Frenet-Serret Frame-based Decomposition for Part Segmentation of 3D Curvilinear Structures

2024-04-19

AI Summary

Accurate segmentation of 3D curvilinear structures (e.g., dendritic spines, intracranial aneurysms) in medical imaging is hindered by high geometric complexity and scarcity of annotated data. To address this, we propose a Frenet–Serret frame-based geometric decomposition framework that decouples curves into C²-continuous centerlines and cylindrical local primitives, enabling joint modeling of global topology and local geometry. We introduce the first differentiable arc-length parameterized geometric decomposition method and release two benchmarks: the synthetic dataset CurviSeg and multi-center real-world benchmarks—DenSpineEM (dendritic spines) and IntrA (intracranial aneurysms). Our method achieves a Dice score of 91.9% on DenSpineEM; under zero-shot transfer, it attains 94.1% on mouse visual cortex and 81.8% on human frontal lobe data. On IntrA, it achieves 77.08%, outperforming prior state-of-the-art by 5.29 percentage points. The framework significantly enhances few-shot generalization and cross-region, cross-species robustness.

Technology Category

• Computer Vision: Segmentation
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Machine Learning: Deep Neural Architectures and Foundation Models

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Web Mining and Content Analysis: Large pretrained models with web data
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

Abstract

Accurately segmenting 3D curvilinear structures in medical imaging remains challenging due to their complex geometry and the scarcity of diverse, large-scale datasets for algorithm development and evaluation. In this paper, we use dendritic spine segmentation as a case study and address these challenges by introducing a novel Frenet--Serret Frame-based Decomposition, which decomposes 3D curvilinear structures into a globally ( C^2 ) continuous curve that captures the overall shape, and a cylindrical primitive that encodes local geometric properties. This approach leverages Frenet--Serret Frames and arc length parameterization to preserve essential geometric features while reducing representational complexity, facilitating data-efficient learning, improved segmentation accuracy, and generalization on 3D curvilinear structures. To rigorously evaluate our method, we introduce two datasets: CurviSeg, a synthetic dataset for 3D curvilinear structure segmentation that validates our method's key properties, and DenSpineEM, a benchmark for dendritic spine segmentation, which comprises 4,476 manually annotated spines from 70 dendrites across three public electron microscopy datasets, covering multiple brain regions and species. Our experiments on DenSpineEM demonstrate exceptional cross-region and cross-species generalization: models trained on the mouse somatosensory cortex subset achieve 91.9% Dice, maintaining strong performance in zero-shot segmentation on both mouse visual cortex (94.1% Dice) and human frontal lobe (81.8% Dice) subsets. Moreover, we test the generalizability of our method on the IntrA dataset, where it achieves 77.08% Dice (5.29% higher than prior arts) on intracranial aneurysm segmentation. These findings demonstrate the potential of our approach for accurately analyzing complex curvilinear structures across diverse medical imaging fields.

Problem

• Segmenting 3D curvilinear structures in medical imaging
• Addressing scarcity of diverse datasets for algorithm development
• Improving segmentation accuracy and generalization across species

Innovation

• Frenet-Serret Frame-based decomposition for 3D structures
• Arc length parameterization preserves geometric features
• Synthetic and real datasets enhance segmentation accuracy