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

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