H2AL: Hyperbolic Hierarchy-aware Aggregative Learning for Registration-based Few-shot Medical Image Segmentation

H2AL: Hyperbolic Hierarchy-aware Aggregative Learning for Registration-based Few-shot Medical Image Segmentation Jia Wang

Jiaming Cai

Zunying Hu

Zhanjie Wu

Beijing Children’s Hospital, Dalian University of Capital Medical University Technology Beijing, China Dalian, China 2961885858@mail.dlut.edu.cn huzy0628@163.com

Chongqing University of Posts and Telecommunications Chongqing, China 3195863842@qq.com

Jinyuan Liu

Hua Cheng

Yun Peng

Xin Fan✉

Dalian University of Technology Dalian, China atlantis918@hotmail.com

Beijing Children’s Hospital, Capital Medical University Beijing, China 64954966@qq.com

Beijing Children’s Hospital, Capital Medical University Beijing, China pengyun@mail.ccmu.edu.cn

Dalian University of Technology Dalian, China xin.fan@dlut.edu.cn

Pseudo-label Performance

Supervised R PC 66 . 81

BRBS s Our 83.53 83.29 4 .2 0 + l1 ve Le

79.3 3 PCR

Small structure(<1%) is prone to ambiguous

Hyperbolic Hierarchy Awareness

(a) Motivation of Our H2AL

71.87 TBI

81.41 BiJ

18 82. S B BR

+ 85 0.9 3 Ou .19 rs

𝑑𝔼

Small Large Total

4 +0.2 5 86.5 rs Ou

Large structure is easy to recognize

Small Large Total

PCR

𝑑𝔹

75.62 TBI 69.57

BiJ 82.7 5

Infusion

Ours 83.02 B +1.84 8 RBS 1.1 8

R PC 5 .4 82

BI J T 0 Bi 4 80.0 PCR .7 75.81 80

Challenge

T 85 B I .30

Learning Seg.

Small labeled data

Segmentation Performance

Ours 81.70 BR BS +1.47 80 .23

BiJ 85.3 2

…

BRBS 86.18

Learning Reg.

Pipeline of RFMIS

+ 82 0.72 Ou .90 rs

Large (pseudo-) labeled data

Unsupervised

T 73 BI .30

Large unlabeled data …

J Bi 7 .2 79

arXiv:2608.07340v1 [cs.CV] 7 Aug 2026

Dalian University of Technology Dalian, China jiawang0704@outlook.com

79. 9 PC 0 R 83.25 TBI

83.55 BiJ

26 84. S B BR

(b) Performance Comparison

Figure 1: (a) The upper part shows the pipeline of RFMIS, where unsupervised registration on large unlabeled data produces pseudo-labeled images for supervised segmentation. The bottom row highlights that large anatomical structures are easy to recognize, whereas small structures (<1% volume) are highly ambiguous. The right panel shows our hyperbolic hierarchy-aware modeling, where hyperbolic distance 𝑑 B between separated regions is much larger than the corresponding Euclidean distance 𝑑 E (𝑑 B ≫ 𝑑 E ), enlarging inter-class margins and improving discrimination for small structures. (b) Quantitative comparison of pseudo-label (from registration) and segmentation, which reports Dice scores (%) for large, small, and average structures, with red values indicating the improvement over the second-best results.

Abstract Registration-based Few-shot medical image segmentation (RFMIS) aims to generate pseudo-labels for unlabeled images by warping a labeled image through registration. However, existing methods primarily perform pixel-level optimization and inference in Euclidean space, treating anatomical structures as flat and disjoint. This neglect of inherent hierarchies degrades pseudo-label quality and weakens the discrimination of ambiguous regions, limiting the segmentation performance. To overcome this challenge, we propose a Hyperbolic Hierarchy-aware Aggregative Learning framework for RFMIS, termed H2AL, that enhances both deformation

This work is licensed under a Creative Commons Attribution 4.0 International License. MM ’26, Rio de Janeiro, Brazil © 2026 Copyright held by the owner/author(s). ACM ISBN 979-8-4007-2213-4/2026/11 https://doi.org/10.1145/3767308.3834907

plausibility and anatomical discrimination for dual-task learning. Specifically, we introduce a Hyperbolic Hierarchy-aware Infusion (H2I) module, which leverages the hierarchical modeling capability of hyperbolic space to learn precise hierarchy-aware representations via transformation-guided supervised hyperbolic contrastive learning, and injects such hierarchical priors into Euclidean space through a gated infusion block while preserving semantic richness. Furthermore, we propose an end-to-end joint optimization algorithm by gradient aggregation, where the gradients from the registration and segmentation decoders, embedding semantic and hierarchical cues, are aggregated to update the shared encoder to promote collaborative learning across tasks. Extensive experiments on two anatomical regions, with five experimental settings, demonstrate the effectiveness and efficiency of our method in both registration and segmentation. The code is publicly available at https://github.com/JiamingCai469/H2AL.

MM ’26, November 10–14, 2026, Rio de Janeiro, Brazil

CCS Concepts • Applied computing → Health care information systems.

Keywords Registration-based Few-shot Medical Image Segmentation, Hyperbolic Hierarchy-aware Infusion, Gradient Aggregation Learning ACM Reference Format: Jia Wang, Jiaming Cai, Zunying Hu, Zhanjie Wu, Jinyuan Liu, Hua Cheng, Yun Peng, and Xin Fan. 2026. H2AL: Hyperbolic Hierarchy-aware Aggregative Learning for Registration-based Few-shot Medical Image Segmentation. In Proceedings of the 34th ACM International Conference on Multimedia (MM ’26), November 10–14, 2026, Rio de Janeiro, Brazil. ACM, New York, NY, USA, 10 pages. https://doi.org/10.1145/3767308.3834907

1

Introduction

Few-shot medical image segmentation (FMIS) has recently garnered increasing attention as an effective solution for learning from limited labeled data. A prevalent paradigm is registration-based FMIS (RFMIS) which propagates labels via image warping and leverages anatomical correspondence to preserve geometric consistency. By learning unsupervised registration to warp labeled images onto unlabeled ones, it propagates annotations and generates pseudo-labels for training the segmentation network, as shown in Fig. 1 (a) (top). The key to this task lies in the quality of pseudo-labels, since inaccurate or anatomically inconsistent labels can degrade the segmentation performance, particularly for small anatomical structures. Existing RFMIS methods [8, 21, 29, 35] mainly focus on strengthening supervision to improve pseudo-label quality. A common strategy is to ensure consistency in appearance and distribution between labeled and unlabeled images. These constraints guide registration to preserve topology and anatomy, and enable the synthesis of styleconsistent warped labeled images that augment the scarce labeled set and yield more robust pseudo-labels. Despite these advancements, most RFMIS methods optimize and infer at the pixel level in Euclidean output embedding spaces, treating anatomical regions as flat and disjoint classes. In practice, medical anatomical categories exhibit an intrinsic coarse-to-fine hierarchy defined by radiologists1 . Such hierarchy ignored by existing methods causes confused small or ambiguous anatomical structures (see Fig. 1 (a) (down left)), inducing deformation fields that fit local intensities but violate global hierarchical anatomical consistency, leading to predicted segmentation results with weakened anatomical discrimination. To model anatomical hierarchies, recent advanced medical image analysis methods, such as segmentation [1, 27], registration [33, 40], and image–text alignment [14, 28], leverage hyperbolic space for representation learning, owing to its exponentially expanding geometry and natural ability to encode hierarchical structures (see Fig. 1 (a) (down right)). For example, Hsu et al. [19] employed a hyperbolic variational autoencoder and a self-supervised hierarchical loss to learn representations for capturing implicit hierarchical relationships among structures. However, existing hyperbolic methods primarily focus on hyperbolic embedding, while neglecting the rich semantic information embedded in Euclidean space, resulting in incomplete modeling of anatomical semantics. In addition, no prior methods have investigated its potential in RFMIS, which necessitates 1 Radiologist-defined coarse-to-fine hierarchy details are in the supplementary.

Wang et al.

the joint optimization of registration and segmentation and is more challenging than a single-task setting. Based on the above observations, a key question arises for RFMIS: how to effectively leverage both rich semantic information in Euclidean space and anatomical hierarchies in hyperbolic space within a complex dual-task framework. To this end, we propose a Hyperbolic Hierarchy-aware Aggregative Learning framework for RFMIS, named H2AL, that enhances both deformation plausibility and anatomical discrimination for dual-task learning. Building upon a shared encoder and task-specific decoder architecture, Hyperbolic Hierarchy-aware Infusion (H2I) modules explicitly capture anatomical hierarchy from pseudo-label supervision and inject hyperbolic priors into Euclidean features while preserving the semantic richness. Equipped with learned semantic and hierarchical cues, we design a gradient aggregation (GA) strategy that enables efficient one-stage end-to-end training by jointly optimizing the shared encoder to boost collaborative learning across tasks. Overall, H2AL offers a unified framework for anatomically plausible deformation and more discriminative segmentation, especially for small anatomical structures. As shown in Fig. 1 (b), H2AL leads to better pseudo-label quality (left) and superior segmentation performance (right). Notably, for small anatomical structures, it improves Dice scores by 1.47% and 1.84% for registration and segmentation than SOTA methods respectively. Our main contributions are as summarized as: • We propose H2AL for RFMIS, which enhances both consistent deformation and anatomical representation to increase final segmentation performance. • We introduce an H2I module that jointly exploits the hyperbolic hierarchical priors and the Euclidean semantic richness, learning precise and anatomically discriminative representations. • We devise a GA-based joint optimization strategy for one-stage end-to-end training, which aggregates task-specific gradients infused with semantic and hierarchical cues to collaboratively optimize the shared encoder across dual tasks. • Extensive experiments on brain and cardiac datasets show that H2 AL outperforms state-of-the-art RFMIS methods in both segmentation and registration. Comprehensive visualizations further verify the effectiveness of jointly modeling Euclidean semantics and hyperbolic hierarchy in improving the discrimination of small anatomical structures.

2 Related Works 2.1 Few-shot Medical Image Segmentation Few-shot medical image segmentation [5, 11, 15, 25, 32] has become an important topic in medical image analysis, which can be divided into two categories: prototype-based and registrationbased segmentation. Prototype-based methods typically learn classrepresentative feature embeddings from support images and segment query images through support–query feature matching. Tang et al. [36] proposed a prototypical network with a context encoder and recurrent refinement to enhance foreground–background separation. Zhu et al. [44] introduced regional prototypes to reduce intra-class variation and improve support–query matching. Despite their effectiveness, these methods rely mainly on feature-space similarity and often lack explicit anatomical and spatial modeling,

H2AL: Hyperbolic Hierarchy-aware Aggregative Learning for Registration-based Few-shot Medical Image Segmentation

(a) H²AL Framework

𝜑𝑟𝑒𝑔

Seg Dec

Ⓦ

𝜙r𝑒𝑔

Shared

Enc

Reg Head

𝒊−𝟏 ) H2I (𝒚aab

H2I (𝒚𝒊 )

𝜗

Supervision

Euclidean space

𝜙𝑠𝑒𝑔 Infusing Hierarchical information

Reg Branch

Ⓧ Element-wise multiplication

Seg Branch

C

Supervision

⊕ Element-wise adding

𝑦𝑝

𝑦ො 𝑢

Task Head

Gate

c

Logx ()

Expx ()

Tangent space

Supervision

Ⓦ Warp operation

Concatenation

(b-II) Gated Infusion Block (GIB)

c

Seg Head

𝜑𝑠𝑒𝑔

𝑥𝑢

𝑦𝑙

Conv Batch Norm ReLU Conv Batch Norm ReLU

𝑥𝑙

Reg Dec

C

(b) Hyperbolic hierarchical-aware infusion (H2I) (b-I) Transformation-guided Supervised Hyperbolic Contrastive Learning (TSHCL) Euclidean Embedding Cluster 1 Cluster 2 Cluster 3 Cluster 4 Cluster 5 …

Möbius Layer

Enc

MM ’26, November 10–14, 2026, Rio de Janeiro, Brazil

Gate

c

Adaptive Push and Pull

Logx ()

Gate

Ⓧ⊕

𝜑𝑠𝑒𝑔

Poincarémodel Hyperbolic space

Hierarchy-aware

Labeled image: 𝑥 𝑙 Unlabeled image: 𝑥 𝑢 Euclidean embedding (Reg/Seg) before TSHCL: 𝜑𝑟𝑒𝑔 / 𝜑𝑠𝑒𝑔 Euclidean embedding (Reg/Seg) after TSHCL: 𝜙𝑟𝑒𝑔 / 𝜙𝑠𝑒𝑔 Predict label: 𝑦ො 𝑢 Predict deformation field: 𝜗 Pesudo label: 𝑦 𝑝

Figure 2: Overview of the proposed H2 AL framework. (a) The framework jointly performs registration and segmentation with a shared encoder and two task-specific decoders. (b) H2I consists of two parts: (b-I) TSHCL in hyperbolic space to model class hierarchy with adaptive push–pull, and (b-II) GIB for mapping hyperbolic features back to Euclidean space for final prediction. limiting their robustness to large inter-subject variation. To address these limitations, registration-based FMIS (RFMIS) has emerged as a more structure-aware alternative by transferring support annotations through learned anatomical alignment. He et al. [16] improved registration realism and robustness through knowledge consistency and misalignment regularization, while Fan et al. [10] adopted a bilevel optimization framework jointly learning registration and segmentation with appearance constraints. Although these methods have achieved promising results, they generally overlook the hierarchical organization of anatomical categories. In this work, we focus on registration-based FMIS and offer insights for hyperbolic hierarchical representation learning in broader few-shot settings.

2.2

Hyperbolic Hierarchy-Aware Learning

Recent works have explored hyperbolic hierarchy-aware learning [20, 34, 37, 38, 41], leveraging hyperbolic spaces to model hierarchical structures in data. Dong et al. [9] conducted hierarchical representation and reasoning entirely in hyperbolic space by preserving knowledge graph hierarchies. Pan and Wang [26] developed a hyperbolic embedding method that models hierarchical structures through geometry-aware mapping. However, these methods mainly focus on hyperbolic embedding itself while overlooking the rich semantic information preserved in Euclidean space, which may lead to incomplete representation learning. To address this issue, we inject hierarchy-aware hyperbolic information into Euclidean space to exploit the complementary strengths of both geometries.

3

Preliminary: Hyperbolic Geometry

A Riemannian manifold (M, 𝑔) of dimension 𝑛 is a smooth real manifold endowed with a metric 𝑔 that assigns each 𝑥 ∈ M an inner product 𝑔𝑥 : 𝑇𝑥 M × 𝑇𝑥 M → R on the tangent space 𝑇𝑥 M at each point 𝑥 ∈ M. Hyperbolic space is a Riemannian manifold with constant negative curvature, exhibiting exponential volume growth and a tree-like geometry that naturally captures hierarchical relationships, which is beneficial for complex medical data. Poincaré ball model. Following the previous work [12, 18, 27], we adopt an open 𝑛-dimensional Poincaré ball defined as (B𝑐𝑛 , 𝑔B ), with  √ manifold B𝑐𝑛 = 𝑐 ∥𝑥 ∥ 2 < 1 , where radius is 1/ 𝑐. Its Riemannian metric is conformal to the Euclidean metric 𝑔𝑥E as 2 𝑔𝑥B = 𝜆𝑐,𝑥 𝑔𝑥E =

4 𝑔E . (1 − 𝑐 ∥𝑥 ∥ 2 ) 2 𝑥

(1)

Since standard Euclidean vector operations are not directly valid in hyperbolic space, we use Möbius addition (⊕𝑐 ) as 𝑥 ⊕𝑐 𝑦 =

(1 + 2𝑐 ⟨𝑥, 𝑦⟩ + 𝑐 ∥𝑦∥ 2 ) 𝑥 + (1 − 𝑐 ∥𝑥 ∥ 2 ) 𝑦 , 1 + 2𝑐 ⟨𝑥, 𝑦⟩ + 𝑐 2 ∥𝑥 ∥ 2 ∥𝑦∥ 2

(2)

with analogous Möbius scalar and matrix multiplications. The hyperbolic distance is √  2 𝑑 B (𝑥, 𝑦) = √ tanh−1 𝑐 ∥(−𝑥) ⊕𝑐 𝑦∥ . (3) 𝑐 Exponential and logarithmic maps. The tangent space T𝑥 B𝑐𝑛 at a point 𝑥 ∈ B𝑐𝑛 is a Euclidean space composed of vectors, aiming to perform optimization and representation learning in hyperbolic space. Specifically, the mapping between the tangent space T𝑥 B𝑐𝑛 and the Poincaré ball model B𝑐𝑛 is established by exponential (T𝑥 B𝑐𝑛 → B𝑐𝑛 ) and its inverse, the logarithmic (B𝑐𝑛 → T𝑥 B𝑐𝑛 ). For any two points 𝑥, 𝑦 ∈ B𝑐𝑛 and a tangent vector 𝑣 ∈ T𝑥 B𝑐𝑛 , where 𝑣 ≠ 0 and 𝑦 ≠ 𝑥, the map function is given by  √   𝑐 𝜆𝑐,𝑥 ∥𝑣 ∥ 𝑣 exp𝑥B𝑐 (𝑣) = 𝑥 ⊕𝑐 tanh , (4) √ 2 𝑐 ∥𝑣 ∥  (−𝑥) ⊕ 𝑦 √ 2 𝑐 . (5) log𝑥B𝑐 (𝑦) = √ tanh−1 𝑐 ∥(−𝑥) ⊕𝑐 𝑦 ∥ ∥(−𝑥) ⊕𝑐 𝑦 ∥ 𝑐 𝜆𝑐,𝑥

4 Methodology 4.1 Framework Overview Registration-based few-shot medical image segmentation (RFMIS) exploits registration (reg.) to generate pseudo-labels, thereby facilitating segmentation (seg.) under limited supervision. In the fewshot setting, the training data consists of a small labeled subset, 𝑁 , and a larger unlabeled subset, dedenoted as D𝑙 = {(𝑥𝑖𝑙 , 𝑦𝑖𝑙 )}𝑖=1 𝑢 𝑀 noted as D𝑢 = {𝑥 𝑗 } 𝑗=1 , where 𝑁 ≪ 𝑀. Here, each 3D medical volume is 𝑥 𝑙 ∈ R𝐷 ×𝐻 ×𝑊 , and the corresponding ground truth segmentation is 𝑦𝑙 ∈ {0, 1, ..., 𝐶−1}𝐷 ×𝐻 ×𝑊 . For brevity, the sample indices 𝑖 and 𝑗 are omitted in the following descriptions. To this end, we propose a Hyperbolic Hierarchy-aware Aggregative Learning framework, termed H2AL, which consists of a shared encoder and two task-specific decoders, H2I modules, and dedicated task heads for registration and segmentation, respectively. As shown in Fig. 2, both labeled and unlabeled volumes are first fed

MM ’26, November 10–14, 2026, Rio de Janeiro, Brazil

into the shared encoder to extract their feature representations. The unlabeled features are then concatenated with the labeled branch features and passed to the registration decoder to produce the deformation field embeddings 𝜙𝑟𝑒𝑔 . Meanwhile, the unlabeled features are forwarded through the segmentation decoder to generate the segmentation embeddings 𝜙𝑠𝑒𝑔 . To effectively leverage anatomical prior knowledge, the deformation embedding is further fed into the H2I module to inject hyperbolic hierarchical information into the Euclidean feature space. Specifically, the H2I module consists of a Transformation-guided Supervised Hyperbolic Contrastive Learning (TSHCL) strategy and a Gated Infusion Block (GIB). The resulting hierarchy-aware features are finally delivered to the registration head to predict the final deformation field 𝜗 . The segmentation branch follows a similar process to generate the predicted label 𝑦ˆ𝑢 . It is worth noting that for the registration branch, the TSHCL module is supervised using the previous-iteration pseudo-label (i.e., reg.-warped label), while for the segmentation branch, it uses the current pseudo-label. Finally, aiming at a more robust and generalizable encoder, we propose a gradient aggregation strategy to effectively integrate Euclidean and hyperbolic cues, yielding stable optimization and stronger representations.

4.2

Hyperbolic Hierarchy-aware Infusion

Given the Euclidean embedding 𝜙, we propose the hyperbolic hierarchy-aware Infusion (H2I) module to inject hierarchical information from hyperbolic space into Euclidean feature maps. The H2I module consists of two key components: (1) Transformation-guided supervised hyperbolic contrastive learning (TSHCL) strategy, which exploits hierarchy-aware representations in hyperbolic space. (2) Gated infusion block (GIB), which injects these representations into the Euclidean feature stream to learn richer feature representations. TSHCL strategy. To model the implicit hierarchical relationships in medical data, we map Euclidean embeddings into hyperbolic space using the Poincaré ball model. Leveraging the natural ability of hyperbolic geometry to model tree-like structures, this yields more discriminative and hierarchy-aware representation learning. Such hierarchical embeddings are particularly beneficial for improving downstream registration and segmentation performance. To this end, we propose a Transformation-guided Supervised Hyperbolic Contrastive Learning (TSHCL) strategy, which adaptively pushes and pulls class embeddings based on their hyperbolic distances with pseudo-labels from registration. Unlike previous methods that solely rely on the hyperbolic geometry for implicit representation learning, we incorporate multi-label supervision to explicitly guide the formation of a structured embedding space in the Poincaré ball. 𝑁 ⊂ B𝑛 and pseudoSpecifically, given feature embeddings {𝑧𝑖 }𝑖=1 𝑐 𝑝 𝑁 labels {𝑦ˆ𝑖 }𝑖=1 obtained from the registration branch, we first define a binary mask that distinguishes positive and negative pairs as ( 1, if 𝑦ˆ𝑖 = 𝑦ˆ 𝑗 and 𝑖 ≠ 𝑗, I𝑖,𝑗 = (6) 0, otherwise. We compute pairwise similarity between hyperbolic embeddings using the geodesic distance in Eq. 3. Accordingly, we design distanceaware contrastive weights to regulate attractive and repulsive forces: a pull weight for positive pairs that increases with distance to promote compactness, and a push weight for negative pairs that decays

Wang et al. Stage 1: AT of Pretraining the encoder Stage 2: AT of Reg Dec.

Enc.

𝓛𝒓𝒆𝒈

Shared

Joint training of

𝓛𝒓𝒆𝒈 GA

Shared

Seg Dec.

Enc.

: Data Flow

𝓛𝒔𝒆𝒈

𝓛𝒓𝒆𝒈

𝓛𝒔𝒆𝒈

𝓛𝒔𝒆𝒈

Limitation: Complex and Time-consuming (a) SOTA JRFS method : Gradient Flow G A : GradientAggregation

Advantage: Efficient and effective

(b) Learning with GA : Fixed Parameters

: Alternative training

Figure 3: Comparison between the state-of-the-art RFMIS method and our proposed learning strategy with gradient aggregation (GA). with distance to avoid excessive repulsion between unrelated samples. The corresponding weight functions are defined as   𝑝𝑢𝑙𝑙 𝑤𝑖,𝑗 = 1 − 𝑒 −𝛾 ·𝑑B (𝑧𝑖 ,𝑧 𝑗 ) , (7) 𝑝𝑢𝑠ℎ

𝑤𝑖,𝑗

= 𝑒 −𝛿 ·𝑑B (𝑧𝑖 ,𝑧 𝑗 ) .

(8)

This design ensures stronger attraction between dissimilar but true positive samples, and softer repulsion between negatives that are already distant. Finally, the TSHCL loss is defined as   Í pull I𝑖,𝑗 exp 𝑤𝑖,𝑗 /𝜏 ∑︁ 𝑗 ∈𝐷    , (9) LTSHCL = log Í pull push exp 𝑤𝑖,𝑗 I𝑖,𝑗 + 𝑤𝑖,𝑗 (1 − I𝑖,𝑗 ) /𝜏 𝑖 ∈𝐷 𝑗 ∈𝐷

where 𝜏 denotes the temperature parameter. With the proposed TSHCL strategy, we further adopt Möbius layer defined in Eq. 2 to refine hyperbolic embeddings. Thus, leveraging the geometric properties of hyperbolic space, we can generate embeddings that are structurally aligned with the underlying hierarchy. GIB. Leveraging the rich hierarchical representations encoded in hyperbolic space, we propose the Gated Infusion Block (GIB) to inject such structural knowledge into Euclidean features for downstream registration and segmentation tasks. Specifically, GIB first projects the hierarchy-aware hyperbolic embeddings into Euclidean space, as defined in Eq. 5, to ensure geometric compatibility. Then, the projected embeddings are passed through a gated attention mechanism to generate hierarchy-informed attention maps, which are subsequently used to modulate the Euclidean features via an affine transformation as 𝜙 = 𝜑 × 𝐺𝑎𝑡𝑒 1 (log𝑥B𝑐 (𝜃 )) + 𝐺𝑎𝑡𝑒 2 (log𝑥B𝑐 (𝜃 )),

(10)

where 𝜑, 𝜃 , and 𝜙 denote the Euclidean embedding, hyperbolic embedding, and the Euclidean embedding with hierarchical information. The proposed GIB employs a simple yet effective design that takes advantage of the rich semantic representations from the Euclidean space while incorporating the hierarchical priors embedded in hyperbolic geometry. To better adapt to different tasks, we instantiate two task-specific GIBs for registration and segmentation, respectively, allowing each task to selectively exploit the infused hierarchical cues. This fusion yields task-specific embeddings that are simultaneously semantically discriminative and hierarchically structured, leading to improved registration accuracy and segmentation robustness.

4.3

Network Architecture and Optimization

Existing RFMIS methods adopt the shared-encoder and task-specific framework [10, 42], proving to be an effective framework. Thus, we

H2AL: Hyperbolic Hierarchy-aware Aggregative Learning for Registration-based Few-shot Medical Image Segmentation

MM ’26, November 10–14, 2026, Rio de Janeiro, Brazil

Table 1: Quantitative results of segmentation methods on the Brain and the Cardiac datasets. The numbers in parentheses after each dataset name indicate the modality of the dataset. F : Fully supervised

A : Atlas-based

F : Few-shot

: Best performance

: Second best performance

Brain(T1 MRI)

Cardiac(CT)

Methods

Type

UNet [30] MASSL [4] Co-manifold [27]

F F F

46.36 ± 19.87 58.01 ± 2.16 64.41 ± 6.72

19.83 ± 8.37 15.63 ± 7.11 12.07 ± 1.70

53.41 ± 16.83 61.73 ± 2.28 66.28 ± 6.64

13.75 ± 5.79 10.47 ± 5.67 11.52 ± 1.01

52.18 ± 18.73 60.15 ± 0.05 67.94 ± 5.92

9.90 ± 7.08 8.82 ± 4.38 8.03 ± 0.77

57.59 ± 16.38 61.23 ± 5.86 65.36 ± 6.88

33.70 ± 7.35 22.94 ± 6.71 19.58 ± 1.92

85.96 ± 9.57 65.49 ± 5.03 69.55 ± 7.04

9.38 ± 7.96 15.53 ± 3.07 13.42 ± 1.39

DeepAtlas [39] DataAug [6] TBIOneShot [43]

A A A

70.15 ± 8.20 73.52 ± 3.51 80.60 ± 6.82

2.90 ± 0.67 3.57 ± 0.87 2.10 ± 0.31

67.87 ± 5.45 76.39 ± 2.55 83.51 ± 5.97

2.74 ± 0.97 2.32 ± 0.35 1.55 ± 0.15

70.36 ± 9.86 75.69 ± 2.65 84.30 ± 5.21

3.14 ± 0.92 2.65 ± 0.41 1.60 ± 0.25

73.43 ± 5.59 82.26 ± 7.21 84.30 ± 10.42

10.21 ± 3.21 10.16 ± 4.08 10.07 ± 4.59

82.29 ± 4.42 83.01 ± 5.32 88.93 ± 7.51

10.59 ± 4.45 9.32 ± 2.15 6.66 ± 3.86

BRBS [16] PC-Reg-RT [17] Bi-JROS [10]

F F F

82.86 ± 1.45 78.30 ± 3.01 83.04 ± 1.08

1.75 ± 0.47 2.15 ± 0.33 1.74 ± 0.16

84.26 ± 1.48 79.90 ± 2.12 83.55 ± 1.41

1.49 ± 0.16 1.82 ± 0.25 1.50 ± 0.16

85.03 ± 1.78 79.14 ± 3.43 84.75 ± 1.86

1.55 ± 0.21 1.92 ± 0.36 1.74 ± 0.28

88.31 ± 2.87 82.16 ± 8.59 88.35 ± 3.11

4.76 ± 1.94 13.28 ± 9.10 4.41 ± 1.59

90.38 ± 3.76 89.42 ± 3.01 89.81 ± 3.10

3.00 ± 1.34 4.01 ± 2.23 4.38 ± 1.09

Ours

F

84.17 ± 1.09

1.70 ± 0.17

85.19 ± 1.23

1.41 ± 0.14

85.68 ± 1.52

1.32 ± 0.15

89.24 ± 2.11

4.15 ± 1.47

90.24 ± 2.01

3.56 ± 1.30

CrWM

CrC

Background

Ven

Atlas±std Dice%↑ HD95 mm↓

1-shot±std Dice%↑ HD95 mm↓

LV

ClWM

TP

1-shot Brain 5-shot Cardiac

Put

Cau

1-shot±std Dice%↑ HD95 mm↓

Pal

5-shot±std Dice%↑ HD95 mm↓

Hip

BS

Amy

ClC

Sagittal

Axial

Background

5-shot±std Dice%↑ HD95 mm↓

UNet

DataAug

PC-Reg-RT

BRBS

Bi-JROS

Ours

LVM

LAC

TBIOneShot

GT LVC

RAC

UNet

DataAug

PC-Reg-RT

BRBS

Bi-JROS

Ours

RVC

AAo

TBIOneShot

GT PA

Sagittal

Axial

UNet

DataAug

PC-Reg-RT

TBIOneShot

UNet

DataAug

PC-Reg-RT

TBIOneShot

BRBS

Bi-JROS

Ours

GT

BRBS

Bi-JROS

Ours

GT

Figure 4: Qualitative segmentation results on the Brain and Cardiac datasets. Different colors indicate different anatomical structures, whose names are shown above the panels. Red arrows highlight erroneous predictions. also adopt this framework as the basis of our method due to its outstanding performance. However, these methods often employ a twostage training strategy that the shared encoder is pretrained and then followed by alternating optimization of task-specific decoders, resulting in time-consuming and suboptimal task interaction modeling as shown in Fig. 3 (a). While the proposed H2I effectively enriches the feature representations with structural priors, a suitable training strategy is required to fully exploit such enriched features across tasks. We propose a one-stage, end-to-end training strategy, termed learning with Gradient Aggregation (GA), that enables efficient and consistent multi-task learning as shown in Fig. 3 (b), and the pseudo-code is shown in Algorithm 1. Specifically, we first perform task-specific decoder updates during backpropagation as 𝜃 𝑟𝑑 ← 𝜃 𝑟𝑑 − ∇𝜃𝑟𝑑 Lreg,

(11)

𝜃 𝑠𝑑 ← 𝜃 𝑠𝑑 − ∇𝜃𝑠𝑑 Lseg,

(12)

where 𝜃 𝑟𝑑 and 𝜃 𝑠𝑑 denote the parameters of registration and segmentation decoders, and L𝑟𝑒𝑔 and L𝑠𝑒𝑔 denote the loss function of registration and segmentation task. After obtaining the gradients from the task-specific decoders embedding semantic and hierarchical cues, we aggregate them to update the shared encoder in a unified manner as
𝜃 𝑠𝑒 ← 𝜃 𝑠𝑒 − ∇𝜃𝑠𝑒 L𝑟𝑒𝑔 + ∇𝜃𝑠𝑒 L𝑠𝑒𝑔 , (13) where 𝜃 𝑠𝑒 denotes the parameter of the shared encoder. By combining gradients before applying updates to 𝜃𝑠𝑒, we facilitate synergistic representation learning, encouraging the encoder to learn features that are beneficial to both registration and segmentation tasks. This tightly coupled training regime allows the model to better capture inter-task dependencies and avoid task dominance. Reg Loss. We use a smoothness loss Lsmo to enforce deformation smoothness, and adopt L𝑠𝑖𝑚 to measure the similarity between

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Wang et al.

Table 2: Quantitative comparison of registration performance among different methods on the Brain dataset under the 5-shot setting. The symbols A and F denote atlas-based and few-shot methods, respectively. R : Registration-only Methods

: Best performance

Type

: Second best performance

Dice%↑

NCC↑

|𝐽𝜙 | ≤ 0 % ↓

Initial

–

63.04 ± 7.13

0.151 ± 0.012

–

SyN [2] VoxelMorph [3]

R R

77.42 ± 3.54 71.13 ± 8.92

0.269 ± 0.014 0.258 ± 0.027

0.00 ± 0.00 0.42 ± 0.35

DeepAtlas [39] DataAug [6] TBIOneShot [43]

A A A

64.12 ± 14.08 78.27 ± 3.56 74.02 ± 2.83

0.154 ± 0.011 0.365 ± 0.010 0.297 ± 0.008

3.12 ± 0.56 0.52 ± 0.09 0.00 ± 0.00

BRBS [16] PC-Reg-RT [17] Bi-JROS [10]

F F F

82.53 ± 1.81 76.45 ± 4.43 81.47 ± 2.34

0.335 ± 0.009 0.289 ± 0.014 0.377 ± 0.011

2.86 ± 0.33 1.59 ± 0.22 0.15 ± 0.07

Ours

F

83.36 ± 1.64

0.386 ± 0.011

0.36 ± 0.09

PC-Reg-RT DataAug TBIOneShot

BRBS

Bi-JROS

Ours

GT

Source

PC-Reg-RT DataAug TBIOneShot

BRBS

Bi-JROS

Ours

GT

1-shot Brain (S)

1-shot Brain (A)

Source

Figure 5: Qualitative registration results on the Brain dataset. “A” and “S” denote axial and sagittal views, respectively. Red arrows highlight misaligned regions. the warped image and target image. The total registration loss with the proposed TSHCL strategy is then a weighted sum of these components as 𝑟𝑒𝑔

𝑟𝑒𝑔

Lreg = 𝜆𝑠𝑚𝑜 Lsmo + 𝜆𝑠𝑖𝑚 Lsim + 𝜆𝑇 𝑆𝐻𝐶𝐿 L𝑇 𝑆𝐻𝐶𝐿 ,

(14)

𝑟𝑒𝑔 where 𝜆𝑠𝑚𝑜 , 𝜆𝑠𝑖𝑚 , 𝜆𝑇 𝑆𝐻𝐶𝐿 are the hyper-parameters to balance the

trade-off of the three components. Seg loss. We take a multi-class Dice coefficient loss as the segmentation metric with the proposed TSHCL as 𝑠𝑒𝑔

Lseg = 𝜆𝑑𝑖𝑐𝑒 Ldice + 𝜆𝑇 𝑆𝐻𝐶𝐿 L𝑇 𝑆𝐻𝐶𝐿 ,

(15)

𝑠𝑒𝑔 where 𝜆𝑑𝑖𝑐𝑒 and 𝜆𝑇 𝑆𝐻𝐶𝐿 are the hyperparameters used to balance

the relative contributions of the two components.

5

Experiments

We evaluate H2 AL from four perspectives: overall superiority over state-of-the-art methods, behavior under challenging cases, mechanism of performance gains, and reliability of the proposed design. We first describe the experimental settings, datasets, implementation details, and evaluation metrics. Experimental Settings and Datasets. We evaluate the proposed method under three settings: Atlas-based, 1-shot, and 5-shot, on the Brain and Cardiac datasets. The Brain dataset is used in all three settings, while the Cardiac dataset is evaluated under the

1-shot and 5-shot settings. In the few-shot setting, instead of using a predefined atlas dataset, we randomly select one or five labeled images from the same dataset as the atlas set. All images and labels are resampled to a uniform size after intensity normalization and label mapping, respectively. The Brain dataset comprises 410 3D T1-weighted MRI scans from four public datasets: OASIS [22], PPMI [23], ADNI [24], and ABIDE [7]. These data span a wide range of ages and imaging conditions, providing diverse anatomical variability for model evaluation. Following standard practice, 330 volumes are used for training and 80 for testing. All scans are resampled to 128 × 128 × 128. The Cardiac dataset comprises 125 3D CT scans from MM-WHS [45], ASOCA [13], and CAT08 [31], following BRBS [16]. The data include different cardiac phases and anatomical variations, supporting evaluation under realistic inter-subject and inter-site conditions. Among them, 100 images are used for training and 25 for testing. Each image is resampled to 144 × 144 × 128. Implementation details. The proposed method is implemented in PyTorch and trained on an NVIDIA A40 GPU with 48 GB memory. We apply consistent 3D spatial augmentations, including random rotations and isotropic scaling. The registration and segmentation branches are jointly optimized using a single Adam optimizer. The initial learning rate is set to 1 × 10−4 , and the models are trained with a batch size of 1. Metrics. We adopt three standard metrics for evaluation: Dice, NCC, and HD95. Dice measures the volumetric overlap between prediction and ground truth. NCC evaluates the intensity alignment between the warped source image and the target. HD95 quantifies boundary accuracy using the 95th-percentile Hausdorff distance.

5.1

Comparison with State-of-the-art Methods

We comprehensively evaluate the segmentation and registration performance of H2AL through both quantitative and qualitative analyses on multiple benchmarks and settings. Quantitative Comparison. For segmentation, we compare H2AL with nine representative methods from three categories, including: i) fully supervised methods, UNet [30], MASSL [4], and Comanifold [27]; ii) atlas-based methods, DeepAtlas [39], DataAug [6], and TBIOneShot [43], which rely on a single annotated atlas for label propagation via registration; iii) few-shot methods, BRBS [16], PC-Reg-RT [17], and Bi-JROS [10]. The segmentation results are summarized in Table 1. Overall, few-shot methods outperform both fully supervised and atlas-based methods, demonstrating their effectiveness in low-label scenarios. Although not specifically designed for the atlas-based setting, H2 AL consistently achieves superior performance, demonstrating strong generalization. Attributed to enhanced anatomical discrimination enabled by hierarchy-aware representation learning, H2 AL achieves the best performance across all settings on the Brain dataset, significantly outperforming leading few-shot methods such as BRBS and Bi-JROS. On the Cardiac dataset, it ranks first in the 1-shot setting and second in the 5-shot setting, consistently surpassing Bi-JROS. For registration, we compare our method against eight representative approaches spanning three categories: i) registration-only methods, SyN [2] and VoxelMorph [3]; ii) atlas-based methods, DeepAtlas [39], DataAug [6], and TBIOneShot [43]; iii) few-shot methods, BRBS [16], PC-Reg-RT [17], and Bi-JROS [10].

H2AL: Hyperbolic Hierarchy-aware Aggregative Learning for Registration-based Few-shot Medical Image Segmentation

MM ’26, November 10–14, 2026, Rio de Janeiro, Brazil

Figure 6: t-SNE visualizations of feature embeddings learned from the segmentation branch for the Brain (a) and Cardiac (b) datasets. The legend reflects the hierarchical relationships among anatomical structures.

SyN

Bi-JROS

BRBS

Ours

Table 3: Registration failure case analysis on Brain (Image A, Image C) and Cardiac (Image B, Image D) datasets. "↓" indicates the decrease in Dice compared to the average Dice over the test set, while "⇑" indicates the increase. : Best performance

: Second best performance

BRBS

Bi-JROS

Pseudo-label (from registration)

Cases

BRBS

Ours

Segmentation

Figure 7: Confusion matrices of small anatomical structures (<1% volume) on the Brain dataset under the 1-shot setting for both registration and segmentation. Pseudo-labels are derived from registration. As shown in Table 2, both atlas-based and few-shot methods consistently outperform registration-only approaches, underscoring the importance of label supervision for anatomically consistent deformation. Building on this paradigm, H2 AL further leverages hierarchical anatomical information by first aligning coarse parent structures and then refining finer child structures, achieving the highest Dice and NCC scores. Importantly, these gains are not obtained at the expense of topology preservation. H2 AL maintains a low percentage of non-diffeomorphic regions (|𝐽𝜙 | ≤ 0), outperforming most competing methods. This demonstrates a favorable balance between deformation flexibility and topology preservation, leading to more reliable and anatomically consistent registration. Qualitative Results. As illustrated in Fig. 4, H2AL produces segmentation results that are most consistent with the ground truth across both datasets, particularly for small and structurally complex anatomical regions. Fully supervised methods are limited by scarce annotations, while methods relying solely on Euclidean representations tend to over-smooth fine boundaries due to insufficient modeling of hierarchical context. In contrast, H2AL effectively captures both local and global anatomical structures by jointly leveraging Euclidean and hyperbolic spaces, resulting in more precise and structurally consistent segmentation. The qualitative registration results in Fig. 5 further demonstrate that H2AL achieves more accurate alignment, especially in regions with ambiguous boundaries and small anatomical structures. This improvement stems from its ability to model hierarchical relationships, leading to better structural correspondence and higherquality pseudo-labels that further benefit segmentation. As a result, H2AL produces anatomically more consistent registration results.

ΔDice

MAE

Dice

ΔDice

MAE

Dice

ΔDice

Image A

0.0582

83.45

0.81↓

0.0435

82.42

1.13↓

0.0545

84.47

0.72⇑

Image B

0.0326

86.40

0.92↓

0.0260

85.68

4.13↓

0.0265

90.31

0.07⇑

Image C

0.0481

83.06

1.20↓

0.0403

82.13

1.42↓

0.0500

84.36

0.83↓

Image D

0.0182

84.23

6.15↓

0.0213

78.16

11.65↓

0.0260

85.38

4.86↓

Image A

1-shotBrain

Bi-JROS

Dice

Image B

5-shotCardiac

TBIOneShot

Ours

MAE

Error map

Segmentation visualization

Figure 8: Visualization of the most severe registration failure cases from each dataset, with Image A from Brain and Image B from Cardiac.

5.2

Challenging-case Analysis

Performance on Small Anatomical Structures. To further evaluate performance on small anatomical regions, we present confusion matrices of representative structures in Fig. 7. Our method shows higher agreement with the ground truth than competing approaches, indicating more accurate segmentation and improved registration performance on small structures. We attribute this improvement to two key factors. First, the strong registration capability enables high-quality pseudo-label generation. Second, joint modeling of hierarchical structures facilitates effective integration of structural priors. As shown in Fig. 4 and Fig. 5, our method better preserves fine structural boundaries in small regions while avoiding the over-smoothing and misalignment observed in competing methods, demonstrating its effectiveness in capturing fine-grained details with strong structural consistency. Robustness under Registration Failure. A practical concern for registration-based FMIS is whether segmentation degrades under registration failure. To investigate this, we select the two most

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Wang et al.

Table 4: Ablation study results on the Brain dataset under the Atlas setting. “E” and “H” denote Euclidean and hyperbolic spaces, respectively. S : Small structure Methods baseline

Setting Reg

Seg

-

-

L : Large structure

T : Total

Reg-Dice (%)

Space

Seg-Dice (%)

S

L

T

S

L

T

E

77.18

78.53

78.01

78.06

81.29

80.05

+GA

-

-

E

77.76

79.10

78.58

78.63

82.05

80.73

+Hyperbolic

✓ ✗ ✓

✗ ✓ ✓

H H H

78.06 77.88 78.28

79.46 79.16 79.52

78.92 78.66 79.04

79.15 79.29 79.34

81.90 81.92 81.96

80.84 80.91 80.95

+TSHCL

✓ ✗ ✓

✗ ✓ ✓

E&H E&H E&H

79.52 78.54 79.59

80.67 79.71 81.89

80.23 79.26 80.75

79.37 80.64 81.07

82.15 83.41 83.69

81.08 82.34 82.69

+GIB

✓ ✗ ✓

✗ ✓ ✓

E&H E&H E&H

81.16 80.45 81.21

82.04 81.31 82.42

81.70 80.98 81.96

81.30 82.29 82.37

84.16 85.01 85.30

83.05 83.96 84.17

83.72

5.4

83.04 75.17

0.68 Higher 62.81% Faster

Figure 9: Growth curves of segmentation Dice for the SOTA RFMIS [10] training strategy and our proposed strategy on the Brain dataset (Atlas setting). severe failure cases per dataset based on MAE error maps, corresponding to the largest discrepancies between warped source and target images. Table 3 reports Dice variations under these extreme scenarios, compared with state-of-the-art methods, along with qualitative results of the worst case per dataset in Fig. 8. Despite substantial registration errors, H2 AL consistently achieves superior segmentation performance and even yields positive Dice gains in two of four cases. This robustness stems from the hierarchical modeling strategy, which first aligns parent structures to establish stable global anchors and then refines child structures, mitigating error propagation caused by misalignment.

5.3

is especially critical for small anatomical structures. By enabling global hierarchical anatomical consistency and enhanced anatomical discrimination, our method better captures them, leading to improved segmentation performance. Why Gradient Aggregation Matters? Gradient aggregation (GA) plays a key role in stabilizing optimization across heterogeneous geometric spaces. As shown in Fig. 9, it accelerates convergence and improves the final performance, as separately induced task updates may lead to inconsistent optimization dynamics and unstable training. To overcome this issue, we propose a GA strategy that integrates task-specific gradients enriched with semantic and hierarchical cues to jointly optimize the shared encoder for registration and segmentation. Such a design encourages more coordinated dual-task learning, alleviates optimization inconsistency, and enhances training stability. This is well aligned with the motivation in Fig. 3, underscoring the necessity of coordinated optimization in multi-space learning.

Mechanism Analysis of H2 AL

Why Infusing Hyperbolic into Euclidean Matters? Euclidean and hyperbolic geometries provide complementary inductive biases for representation learning. As shown in Table 4, Euclidean modeling already provides a strong baseline, while hyperbolic modeling further improves performance, particularly in registration, due to its ability to capture hierarchical structures. However, each geometry has inherent limitations. As illustrated in Fig. 6, Euclidean embeddings exhibit compact clusters but weak global structure, whereas hyperbolic embeddings capture clear hierarchies at the cost of compactness. In contrast, our method integrates both spaces via H2I, achieving both compact intra-class clustering and well-structured inter-class separation. This balance

Ablation Study

Table 4 presents the component-wise ablation results. The baseline is constructed by pre-training a shared encoder, then freezing it and alternately optimizing the registration and segmentation decoders. Effect of GA. After introducing the GA strategy, the model performs end-to-end joint optimization within a single stage. Compared with the baseline, both registration and segmentation show consistent performance improvements. These results indicate that jointly optimizing the two tasks leads to more effective feature learning, suggesting that the two objectives provide complementary supervisory signals rather than competing ones. Effect of H2I. Table 4 further reports the performance across anatomical structures of different scales. Incorporating TSHCL and GIB into H2I brings consistent gains in both registration and segmentation, especially for small-scale structures. This verifies that H2I can effectively bridge the complementary strengths of Euclidean and hyperbolic spaces by preserving the semantic richness of Euclidean representations while injecting the hierarchy-aware priors encoded in hyperbolic geometry. Such a design enables the model to learn more discriminative and anatomically structured features, thereby simultaneously improving deformation quality and segmentation performance.

6

Conclusion

In this paper, we propose H2AL that enhances both deformation plausibility and anatomical discrimination for dual-task learning. Specifically, we introduce a Hyperbolic Hierarchy-aware Infusion (H2I) module, which leverages the hierarchical capacity of hyperbolic space to learn precise hierarchy-aware representations and injects such priors into Euclidean space via a gated infusion block. Then, we develop an end-to-end training strategy with Gradient Aggregation (GA) to ensure consistent optimization between registration and segmentation. Extensive experiments on brain and cardiac datasets demonstrate the superior performance of our method, especially for small anatomical structures. More broadly, we believe that jointly modeling Euclidean semantics, hyperbolic hierarchy, and cross-task gradient interaction provides a promising and extensible direction for future medical image analysis.

H2AL: Hyperbolic Hierarchy-aware Aggregative Learning for Registration-based Few-shot Medical Image Segmentation

Acknowledgments This work was supported by the National Natural Science Foundation of China under Grant No. 61733002.

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