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AGENet: Adaptive Edge-aware Geodesic Distance Learning for Few-Shot Medical Image Segmentation

Ziyuan Gao

TL;DR

AGENet tackles the challenge of precise boundary segmentation in few-shot medical imaging by introducing an edge-aware geodesic distance learning framework that guides prototype extraction through anatomically constrained distance fields. The method combines EDT-based initialization, edge-aware speed control, iterative refinement, and adaptive parameter learning to produce spatial importance maps, paired with a dual-prototype strategy of global and adaptive grid prototypes. A three-part loss (segmentation, edge-aware, alignment) and a comprehensive ablation study demonstrate the critical contributions of geodesic learning, adaptive grids, and parameter adaptation, yielding state-of-the-art Dice scores and improved boundary accuracy across nine diverse datasets with limited annotations. The lightweight geometric modeling approach achieves superior clinical practicality by delivering accurate segmentation with reduced computational demands compared to heavier architectures. This work enhances cross-domain generalization and boundary precision in medical image segmentation under data scarcity, enabling more reliable clinical decision support.

Abstract

Medical image segmentation requires large annotated datasets, creating a significant bottleneck for clinical applications. While few-shot segmentation methods can learn from minimal examples, existing approaches demonstrate suboptimal performance in precise boundary delineation for medical images, particularly when anatomically similar regions appear without sufficient spatial context. We propose AGENet (Adaptive Geodesic Edge-aware Network), a novel framework that incorporates spatial relationships through edge-aware geodesic distance learning. Our key insight is that medical structures follow predictable geometric patterns that can guide prototype extraction even with limited training data. Unlike methods relying on complex architectural components or heavy neural networks, our approach leverages computationally lightweight geometric modeling. The framework combines three main components: (1) An edge-aware geodesic distance learning module that respects anatomical boundaries through iterative Fast Marching refinement, (2) adaptive prototype extraction that captures both global structure and local boundary details via spatially-weighted aggregation, and (3) adaptive parameter learning that automatically adjusts to different organ characteristics. Extensive experiments across diverse medical imaging datasets demonstrate improvements over state-of-the-art methods. Notably, our method reduces boundary errors compared to existing approaches while maintaining computational efficiency, making it highly suitable for clinical applications requiring precise segmentation with limited annotated data.

AGENet: Adaptive Edge-aware Geodesic Distance Learning for Few-Shot Medical Image Segmentation

TL;DR

AGENet tackles the challenge of precise boundary segmentation in few-shot medical imaging by introducing an edge-aware geodesic distance learning framework that guides prototype extraction through anatomically constrained distance fields. The method combines EDT-based initialization, edge-aware speed control, iterative refinement, and adaptive parameter learning to produce spatial importance maps, paired with a dual-prototype strategy of global and adaptive grid prototypes. A three-part loss (segmentation, edge-aware, alignment) and a comprehensive ablation study demonstrate the critical contributions of geodesic learning, adaptive grids, and parameter adaptation, yielding state-of-the-art Dice scores and improved boundary accuracy across nine diverse datasets with limited annotations. The lightweight geometric modeling approach achieves superior clinical practicality by delivering accurate segmentation with reduced computational demands compared to heavier architectures. This work enhances cross-domain generalization and boundary precision in medical image segmentation under data scarcity, enabling more reliable clinical decision support.

Abstract

Medical image segmentation requires large annotated datasets, creating a significant bottleneck for clinical applications. While few-shot segmentation methods can learn from minimal examples, existing approaches demonstrate suboptimal performance in precise boundary delineation for medical images, particularly when anatomically similar regions appear without sufficient spatial context. We propose AGENet (Adaptive Geodesic Edge-aware Network), a novel framework that incorporates spatial relationships through edge-aware geodesic distance learning. Our key insight is that medical structures follow predictable geometric patterns that can guide prototype extraction even with limited training data. Unlike methods relying on complex architectural components or heavy neural networks, our approach leverages computationally lightweight geometric modeling. The framework combines three main components: (1) An edge-aware geodesic distance learning module that respects anatomical boundaries through iterative Fast Marching refinement, (2) adaptive prototype extraction that captures both global structure and local boundary details via spatially-weighted aggregation, and (3) adaptive parameter learning that automatically adjusts to different organ characteristics. Extensive experiments across diverse medical imaging datasets demonstrate improvements over state-of-the-art methods. Notably, our method reduces boundary errors compared to existing approaches while maintaining computational efficiency, making it highly suitable for clinical applications requiring precise segmentation with limited annotated data.

Paper Structure

This paper contains 46 sections, 6 theorems, 25 equations, 11 figures, 7 tables.

Key Result

Lemma B.2

The speed function $\mathbf{F}_{i,j} = \frac{1}{1 + \boldsymbol{\beta} \|\nabla \mathbf{M}_{i,j}\|_2}$ satisfies: for $\boldsymbol{\beta} \in [0.5, 5.0]$.

Figures (11)

  • Figure 1: This figure compares two prototype extraction methods: (a) Conventional prototype-based approach (e.g., PANet) that relies on uniform spatial averaging to extract a single global prototype from the support mask. (b) Our method employs edge-aware geodesic distance learning with adaptive multi-scale extraction.
  • Figure 2: Pipeline of AGENet. Our approach fundamentally transforms prototype extraction by incorporating spatial importance through geodesic distance fields, which respect anatomical boundaries and spatial guidance.
  • Figure 3: Comparison of distance computation. (a) Uniform distance computation creates regular propagation patterns treating all pixels equally. (b) Edge-aware computation produces boundary-aware spatial weighting that respects anatomical constraints.
  • Figure 4: Visualization from left to right on CVC-300, Drishti-GS, PH2(Melanomas), PH2(Atypical Nevus), DCA1 and CHASE-DB1 datasets. Top row to bottom: Support, Ground-truth. Ours prediction, RPT's prediction and DSPNet's prediction.
  • Figure 5: Visualization from left to right on ABD-MRI, ABD-CT and ACDC datasets with all organs. Top row to bottom: Support, Ground-truth. Ours prediction, RPT's prediction and DSPNet's prediction.
  • ...and 6 more figures

Theorems & Definitions (9)

  • Definition B.1: EDT Edge Detection
  • Lemma B.2: Speed Function Bounds
  • Theorem B.3: Geodesic Refinement Convergence
  • Lemma B.4: Numerical Stability
  • Remark B.5
  • Definition B.6: Unified Prototype Space
  • Lemma B.7: Adaptive Density Bounds
  • Theorem B.8: Prototype Bounds
  • Corollary B.9: Prototype Convergence