Capturing implicit hierarchical structure in 3D biomedical images with self-supervised hyperbolic representations

We consider the task of representation learning for unsupervised segmentation\nof 3D voxel-grid biomedical images. We show that models that capture implicit\nhierarchical relationships between subvolumes are better suited for this task.\nTo that end, we consider encoder-decoder architectures with a hyperbolic latent\nspace, to explicitly capture hierarchical relationships present in subvolumes\nof the data. We propose utilizing a 3D hyperbolic variational autoencoder with\na novel gyroplane convolutional layer to map from the embedding space back to\n3D images. To capture these relationships, we introduce an essential\nself-supervised loss -- in addition to the standard VAE loss -- which infers\napproximate hierarchies and encourages implicitly related subvolumes to be\nmapped closer in the embedding space. We present experiments on both synthetic\ndata and biomedical data to validate our hypothesis.\n