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DeepVesselNet: Vessel Segmentation, Centerline Prediction, and Bifurcation Detection in 3-D Angiographic Volumes

Giles Tetteh, Velizar Efremov, Nils D. Forkert, Matthias Schneider, Jan Kirschke, Bruno Weber, Claus Zimmer, Marie Piraud, Bjoern H. Menze

arXiv:1803.09340v3cs.CV

TL;DR

DeepVesselNet targets slow, memory-intensive 3-D convolution, extreme vessel-versus-background imbalance, and limited accurate annotations in angiographic volumes. It combines cross-hair filters, a class-balancing loss with false-positive correction, and synthetic-data pretraining. Cross-hair filters improve speed and memory usage while retaining comparable accuracy, while synthetic-data transfer learning improves segmentation and detection results across angiography tasks.

  • Problem

    3-D angiographic analysis is hindered by slow and memory-intensive full 3-D convolutions, extreme class imbalance, and scarce accurately annotated training data.

  • Method

    DeepVesselNet uses orthogonal 2-D cross-hair filters, stable class balancing with false-positive-rate correction, and physiologically constrained synthetic vascular trees for transfer learning.

  • Results

    Cross-hair filters perform comparably to 3-D filters while improving speed and memory usage, and synthetic-data pretraining improves segmentation and detection results.

  • Takeaways & Limitations

    The approach supports vessel segmentation and feature analysis across varied angiographic data, including human-brain MRA and rat-brain X-ray tomographic microscopy.

Abstract

from arXiv · show

We present DeepVesselNet, an architecture tailored to the challenges faced when extracting vessel networks or trees and corresponding features in 3-D angiographic volumes using deep learning. We discuss the problems of low execution speed and high memory requirements associated with full 3-D convolutional networks, high-class imbalance arising from the low percentage of vessel voxels, and unavailability of accurately annotated training data - and offer solutions as the building blocks of DeepVesselNet. First, we formulate 2-D orthogonal cross-hair filters which make use of 3-D context information at a reduced computational burden. Second, we introduce a class balancing cross-entropy loss function with false positive rate correction to handle the high-class imbalance and high false positive rate problems associated with existing loss functions. Finally, we generate synthetic dataset using a computational angiogenesis model capable of generating vascular trees under physiological constraints on local network structure and topology and use these data for transfer learning. DeepVesselNet is optimized for segmenting and analyzing vessels, and we test the performance on a range of angiographic volumes including clinical MRA data of the human brain, as well as X-ray tomographic microscopy scans of the rat brain. Our experiments show that, by replacing 3-D filters with cross-hair filters in our network, we achieve over 23% improvement in speed, lower memory footprint, lower network complexity which prevents overfitting and comparable accuracy (with a Cox-Wilcoxon paired sample significance test p-value of 0.07 when compared to full 3-D filters). Our class balancing metric is crucial for training the network and transfer learning with synthetic data is an efficient, robust, and very generalizable approach leading to a network that excels in a variety of angiography segmentation tasks.

I. INTRODUCTION

DeepVesselNet addresses the practical barriers to extracting vessel networks and features from 3-D angiographic volumes: extreme class imbalance, unstable loss functions, and scarce expert annotations.

  • Vessels occupy less than 3% of patient-volume voxels, while centerlines and visible bifurcations represent progressively smaller and rarer targets.Even volumes containing 10^6 or more voxels may have only hundreds of visible bifurcations.
  • Existing class-balancing loss functions can become numerically unstable under this extreme background-class bias.The paper introduces a new loss function to address instability and demonstrates it on vascular-feature tasks.
  • Manual annotation of vessels, centerlines, and bifurcations requires substantial time and expertise, limiting supervised training data.Synthetic vascular-tree simulations provide accurately labeled data for network pretraining.
  • Transfer learning from synthetic data supports CNN training across angiography tasks ranging from CT micrographs to time-of-flight MRA.The synthesized and clinical MRA datasets are publicly available for research and validation.

II. PRIOR WORK AND OPEN CHALLENGES

Prior work established vessel segmentation methods but left dedicated 3-D architectures and learning strategies for vessel networks and features underdeveloped.

  • Vessel segmentation has been studied with interactive propagation, statistical models, path tracing, Hessian filters, and optimally oriented flux detectors.These approaches reflect multiple generations of medical-image processing methods.
  • The paper’s overview covers vessel segmentation, centerline prediction, and bifurcation detection, with bifurcations represented by predicted neighborhood cubes.
  • Existing deep-learning architectures are not dedicated to 3-D volumetric vessel segmentation and may be suboptimal for vasculature.The paper therefore identifies a need for specialized architectures and training strategies.
  • Deep-learning extraction of vessel centerlines had not been explored, partly because annotated 3-D training data are difficult to obtain.
  • Bifurcations are rare, point-like features with substantial variation in size and shape, making volumetric detection difficult.They are vascular-tree nodes useful for network extraction, structural analysis, image-registration landmarks, and identifying altered flow conditions.

A. Cross-hair Filters Formulation

Cross-hair filters approximate 3-D convolution using orthogonal 2-D kernels, reducing computation and memory while retaining 3-D context at the layer level.

  • Computational complexity: 27 multiplications and 26 additions are required per voxel for a 3 × 3 × 3 classical 3-D kernel.
  • Cross-hair formulation: A cross-hair convolution approximates a 3-D kernel with 2-D kernels applied along the i, j, and k axes.The filter stack uses M_i, M_j, and M_k as orthogonal 2-D kernels.
  • Computational complexity: Less than 158 × 10^6 multiplications and 156 × 10^6 additions are required for a 128 × 128 × 128 volume with a 5 × 5 × 5 cross-hair kernel.This reduces computation by more than 100 × 10^6 multiplications and additions versus classical 3-D convolution.
  • Efficient implementation: Cross-hair filters combine three plane-wise convolution results through weighted matrix addition using a single volume in memory.The experiments use β_c = β_s = β_a = 1, while kernel rotation matches different slice orientations.
  • 2.5-D comparison: Unlike 2.5-D preprocessing, cross-hair filters operate at the network-layer level and retain 3-D information throughout the network.For filter size k, cross-hair filters use 3k^2 parameters and scale quadratically rather than cubically with filter size.

B. Extreme Class Balancing with Stable Weights

DeepVesselNet addresses extreme voxel-level class imbalance by replacing unstable class-weighted losses with a numerically stable, false-positive-corrected objective.

  • Problem: Less than 2.5% of voxels belong to objects of interest in the datasets used for this work.This extreme imbalance can bias standard cross-entropy toward background predictions.
  • Problem: Standard cross-entropy can favor background detection under extreme imbalance, producing high precision but low recall for the object of interest.
  • Class balancing: Class-balancing weights β and 1−β are calculated from the sizes of the negative and positive label sets.The cited formulation weights the two classes according to their observed voxel counts.
  • Proposed loss: The proposed loss combines a numerically stable class-balanced term with false-positive-rate correction.L1 scales voxel-wise costs with dataset or batch size, while L2 penalizes false predictions based on their distance from probability 0.5.

C. Synthetic Data for Transfer Learning

The paper generates synthetic vascular trees using a physiologically constrained angiogenesis simulator and reconstructs volumetric data for CNN training.

  • Synthetic tree generation: The simulator generates vascular trees through a biologically inspired angiogenesis process under physiological constraints.It incorporates arterial oxygen supply, Murray’s law, bifurcation-angle constraints, and a minimum-volume principle.
  • Synthetic tree generation: The generated network records node positions, node types, connectivity, and vessel radii.Nodes include roots, bifurcations, intermediate nodes, and leaves, with edges linking node pairs.
  • Synthetic data construction: The abstract vascular network is reconstructed as a 3-D volume for training convolutional neural networks.

A. Datasets

The study uses synthetic, clinical MRA, and µCTA datasets, separating test cases from training data and highlighting severe label sparsity in vascular tasks.

  • Dataset composition: Three datasets are used to train and test the networks, with test cases kept separate from training data.The datasets include synthetic data, clinical MRA, and µCTA volumes.
  • Dataset availability: The datasets are available for public research through the paper’s GitHub page.
  • Synthetic Dataset: Synthetic volumes provide labels for vessel segmentation, centerlines, and bifurcation detection.Twenty of 136 synthetic volumes are reserved for testing, while the remainder support pretraining.
  • Synthetic Dataset: Vessel, centerline, and bifurcation labels occupy 2.1%, 0.2%, and 0.05% of total intensities, respectively.

B. Network Architecture and Implementations

DeepVesselNet uses fully convolutional architectures with cross-hair filters, retaining voxel resolution while replacing conventional 3-D convolutions in comparative networks.

  • DeepVesselNet-FCN: The architecture avoids down-sampling because vessel centerlines and bifurcations require fine voxel-level detail.
  • DeepVesselNet-FCN: DeepVesselNet-FCN uses four convolutional layers and a sigmoid classification layer without down-sampling or up-sampling.Zero-padding preserves the output image size relative to the input.
  • Comparative architectures: DeepVesselNet-VNet and DeepVesselNet-UNet replace all 3-D convolutions in VNet and 3-D UNet with cross-hair filters.These variants are used to compare parameter size and execution time with the original architectures.
  • Training implementation: Training extracts non-overlapping 64 × 64 × 64 boxes during training, while full volumes can be processed at test time.

C. Evaluating the DeepVesselNet Components

Component experiments evaluate cross-hair filters, false-positive-rate correction, and synthetic pretraining using memory, speed, accuracy, precision-recall balance, and convergence measures.

  • Fast Cross-hair Filters: Cross-hair filters reduce memory footprint by more than 27% and improve computational speed by more than 23% relative to corresponding full 3-D architectures.The reported parameter reductions are 16.56m versus 22.89m and 4.45m versus 7.41m for the compared architectures.
  • FP Rate Correction Loss Function: FP rate correction keeps the precision-to-recall ratio closer to 1.0 than training with the class-balancing term alone.The authors associate this balance with reduced bias toward background or foreground and prevention of over-segmentation.
  • Pretraining on Synthetic Data: Synthetic pretraining produces a Dice score of 86.68%, compared with 86.39% when training from scratch on clinical MRA.
  • Pretraining on Synthetic Data: Training from scratch requires about 600 additional iterations, or 50% longer, for convergence than synthetic pretraining.

D. Evaluating DeepVesselNet Performance

DeepVesselNet is evaluated for vessel segmentation, centerline prediction, and bifurcation detection, with task-specific comparisons against available architectures and methods. The results emphasize centerline performance and quantify a precision–recall trade-off affecting overall detection quality.

  • Evaluation scope: DeepVesselNet is evaluated primarily on vessel segmentation, with centerline prediction and bifurcation detection providing further validation of the methodology.The authors note that these feature-extraction tasks are classically handled through vessel skeletonization and graph search.
  • Vessel segmentation: Table III defines pretrained scores as test-set results after pretraining and finetuned scores as results after training with annotated TOF-MRA data.The table evaluates TOF-MRA within the brain region only.
  • Centerline prediction: Table IV reports that architectures with sub-sampling suffer performance loss in centerline prediction because fine details are crucial for the task.This provides the stated interpretation for the centerline-prediction comparison.
  • Centerline prediction: 86.03% versus 82.35% centerline recall shows that the alternative method detects more centerline points than DeepVesselNet-FCN.The comparison favors the alternative method on centerline-point detection.
  • Centerline prediction: 48.07% versus 77.63% precision reflects DeepVesselNet-FCN’s advantage over the alternative method in limiting false positives.The lower precision is attributed to a higher false positive rate.
  • Centerline prediction: 61.68% versus 79.92% Dice score gives DeepVesselNet-FCN the higher overall centerline-prediction performance.The cited comparison links the lower alternative-method score to its higher false positive rate.

V. SUMMARY AND CONCLUSIONS

The paper concludes that DeepVesselNet’s cross-hair filters reduce computational demands while preserving comparable performance, and that class balancing and synthetic-data pretraining support vessel-feature analysis. Results also identify weaknesses associated with sub-sampling and motivate future unified multiclass modeling.

  • Summary and conclusions: Cross-hair filters perform comparably to 3-D filters while significantly improving speed and memory usage.The authors state that the reduced resource requirements ease scaling to larger datasets.
  • Summary and conclusions: DeepVesselNet-FCN achieves significantly higher clinical-MRA vessel-segmentation results than the corresponding comparison architectures, with p-value less than 0.001.DeepVesselNet-VNet and DeepVesselNet-UNet obtain results comparable to VNet and UNet, respectively.
  • Summary and conclusions: DeepVesselNet-FCN significantly outperforms other architectures on synthetic centerline prediction, where sub-sampling can remove crucial voxel-sized details.The same pattern is reported for synthetic bifurcation detection.
  • Summary and conclusions: Transfer learning from synthetically generated data improves segmentation and detection results, especially when manually annotated data are difficult to obtain.The conclusion presents synthetic-data pretraining as applicable across segmentation and detection results.
  • Observed limitations: MRA centerline predictions generally contain missing points that may be improved through annotated-data finetuning or post-processing.The figure reports this behavior for DeepVesselNet-FCN on MRA TOF test data.
  • Future work: The current implementation uses three subsequent binary tasks, while future work proposes a single hierarchical multiclass vessel-tree task.The planned unified approach would handle segmentation, centerline prediction, and bifurcation detection together.
  • Observed limitations: Synthetic centerline and bifurcation detections are better in smaller than larger vessels, reflecting an imbalance in training examples.The authors suggest reweighting larger-vessel features or sampling more large-vessel examples.
  • Observed limitations: In densely intersecting MRA regions, the network predicts a large bifurcation rather than resolving the intersecting vessels separately.The behavior is reported in the circled regions of the zoomed images.
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