  Automatic tumor or lesion segmentation is a crucial step in medical image
analysis for computer-aided diagnosis. Although the existing methods based on
Convolutional Neural Networks (CNNs) have achieved the state-of-the-art
performance, many challenges still remain in medical tumor segmentation. This
is because, although the human visual system can detect symmetries in 2D images
effectively, regular CNNs can only exploit translation invariance, overlooking
further inherent symmetries existing in medical images such as rotations and
reflections. To solve this problem, we propose a novel group equivariant
segmentation framework by encoding those inherent symmetries for learning more
precise representations. First, kernel-based equivariant operations are devised
on each orientation, which allows it to effectively address the gaps of
learning symmetries in existing approaches. Then, to keep segmentation networks
globally equivariant, we design distinctive group layers with layer-wise
symmetry constraints. Finally, based on our novel framework, extensive
experiments conducted on real-world clinical data demonstrate that a Group
Equivariant Res-UNet (named GER-UNet) outperforms its regular CNN-based
counterpart and the state-of-the-art segmentation methods in the tasks of
hepatic tumor segmentation, COVID-19 lung infection segmentation and retinal
vessel detection. More importantly, the newly built GER-UNet also shows
potential in reducing the sample complexity and the redundancy of filters,
upgrading current segmentation CNNs and delineating organs on other medical
imaging modalities.
