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Dense Dilated Network with Probability Regularized Walk for Vessel Detection

Lei Mou, Li Chen, Jun Cheng, Zaiwang Gu, Yitian Zhao, Jiang Liu

arXiv:1910.12010v1eess.IVcs.CV

TL;DR

Tiny retinal vessels can be missed, and broken vessel connectivity matters for disease screening and diagnosis. The paper combines DDNet with probability regularized walk to detect vessels and reconnect breaks; it reports better vessel-detection results than other methods.

  • Problem

    Deep-learning vessel detectors can miss tiny vessels and produce fractures, although tiny vessels and connectivity matter for disease diagnosis and screening.

    Source: §I · p. 2

  • Method

    The method uses DDNet for an initial vessel map and probability regularized walk, integrating network probabilities and local vessel directions, to reconnect breaks.

    Source: §I · p. 2, §IV · p. 5

  • Results

    The authors report that the proposed method achieves better vessel-detection results than other methods.

    Source: §I · p. 2, §VI · p. 9

  • Takeaways & Limitations

    The authors conclude that probability regularized walk reconnects fractured vessels and makes segmentation results better.

    Source: §VI · p. 9

Abstract

from arXiv · show

The detection of retinal vessel is of great importance in the diagnosis and treatment of many ocular diseases. Many methods have been proposed for vessel detection. However, most of the algorithms neglect the connectivity of the vessels, which plays an important role in the diagnosis. In this paper, we propose a novel method for retinal vessel detection. The proposed method includes a dense dilated network to get an initial detection of the vessels and a probability regularized walk algorithm to address the fracture issue in the initial detection. The dense dilated network integrates newly proposed dense dilated feature extraction blocks into an encoder-decoder structure to extract and accumulate features at different scales. A multiscale Dice loss function is adopted to train the network. To improve the connectivity of the segmented vessels, we also introduce a probability regularized walk algorithm to connect the broken vessels. The proposed method has been applied on three public data sets: DRIVE, STARE and CHASE_DB1. The results show that the proposed method outperforms the state-of-the-art methods in accuracy, sensitivity, specificity and also are under receiver operating characteristic curve.

I. INTRODUCTION

Retinal-vessel segmentation matters for ocular-disease diagnosis, but tiny vessels and vessel connectivity remain challenging. The paper proposes DDNet for an initial vessel map and probability regularized walk to reconnect broken vessels, and reports better detection than other methods.

I. INTRODUCTION

  • Retinal-vessel structure is associated with diabetes, and vessel segmentation also supports subsequent artery/vein classification for diagnosis and treatment.Source: §I · p. 1
  • The introduction notes that traditional detection algorithms often require manually tuned parameters based on local datasets, limiting scalability.Source: §I · p. 1
  • Tiny vessels can be missed by deep-learning methods, fracturing vessels; improving their detection and reconnecting breaks are important for disease detection.Source: §I · p. 2
  • The method uses DDNet to create an initial vessel map, then applies probability regularized walk to connect broken vessels using network probabilities and local vessel directions.Source: §I · p. 2
  • The authors report that the proposed method outperforms other methods for retinal vessel detection.Source: §I · p. 2

A. Encoder-Decoder

The reviewed work spans encoder-decoder segmentation, retinal-vessel detection, and vessel reconnection. The proposed DDNet combines an encoder-decoder backbone with an integrated dense dilated block and a loss computation component.

A. Encoder-Decoder

  • Encoder-decoder frameworks are end-to-end segmentation algorithms; encoders extract shallow and deep image features, while decoder design also affects segmentation.Source: A. Encoder-Decoder · p. 2

B. Vessel Detection

  • Prior retinal-vessel methods include encoder-decoder and multi-task approaches; the authors distinguish their method by explicitly addressing vessel connectivity.Source: B. Vessel Detection · p. 3

C. Vessel Reconnection

  • Prior reconnection work includes spectral-clustering segment matching, automatic broken-vessel reconnection, and random-walk approaches to vessel segmentation.Source: C. Vessel Reconnection · p. 3

III. DENSE DILATED NETWORK

  • DDNet has an encoder-decoder backbone for feature extraction and up-sampling, an integrated dense dilated block, and a loss-computation component.Source: §III · p. 3

A. Backbone Encoder-Decoder

The encoder-decoder backbone uses ResNet blocks, while dense dilated blocks combine multiscale features without reducing feature-map resolution. Training uses a multiscale Dice loss across decoder layers.

A. Backbone Encoder-Decoder

B. Dense Dilated Block

  • The DDB arranges four blocks of three dilated convolutions at rates 1, 2, and 5, reusing early features while expanding receptive fields without reducing feature-map resolution.Source: B. Dense Dilated Block · p. 4

C. Multi-Scale Dice Loss

  • Training applies Dice loss at each decoder scale using resized labels; Dice is chosen for foreground-background imbalance, with equal weights across layers.Source: C. Multi-Scale Dice Loss · p. 4

IV. PROBABILITY REGULARIZED WALK

The probability regularized walk (PRW) addresses broken vessel connectivity by combining DDNet probabilities with local vessel directions. It iteratively guides walkers between connected components to propose reconnections, with stopping conditions intended to avoid unsuitable links.

IV. PROBABILITY REGULARIZED WALK

  • PRW uses DDNet probability outputs and local vessel directions to reconnect broken segments, addressing connectivity not considered by many segmentation algorithms.It simulates a walker rather than applying a random-walk algorithm in the strict sense.Source: §IV · pp. 4–5
  • A second-order polynomial fitted to Li estimates the missing-vessel direction; pixels of Li inside the ROI seed walkers toward the curve’s intersection with L1.Source: §IV · p. 5
  • Each step blends direction probability with DDNet’s vessel-pixel probability, then moves the walker to the 8-connected neighbor with the highest combined probability.The authors set α = 0.2 empirically.Source: §IV · pp. 5–6
  • Walking stops when surrounding DDNet probabilities remain below 0.1; across k fracture regions of length l, PRW has time complexity O(k × l^2).Source: §IV · p. 6

A. Dataset

The experiments use DRIVE, STARE, and CHASE_DB1, with fixed DRIVE partitions and four-fold cross-validation for STARE and CHASE_DB1. The first observer’s annotations serve as ground truth.

A. Dataset

  • The evaluation uses the public DRIVE, STARE, and CHASE DB1 datasets.Source: A. Dataset · p. 6
  • DRIVE contains 40 images, retaining its original split of 20 training and 20 testing images.Images are 565 × 584 pixels.Source: A. Dataset · p. 6
  • STARE contains 20 images, half with pathological indications; four-fold cross-validation uses 15 images for training and 5 for testing per fold.Source: A. Dataset · p. 6
  • CHASE DB1 contains 28 images; each cross-validation fold uses 21 images for training and 7 for testing.Source: A. Dataset · p. 6
  • Ground truth for all datasets is the manual annotation from the first observer.Source: A. Dataset · p. 6

B. Evaluation Metrics

The section defines thresholded classification metrics for vessel segmentation and introduces Err to evaluate PRW reconnection in fracture regions.

B. Evaluation Metrics

  • Accuracy, sensitivity, and specificity evaluate vessel segmentation; Acc is the proportion of correctly classified pixels.Acc = (TP + TN) / (TP + FP + TN + FN).Source: B. Evaluation Metrics · p. 6
  • AUC measures the area under the receiver operating characteristic curve.Source: B. Evaluation Metrics · p. 6
  • Err is introduced to quantify PRW performance in reconnecting vessels within fracture regions.Source: B. Evaluation Metrics · p. 6

C. Training and Testing Phases

DDNet is trained on augmented retinal images with multiscale labels, then produces a vessel map that PRW converts into a binary map of reconnected vessels.

C. Training and Testing Phases

  • Training uses Adam for up to 1,000 epochs, with learning rate 0.001, weight decay 0.0005, and batch size 6.Images are resized to 512 × 512; batch size is limited by GPU memory.Source: C. Training and Testing Phases · p. 6
  • At testing, OTSU thresholding binarizes DDNet output before PRW returns a binary map of reconnected vessels.Source: C. Training and Testing Phases · pp. 6–7
  • Training augmentation applies random rotations from −45° to 45° and contrast changes in [−2, 2], with labels resized to three scales.Testing inputs are resized to 512 × 512 without enhancement; DDNet averages 145.61 ms inference time with 56.03M parameters and 476.08G FLOPs.Source: C. Training and Testing Phases · p. 7

D. Hyperparameters Setting

The selected PRW settings are l = 100 and α = 0.2, balancing fracture-region coverage and reconnection error against computational cost.

D. Hyperparameters Setting

  • The ROI threshold l controls detection range, while α controls walker movement; too-small l misses fractures and excessive α can divert walkers from vessel trajectories.Source: D. Hyperparameters Setting · p. 7
  • Increasing l raises Acc and Sen but also increases PRW time; the red point marks the paper’s selected threshold.The tested l values range from 0 to 160 in steps of 20, and l = 100 is selected.Source: D. Hyperparameters Setting · p. 7, Figure 5 · p. 7
  • PRW performs best for vessel reconnection at l = 100 and α = 0.2.The reconnection error is lowest at α = 0.2; inference time increases exponentially when α > 0.2.Source: D. Hyperparameters Setting · pp. 7–8

E. Ablation Studies

The ablations test ResNet blocks, the dense dilated block, and multiscale Dice loss as components of the proposed network.

1) Ablation study for replacing original blocks with ResNet blocks:

  • ResNet blocks raise Acc, Sen, Spe, and AUC over the original U-Net on DRIVE.ResUNet scores 0.9501, 0.7887, 0.9632, and 0.9665, respectively, versus U-Net scores of 0.9485, 0.7356, 0.9602, and 0.9641.Source: 1) Ablation study for replacing… · p. 8

2) Ablation study for dense dilated block:

  • The dense dilated block improves results over the ResUNet baseline and performs better than cascade and parallel modes.The comparison uses 12 dilated convolutional layers for each cascade and parallel mode.Source: 2) Ablation study for dense dilated… · p. 8

3) Ablation study for multi-scale dice loss:

4) Ablation study for probability regularized walk:

PRW improves vessel reconnection, and the proposed method improves segmentation consistently across three datasets. The conclusion also notes that PRW remains a post-processing stage after DDNet.

4) Ablation study for probability regularized walk:

F. Comparison With State-of-the-art Methods

VI. CONCLUSIONS

  • DDNet combines context from different layers with multiscale Dice loss, while PRW remains a post-processing stage after DDNet.The conclusion says dense dilated blocks improve deeper feature representation and feature reuse supports parameter efficiency; future work will integrate random walk into deep learning.Source: §VI · p. 9
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