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Filter-decomposition-based group equivariant convolutional neural networks show promising stability and data efficiency for 3D image feature extraction. However, the existing filter-decomposition-based 3D group equivariant neural networks rely on parameter-sharing designs and are mostly limited to rotation transformation groups, where the chosen spherical harmonic filter bases consider only angular orthogonality. These limitations hamper its application to deep neural network architectures for medical image segmentation. To address these issues, this paper describes a non-parameter-sharing affine group equivariant neural network for 3D medical image segmentation based on an adaptive aggregation of Monte Carlo augmented spherical Fourier Bessel filter bases. The efficiency and flexibility of the adopted non-parameter-sharing strategy enable for the first time an efficient implementation of 3D affine group equivariant convolutional neural networks for volumetric data. The introduced spherical Bessel Fourier filter basis combines both angular and radial orthogonality for better feature extraction. The 3D image segmentation experiments on two abdominal medical image sets, BTCV and the NIH Pancreas datasets, show that the proposed methods excel the state-of-the-art 3D neural networks with high training stability and data efficiency. The code will be available at https://github.com/ZhaoWenzhao/WMCSFB.

Group-equivariant convolutional neural networks (G-CNN) heavily rely on parameter sharing to increase CNN's data efficiency and performance. However, the parameter-sharing strategy greatly increases the computational burden for each added parameter, which hampers its application to deep neural network models. In this paper, we address these problems by proposing a non-parameter-sharing approach for group equivariant neural networks. The proposed methods adaptively aggregate a diverse range of filters by a weighted sum of stochastically augmented decomposed filters. We give theoretical proof about how the continuous group convolution can be approximated by our methods. Our method applies to both continuous and discrete groups, where the augmentation is implemented using Monte Carlo sampling and bootstrap resampling, respectively. We demonstrate that our methods serve as an efficient extension of standard CNN. Experiments on group equivariance tests show how our methods can achieve superior performance to parameter-sharing group equivariant networks. Experiments on image classification and image denoising tasks show that in certain scenarios, with a suitable set of filter bases, our method helps improve the performance of standard CNNs and build efficient lightweight image denoising networks. The code will be available at https://github.com/ZhaoWenzhao/MCG_CNN.

Sparsity of annotated data is a major limitation in medical image processing tasks such as registration. Registered multimodal image data are essential for the diagnosis of medical conditions and the success of interventional medical procedures. To overcome the shortage of data, we present a method that allows the generation of annotated multimodal 4D datasets. We use a CycleGAN network architecture to generate multimodal synthetic data from the 4D extended cardiac-torso (XCAT) phantom and real patient data. Organ masks are provided by the XCAT phantom, therefore the generated dataset can serve as ground truth for image segmentation and registration. Realistic simulation of respiration and heartbeat is possible within the XCAT framework. To underline the usability as a registration ground truth, a proof of principle registration is performed. Compared to real patient data, the synthetic data showed good agreement regarding the image voxel intensity distribution and the noise characteristics. The generated T1-weighted magnetic resonance imaging (MRI), computed tomography (CT), and cone beam CT (CBCT) images are inherently co-registered. Thus, the synthetic dataset allowed us to optimize registration parameters of a multimodal non-rigid registration, utilizing liver organ masks for evaluation. Our proposed framework provides not only annotated but also multimodal synthetic data which can serve as a ground truth for various tasks in medical imaging processing. We demonstrated the applicability of synthetic data for the development of multimodal medical image registration algorithms., Comment: 12 pages, 5 figures. This work has been published in the International Journal of Computer Assisted Radiology and Surgery volume