# Beyond Euclidean Prototypes: Spectral Disentanglement and Geodesic Matching for Few-Shot Medical Image Segmentation

arXiv: https://arxiv.org/abs/2605.17904 · HTML: https://mlsanity.com/paper/2605.17904/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 52 references that are in the map.
- First posted on arXiv 18 May 2026.

## Builds on (most cited first, 27 of 27)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Prototypical Networks for Few-shot Learning](https://mlsanity.com/paper/1703.05175/) (2017)
- [TransUNet: Transformers Make Strong Encoders for Medical Image Segmentation](https://mlsanity.com/paper/2102.04306/) (2021)
- [Swin-Unet: Unet-like Pure Transformer for Medical Image Segmentation](https://mlsanity.com/paper/2105.05537/) (2021)
- [PANet: Few-Shot Image Semantic Segmentation with Prototype Alignment](https://mlsanity.com/paper/1908.06391/) (2019)
- [One-Shot Learning for Semantic Segmentation](https://mlsanity.com/paper/1709.03410/) (2017)
- [CHAOS Challenge -- Combined (CT-MR) Healthy Abdominal Organ Segmentation](https://mlsanity.com/paper/2001.06535/) (2020)
- [Prior Guided Feature Enrichment Network for Few-Shot Segmentation](https://mlsanity.com/paper/2008.01449/) (2020)
- [Adaptive Prototype Learning and Allocation for Few-Shot Segmentation](https://mlsanity.com/paper/2104.01893/) (2021)
- [Hypercorrelation Squeeze for Few-Shot Segmentation](https://mlsanity.com/paper/2104.01538/) (2021)
- [U-KAN Makes Strong Backbone for Medical Image Segmentation and Generation](https://mlsanity.com/paper/2406.02918/) (2024)
- [Part-aware Prototype Network for Few-shot Semantic Segmentation](https://mlsanity.com/paper/2007.06309/) (2020)
- [Self-Supervision with Superpixels: Training Few-shot Medical Image Segmentation without Annotation](https://mlsanity.com/paper/2007.09886/) (2020)
- [Learning What Not to Segment: A New Perspective on Few-Shot Segmentation](https://mlsanity.com/paper/2203.07615/) (2022)
- ['Squeeze & Excite' Guided Few-Shot Segmentation of Volumetric Images](https://mlsanity.com/paper/1902.01314/) (2019)
- [Few-shot Medical Image Segmentation using a Global Correlation Network with Discriminative Embedding](https://mlsanity.com/paper/2012.05440/) (2020)
- [Anomaly Detection-Inspired Few-Shot Medical Image Segmentation Through Self-Supervision With Supervoxels](https://mlsanity.com/paper/2203.02048/) (2022)
- [Few-shot Medical Image Segmentation with Cycle-resemblance Attention](https://mlsanity.com/paper/2212.03967/) (2022)
- [Few-Shot Medical Image Segmentation via a Region-enhanced Prototypical Transformer](https://mlsanity.com/paper/2309.04825/) (2023)
- [MIANet: Aggregating Unbiased Instance and General Information for Few-Shot Semantic Segmentation](https://mlsanity.com/paper/2305.13864/) (2023)
- [Q-Net: Query-Informed Few-Shot Medical Image Segmentation](https://mlsanity.com/paper/2208.11451/) (2022)
- [FAMNet: Frequency-aware Matching Network for Cross-domain Few-shot Medical Image Segmentation](https://mlsanity.com/paper/2412.09319/) (2024)
- [Partition-A-Medical-Image: Extracting Multiple Representative Sub-regions for Few-shot Medical Image Segmentation](https://mlsanity.com/paper/2309.11172/) (2023)
- [TBConvL-Net: A Hybrid Deep Learning Architecture for Robust Medical Image Segmentation](https://mlsanity.com/paper/2409.03367/) (2024)
- [SPENet: Self-guided Prototype Enhancement Network for Few-shot Medical Image Segmentation](https://mlsanity.com/paper/2509.02993/) (2025)
- [Controllable Relation Disentanglement for Few-Shot Class-Incremental Learning](https://mlsanity.com/paper/2403.11070/) (2024)

## Abstract (arXiv)

Few-Shot Medical Image Segmentation (FSMIS) aims to delineate novel anatomical targets from one or a few annotated support images, addressing the annotation scarcity in medical imaging. Notwithstanding recent advancements, current prototype-based methods are bottlenecked by two coupled limitations: 1) cue entanglement, where a single spatial-domain prototype is forced to summarise organ silhouette, parenchymal texture and boundary appearance simultaneously, so any support-query mismatch on one cue propagates indiscriminately to the others; and 2) topology-blind matching, where cosine similarity measures distance in the ambient Euclidean space and ignores the connectivity of the underlying feature manifold, causing fragmented activations inside low-contrast organs and leakage into neighbouring tissues. To this end, we propose Spectral-Geodesic Prototype Network (SGP-Net), built around a Spectral-Geodesic Prototype Module with two coupled components. A Spectral Prototype Bank (SPB) decomposes support and query features into low-, mid- and high-frequency bands via learnable radial Fourier filters, yielding three disentangled prototypes per class that separately encode shape, texture and boundary cues. A Geodesic Matcher (GM) then replaces cosine similarity with a differentiable heat-diffusion approximation of geodesic distance, propagating matching signals along a feature affinity graph so that on-manifold pixels accumulate consistent responses while off-manifold look-alikes are suppressed. Experiments on three public FSMIS benchmarks demonstrate that SGP-Net achieves competitive performance against recent state-of-the-art methods.