Accelerated nonrigid intensity-based image registration using importance sampling

Abstract

Nonrigid image registration methods using intensity-based similarity metrics are becoming increasingly common tools to estimate many types of deformations. Nonrigid warps can be very flexible with a large number of parameters and gradient optimization schemes are widely used to estimate them. However, for large datasets, the computation of the gradient of the similarity metric with respect to these many parameters becomes very time consuming. Using a small random subset of image voxels to approximate the gradient can reduce computation time. This work focuses on the use of importance sampling to reduce the variance of this gradient approximation. The proposed importance sampling framework is based on an edge-dependent adaptive sampling distribution designed for use with intensity-based registration algorithms. We compare the performance of registration based on stochastic approximations with and without importance sampling to that using deterministic gradient descent. Empirical results, on simulated magnetic resonance brain data and real computed tomography inhale-exhale lung data from eight subjects, show that a combination of stochastic approximation methods and importance sampling accelerates the registration process while preserving accuracy.

Fig. 1

Comparison of samples obtained using the sampling distribution given by (9) versus samples obtained by Uniform sampling. Images were created when the algorithm was not near registration.

Fig. 2

Comparison of the performance of IS-SA (red/notched) versus US-SA (blue/plain) with variations in step-sizes. Figures show RMS error statistics for 10 nonrigid multimodality registration runs at six step-sizes and four (0.25, 0.5, 1 and 2%) sample-sizes. The line at the center of each boxplot shows the median RMS error value and top and bottom edges are the 75 and 25 percent quantile RMS errors. ‘Outliers’ are shown by (o) for IS and by (+) for US. IS does significantly better than US at all four sample-sizes. Specifically, IS results in lower variance values and shows better tolerance to variations in step-sizes. Trends in the four plots indicate that the performance of both sampling strategies will become comparable with an increase in sample-size.

Fig. 3

Comparison of the speed and accuracy of IS-SA (red/notched) and US-SA (blue/plain) for registration of CT Lung data. The optimal step-size parameter a₀ was empirically chosen to consistently produce warp estimates closest to the pseudo ground-truth warp in an RMSE sense. Fig. 3(a) shows that a₀ = 1 was the best value for both methods. The line at the center of each box-plot is the median RMS error, while top and bottom edges are 75 and 25 percent quantiles. Outliers are represented by (o) for IS-SA and (+) for US-SA. Fig. 3(b) shows how the speed and accuracy of the best IS-SA and US-SA schemes (a₀ = 1 and sample-size = 1%) compare with those using GD (sample-size = 100%) on average. Dotted lines are ±1 standard deviation plots.

Fig. 4

Comparison of the accuracy and variation in trained IS-SA (red/notched) versus US-SA (blue/plain) registration using expert identified feature points for CT inhale-exhale lung data. The line at the center of each box-plot is the median error metric, while top and bottom edges are 75 and 25 percent quantiles. Outliers are represented by (o) for IS-SA and (+) for US-SA. Dataset 5 was used in the training step.