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

We consider the task of representation learning for unsupervised segmentation 3D voxel-grid biomedical images. We show that models that capture implicit relationships between subvolumes are better suited for this task. that end, we consider encoder-decoder architectures with a hyperbolic latent, to explicitly capture hierarchical relationships present in subvolumes the data. We propose utilizing a 3D hyperbolic variational autoencoder with novel gyroplane convolutional layer to map from the embedding space back to3D images. To capture these relationships, we introduce an essential-supervised loss -- in addition to the standard VAE loss -- which infers hierarchies and encourages implicitly related subvolumes to be closer in the embedding space. We present experiments on both synthetic and biomedical data to validate our hypothesis.