Learning a Model-Driven Variational Network for Deformable Image Registration

TL;DR

VR-Net is proposed, a novel cascaded variational network for unsupervised deformable image registration that outperforms state-of-the-art deep learning methods on registration accuracy, while maintains the fast inference speed of deep learning and the data-efficiency of variational model.

Abstract

Data-driven deep learning approaches to image registration can be less accurate than conventional iterative approaches, especially when training data is limited. To address this whilst retaining the fast inference speed of deep learning, we propose VR-Net, a novel cascaded variational network for unsupervised deformable image registration. Using the variable splitting optimization scheme, we first convert the image registration problem, established in a generic variational framework, into two sub-problems, one with a point-wise, closed-form solution while the other one is a denoising problem. We then propose two neural layers (i.e. warping layer and intensity consistency layer) to model the analytical solution and a residual U-Net to formulate the denoising problem (i.e. generalized denoising layer). Finally, we cascade the warping layer, intensity consistency layer, and generalized denoising layer to form the VR-Net. Extensive experiments on three (two 2D and one 3D) cardiac magnetic resonance imaging datasets show that VR-Net outperforms state-of-the-art deep learning methods on registration accuracy, while maintains the fast inference speed of deep learning and the data-efficiency of variational model.

Figures (6)

• Figure 1: Overall architecture of the proposed VR-Net, where WL, ICL, and GDL denote the warping layer, intensity consistency layer, and generalized denoising layer, respectively. These layers are designed according to the minimization of a generic variational model for image registration. The number of cascades is controlled by $N_{warp} \times$$N_{iter}$, which mimics the iterative process for the minimization.
• Figure 2: Detailed structure of each layer in VR-Net. WL, ICL, and GDL stand for warping layer, intensity consistency layer, and generalized denoising layer, respectively.
• Figure 3: (a): Dice scores of R-$\rm{L}_2$-6$\times$1 using the two parameterizations in Sec. \ref{['sec:para']} on the UK Biobank. (b) Impact of using different $\alpha$ in terms of Hausdorff distance on the three datasets. (c): Comparing VR-Net and RC-Net Zhao_2019_ICCV using a different number of cascades on the ACDC dataset.
• Figure 4: Comparing visual results obtained by different registration methods on the ACDC and 3D CMR datasets. The 1st column includes ED image, ED mask, ES image, ES mask, and absolute difference between ES image and the ED image. Excluding the 1st column, for (a) ACDC, from left to right: FFD, TV-$\rm{L}_1$, Siamese Net, VoxelMorph, RC-Net, and VR-Net results, respectively, for (b) 3D CMR, from left to right: Demons, ANTs SyN, FFD, VoxelMorph, RC-Net, and VR-Net results, respectively. From top to bottom: warped ES images, warped ES masks (with ground truth mask shown in green contours), estimated deformations (shown in HSV and grid), the Jacobian map, and absolute differences between warped ES images and the ground truth ED image, respectively.
• Figure 5: Boxplot illustration of Dice (top row) and HD (bottom row) results obtained by different registration methods on the UK Biobank (left), ACDC (middle), and the 3D CMR (right) datasets. The proposed VR-Net outperforms all compared methods on the UK Biobank and ACDC datasets. Although the Dice of VR-Net is lower than that of FFD on the 3D CMR dataset, it achieves the best HD score.