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

arXiv: https://arxiv.org/abs/2012.01644 · HTML: https://mlsanity.com/paper/2012.01644/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Dec 2020.

## Built on by (most cited first, 24 of 24)

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- [A Set-to-Set Distance Measure in Hyperbolic Space](https://mlsanity.com/paper/2506.18529/) (2025)
- [HyperST: Hierarchical Hyperbolic Learning for Spatial Transcriptomics Prediction](https://mlsanity.com/paper/2511.22107/) (2025)
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- [H2AL: Hyperbolic Hierarchy-aware Aggregative Learning for Registration-based Few-shot Medical Image Segmentation](https://mlsanity.com/paper/2608.07340/) (2026)

## Abstract (arXiv)

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