We present a novel computational approach to fast and memory-efficient deformable image registration. In the variational registration model, the computation of the objective function derivatives is the computationally most expensive operation, both in terms of runtime and memory requirements. In order to target this bottleneck, we analyze the matrix structure of gradient and Hessian computations for the case of the normalized gradient fields distance measure and curvature regularization. Based on this analysis, we derive equivalent matrix-free closed-form expressions for derivative computations, eliminating the need for storing intermediate results and the costs of sparse matrix arithmetic. This has further benefits: (1) matrix computations can be fully parallelized, (2) memory complexity for derivative computation is reduced from linear to constant, and (3) overall computation times are substantially reduced.In comparison with an optimized matrix-based reference implementation, the CPU implementation achieves speedup factors between 3.1 and 9.7, and we are able to handle substantially higher resolutions. Using a GPU implementation, we achieve an additional speedup factor of up to 9.2.Furthermore, we evaluated the approach on real-world medical datasets. On ten publicly available lung CT images from the DIR-Lab 4DCT dataset, we achieve the best mean landmark error of 0.93 mm compared to other submissions on the DIR-Lab website, with an average runtime of only 9.23 s. Complete non-rigid registration of full-size 3D thorax-abdomen CT volumes from oncological follow-up is achieved in 12.6 s. The experimental results show that the proposed matrix-free algorithm enables the use of variational registration models also in applications which were previously impractical due to memory or runtime restrictions.
BackgroundDeformable image registration (DIR) is a key component in many radiotherapy applications. However, often resulting deformations are not satisfying, since varying deformation properties of different anatomical regions are not considered. To improve the plausibility of DIR in adaptive radiotherapy in the male pelvic area, this work integrates a local rigidity deformation model into a DIR algorithm.MethodsA DIR framework is extended by constraints, enforcing locally rigid deformation behavior for arbitrary delineated structures. The approach restricts those structures to rigid deformations, while surrounding tissue is still allowed to deform elastically. The algorithm is tested on ten CT/CBCT male pelvis datasets with active rigidity constraints on bones and prostate and compared to the Varian SmartAdapt deformable registration (VSA) on delineations of bladder, prostate and bones.ResultsThe approach with no rigid structures (REG0) obtains an average dice similarity coefficient (DSC) of 0.87 ± 0.06 and a Hausdorff-Distance (HD) of 8.74 ± 5.95 mm. The new approach with rigid bones (REG1) yields a DSC of 0.87 ± 0.07, HD 8.91 ± 5.89 mm. Rigid deformation of bones and prostate (REG2) obtains 0.87 ± 0.06, HD 8.73 ± 6.01 mm, while VSA yields a DSC of 0.86 ± 0.07, HD 10.22 ± 6.62 mm. No deformation grid foldings are observed for REG0 and REG1 in 7 of 10 cases; for REG2 in 8 of 10 cases, with no grid foldings in prostate, an average of 0.08 % in bladder (REG2: no foldings) and 0.01 % inside the body contour. VSA exhibits grid foldings in each case, with an average percentage of 1.81 % for prostate, 1.74 % for bladder and 0.12 % for the body contour. While REG1 and REG2 keep bones rigid, elastic bone deformations are observed with REG0 and VSA. An average runtime of 26.2 s was achieved with REG1; 31.1 s with REG2, compared to 10.5 s with REG0 and 10.7 s with VMS.ConclusionsWith accuracy in the range of VSA, the new approach with constraints delivers physically more plausible deformations in the pelvic area with guaranteed rigidity of arbitrary structures. Although the algorithm uses an advanced deformation model, clinically feasible runtimes are achieved.Electronic supplementary materialThe online version of this article (doi:10.1186/s13014-016-0697-4) contains supplementary material, which is available to authorized users.
In this work a calibration method which is easy to use and is capable of calibrating a combination of a magnetometer and an accelerometer is described. The calibration method accounts for hard and soft iron effects created by the platform, sensor errors like biases, scale factors and non-orthogonalities as well as the relative orientation between the magnetometer and the accelerometer. The algorithm is based on a least squares problem, which is solved using a singular value decomposition. During the calibration process the spatial orientation of the platform is not needed. Therefore no additional hardware is required. The functionality and accuracy of the algorithm is shown using simulated sensor readings
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