agree one concludes that both maps are interchangeable in treatment planning applications, though one cannot conclude that either one agrees with the ground truth. If two DIR maps significantly disagree one concludes that at least one of the maps deviates from the ground truth. We use the method to compare 3 DIR algorithms applied to peak inhale-peak exhale registrations of 4DFBCT data obtained from 13 patients.   Results:  All three algorithms appear to be nearly equivalent when compared using DICE similarity coefficients. A comparison based on Jacobian volume histograms shows that all three algorithms measure changes in total volume of the lungs with reasonable accuracy, but show large differences in the variance of Jacobian distribution on contoured structures. Analysis of voxel-by-voxel subtraction of DIR maps shows differences between algorithms that exceed a centimeter for some registrations.   Conclusion:  Deformation maps produced by DIR algorithms must be treated as mathematical approximations of physical tissue deformation that are not self-consistent and may thus be useful only in applications for which they have been specifically validated. The three algorithms tested in this work perform fairly robustly for the task of contour propagation, but produce potentially unreliable results for the task of DVH accumulation or measurement of local volume change. Performance of DIR algorithms varies significantly from one image pair to the next hence validation efforts, which are exhaustive but performed on a small number of image pairs may not reflect the performance of the same algorithm in practical clinical situations. Such efforts should be supplemented by validation based on a longer series of images of clinical quality.

A Voxel-by-Voxel Comparison of Deformable Vector Fields Obtained by Three Deformable Image Registration Algorithms Applied to 4DCT Lung Studies