A geometric approach to robust medical image segmentation.

Robustness of deep learning segmentation models is crucial for their safe incorporation into clinical practice. However, these models can falter when faced with distributional changes. This challenge is evident in magnetic resonance imaging (MRI) scans due to the diverse acquisition protocols across various domains, leading to differences in image characteristics such as textural appearances. We posit that the restricted anatomical differences between subjects could be harnessed to refine the latent space into a set of shape components. The learned set then aims to encompass the relevant anatomical shape variation found within the patient population. We explore this by utilising multiple MRI sequences to learn texture invariant and shape equivariant features which are used to construct a shape dictionary using vector quantisation. We investigate shape equivariance to a number of different types of groups. We hypothesise and prove that the greater the group order, i.e., the denser the constraint, the better becomes the model robustness. We achieve shape equivariance either with a contrastive based approach or by imposing equivariant constraints on the convolutional kernels. The resulting shape equivariant dictionary is then sampled to compose the segmentation output. Our method achieves state-of-the-art performance for the task of single domain generalisation for prostate and cardiac MRI segmentation. Code is available at https://github.com/AinkaranSanthi/A_Geometric_Perspective_For_Robust_Segmentation.