Hyperbolic U-Net for Robust Medical Image Segmentation

Swasti S. Mishra, Max van Spengler, Erwin Berkhout, Pascal Mettes
Proceedings of The 9th International Conference on Medical Imaging with Deep Learning, PMLR 315:1217-1251, 2026.

Abstract

The U-Net architecture is a leading network in medical image segmentation. Despite its strong segmentation performance, U-Net struggles when dealing with noise in image data, such as random interference and brightness variations. While a common occurrence, the presence of random noise leads to strong performance degradation in U-Net, hampering its clinical integration and robustness. In this work, we investigate the role of geometry in U-Net. All U-Net variations share the same geometric foundations, namely Euclidean geometry. Here, we propose Hyperbolic U-Net, which maintains U-Net’s proven encoder-decoder structure while operating entirely in the Poincaré ball of hyperbolic space. We identify two main roadblocks for training a fully Hyperbolic U-Net and propose a solution for each: (i) fully hyperbolic literature has so far focused on encoders, limiting their applicability to segmentation. We introduce hyperbolic 2D transpose convolution and hyperbolic bilinear upsampling layers that make it possible to create decoders, and (ii) existing hyperbolic parameter initializations are not suitable for hyperbolic decoder blocks. We introduce a Newton’s approximation-scaled weight initialization, which ensures norm preservation for all layers at the start of training. Empirically, we show that our Hyperbolic U-Nets strongly outperform standard Euclidean U-Nets across multiple medical image datasets for Gaussian, Speckle, Poisson, and Rician noise, as well as to brightness and contrast shift. We conclude that a fully Hyperbolic U-Net is highly robust to out-of-the-box noise, without the need for denoising or additional objectives, highlighting the potential of hyperbolic geometry for medical imaging.

Cite this Paper

BibTeX
@InProceedings{pmlr-v315-mishra26a, title = {Hyperbolic U-Net for Robust Medical Image Segmentation}, author = {Mishra, Swasti S. and van Spengler, Max and Berkhout, Erwin and Mettes, Pascal}, booktitle = {Proceedings of The 9th International Conference on Medical Imaging with Deep Learning}, pages = {1217--1251}, year = {2026}, editor = {Huo, Yuankai and Gao, Mingchen and Kuo, Chang-Fu and Jin, Yueming and Deng, Ruining}, volume = {315}, series = {Proceedings of Machine Learning Research}, month = {08--10 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v315/main/assets/mishra26a/mishra26a.pdf}, url = {https://proceedings.mlr.press/v315/mishra26a.html}, abstract = {The U-Net architecture is a leading network in medical image segmentation. Despite its strong segmentation performance, U-Net struggles when dealing with noise in image data, such as random interference and brightness variations. While a common occurrence, the presence of random noise leads to strong performance degradation in U-Net, hampering its clinical integration and robustness. In this work, we investigate the role of geometry in U-Net. All U-Net variations share the same geometric foundations, namely Euclidean geometry. Here, we propose Hyperbolic U-Net, which maintains U-Net’s proven encoder-decoder structure while operating entirely in the Poincaré ball of hyperbolic space. We identify two main roadblocks for training a fully Hyperbolic U-Net and propose a solution for each: (i) fully hyperbolic literature has so far focused on encoders, limiting their applicability to segmentation. We introduce hyperbolic 2D transpose convolution and hyperbolic bilinear upsampling layers that make it possible to create decoders, and (ii) existing hyperbolic parameter initializations are not suitable for hyperbolic decoder blocks. We introduce a Newton’s approximation-scaled weight initialization, which ensures norm preservation for all layers at the start of training. Empirically, we show that our Hyperbolic U-Nets strongly outperform standard Euclidean U-Nets across multiple medical image datasets for Gaussian, Speckle, Poisson, and Rician noise, as well as to brightness and contrast shift. We conclude that a fully Hyperbolic U-Net is highly robust to out-of-the-box noise, without the need for denoising or additional objectives, highlighting the potential of hyperbolic geometry for medical imaging.} }
Endnote
%0 Conference Paper %T Hyperbolic U-Net for Robust Medical Image Segmentation %A Swasti S. Mishra %A Max van Spengler %A Erwin Berkhout %A Pascal Mettes %B Proceedings of The 9th International Conference on Medical Imaging with Deep Learning %C Proceedings of Machine Learning Research %D 2026 %E Yuankai Huo %E Mingchen Gao %E Chang-Fu Kuo %E Yueming Jin %E Ruining Deng %F pmlr-v315-mishra26a %I PMLR %P 1217--1251 %U https://proceedings.mlr.press/v315/mishra26a.html %V 315 %X The U-Net architecture is a leading network in medical image segmentation. Despite its strong segmentation performance, U-Net struggles when dealing with noise in image data, such as random interference and brightness variations. While a common occurrence, the presence of random noise leads to strong performance degradation in U-Net, hampering its clinical integration and robustness. In this work, we investigate the role of geometry in U-Net. All U-Net variations share the same geometric foundations, namely Euclidean geometry. Here, we propose Hyperbolic U-Net, which maintains U-Net’s proven encoder-decoder structure while operating entirely in the Poincaré ball of hyperbolic space. We identify two main roadblocks for training a fully Hyperbolic U-Net and propose a solution for each: (i) fully hyperbolic literature has so far focused on encoders, limiting their applicability to segmentation. We introduce hyperbolic 2D transpose convolution and hyperbolic bilinear upsampling layers that make it possible to create decoders, and (ii) existing hyperbolic parameter initializations are not suitable for hyperbolic decoder blocks. We introduce a Newton’s approximation-scaled weight initialization, which ensures norm preservation for all layers at the start of training. Empirically, we show that our Hyperbolic U-Nets strongly outperform standard Euclidean U-Nets across multiple medical image datasets for Gaussian, Speckle, Poisson, and Rician noise, as well as to brightness and contrast shift. We conclude that a fully Hyperbolic U-Net is highly robust to out-of-the-box noise, without the need for denoising or additional objectives, highlighting the potential of hyperbolic geometry for medical imaging.
APA
Mishra, S.S., van Spengler, M., Berkhout, E. & Mettes, P.. (2026). Hyperbolic U-Net for Robust Medical Image Segmentation. Proceedings of The 9th International Conference on Medical Imaging with Deep Learning, in Proceedings of Machine Learning Research 315:1217-1251 Available from https://proceedings.mlr.press/v315/mishra26a.html.

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