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

arXiv: https://arxiv.org/abs/2404.14435 · HTML: https://mlsanity.com/paper/2404.14435/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 76 references that are in the map.
- First posted on arXiv 19 Apr 2024.

## Builds on (most cited first, 24 of 24)

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [3D U-Net: Learning Dense Volumetric Segmentation from Sparse Annotation](https://mlsanity.com/paper/1606.06650/) (2016)
- [A Survey on Deep Learning in Medical Image Analysis](https://mlsanity.com/paper/1702.05747/) (2017)
- [PointCNN: Convolution On X-Transformed Points](https://mlsanity.com/paper/1801.07791/) (2018)
- [Point Transformer V3: Simpler, Faster, Stronger](https://mlsanity.com/paper/2312.10035/) (2023)
- [RandLA-Net: Efficient Semantic Segmentation of Large-Scale Point Clouds](https://mlsanity.com/paper/1911.11236/) (2019)
- [AMOS: A Large-Scale Abdominal Multi-Organ Benchmark for Versatile Medical Image Segmentation](https://mlsanity.com/paper/2206.08023/) (2022)
- [clDice -- A Novel Topology-Preserving Loss Function for Tubular Structure Segmentation](https://mlsanity.com/paper/2003.07311/) (2020)
- [Topology-Preserving Deep Image Segmentation](https://mlsanity.com/paper/1906.05404/) (2019)
- [Topology-Aware Segmentation Using Discrete Morse Theory](https://mlsanity.com/paper/2103.09992/) (2021)
- [DeepVesselNet: Vessel Segmentation, Centerline Prediction, and Bifurcation Detection in 3-D Angiographic Volumes](https://mlsanity.com/paper/1803.09340/) (2018)
- [Deep Distance Transform for Tubular Structure Segmentation in CT Scans](https://mlsanity.com/paper/1912.03383/) (2019)
- [IntrA: 3D Intracranial Aneurysm Dataset for Deep Learning](https://mlsanity.com/paper/2003.02920/) (2020)
- [3D Medical Point Transformer: Introducing Convolution to Attention Networks for Medical Point Cloud Analysis](https://mlsanity.com/paper/2112.04863/) (2021)
- [RibSeg Dataset and Strong Point Cloud Baselines for Rib Segmentation from CT Scans](https://mlsanity.com/paper/2109.09521/) (2021)
- [Deep Rib Fracture Instance Segmentation and Classification from CT on the RibFrac Challenge](https://mlsanity.com/paper/2402.09372/) (2024)
- [AxonEM Dataset: 3D Axon Instance Segmentation of Brain Cortical Regions](https://mlsanity.com/paper/2107.05451/) (2021)
- [Point-Unet: A Context-aware Point-based Neural Network for Volumetric Segmentation](https://mlsanity.com/paper/2203.08964/) (2022)
- [RibSeg v2: A Large-scale Benchmark for Rib Labeling and Anatomical Centerline Extraction](https://mlsanity.com/paper/2210.09309/) (2022)
- [Efficient Anatomical Labeling of Pulmonary Tree Structures via Deep Point-Graph Representation-based Implicit Fields](https://mlsanity.com/paper/2309.17329/) (2023)
- [Beyond pixel-wise supervision for segmentation: A few global shape descriptors might be surprisingly good!](https://mlsanity.com/paper/2105.00859/) (2021)
- [A Two-step Surface-based 3D Deep Learning Pipeline for Segmentation of Intracranial Aneurysms](https://mlsanity.com/paper/2006.16161/) (2020)

## Abstract (arXiv)

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 ( C2 ) 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.