Ivan Diaz

Ivan Diaz, Mario Geiger, Richard Iain McKinley

Convolutional neural networks (CNNs) allow for parameter sharing and translational equivariance by using convolutional kernels in their linear layers. By restricting these kernels to be SO(3)-steerable, CNNs can further improve parameter sharing. These rotationally-equivariant convolutional layers have several advantages over standard convolutional layers, including increased robustness to unseen poses, smaller network size, and improved sample efficiency. Despite this, most segmentation networks used in medical image analysis continue to rely on standard convolutional kernels. In this paper, we present a new family of segmentation networks that use equivariant voxel convolutions based on spherical harmonics. These networks are robust to data poses not seen during training, and do not require rotation-based data augmentation during training. In addition, we demonstrate improved segmentation performance in MRI brain tumor and healthy brain structure segmentation tasks, with enhanced robustness to reduced amounts of training data and improved parameter efficiency. Code to reproduce our results, and to implement the equivariant segmentation networks for other tasks is available at http://github.com/SCAN-NRAD/e3nn_Unet

Ivan Diaz, Florin Scherer, Yanik Berli et al.

In the setting of clinical imaging, differences in between vendors, hospitals and sequences can yield highly inhomogeneous imaging data. In MRI in particular, voxel dimension, slice spacing and acquisition plane can vary substantially. For clinical applications, therefore, algorithms must be trained to handle data with various voxel resolutions. The usual strategy to deal with heterogeneity of resolution is harmonization: resampling imaging data to a common (usually isovoxel) resolution. This can lead to loss of fidelity arising from interpolation artifacts out-of-plane and downsampling in-plane. We present in this paper a network architecture designed to be able to learn directly from spatially heterogeneous data, without resampling: a segmentation network based on the e3nn framework that leverages a spherical harmonic, rather than voxel-grid, parameterization of convolutional kernels, with a fixed physical radius. Networks based on these kernels can be resampled to their input voxel dimensions. We trained and tested our network on a publicly available dataset assembled from three centres, and on an in-house dataset of Multiple Sclerosis cases with a high degree of spatial inhomogeneity. We compared our approach to a standard U-Net with two strategies for handling inhomogeneous data: training directly on the data without resampling, and resampling to a common resolution of 1mm isovoxels. We show that our network is able to learn from various combinations of voxel sizes and outperforms classical U-Nets on 2D testing cases and most 3D testing cases. This shows an ability to generalize well when tested on image resolutions not seen during training. Our code can be found at: http://github.com/SCAN-NRAD/e3nn\_U-Net.

Vinzenz Uhr, Ivan Diaz, Christian Rummel et al.

Cortical thickness measurements from magnetic resonance imaging, an important biomarker in many neurodegenerative and neurological disorders, are derived by many tools from an initial voxel-wise tissue segmentation. White matter (WM) hypointensities in T1-weighted imaging, such as those arising from multiple sclerosis or small vessel disease, are known to affect the output of brain segmentation methods and therefore bias cortical thickness measurements. These effects are well-documented among traditional brain segmentation tools but have not been studied extensively in tools based on deep-learning segmentations, which promise to be more robust. In this paper, we explore the potential of deep learning to enhance the accuracy and efficiency of cortical thickness measurement in the presence of WM lesions, using a high-quality lesion filling algorithm leveraging denoising diffusion networks. A pseudo-3D U-Net architecture trained on the OASIS dataset to generate synthetic healthy tissue, conditioned on binary lesion masks derived from the MSSEG dataset, allows realistic removal of white matter lesions in multiple sclerosis patients. By applying morphometry methods to patient images before and after lesion filling, we analysed robustness of global and regional cortical thickness measurements in the presence of white matter lesions. Methods based on a deep learning-based segmentation of the brain (Fastsurfer, DL+DiReCT, ANTsPyNet) exhibited greater robustness than those using classical segmentation methods (Freesurfer, ANTs).