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Genetic U-Net: Automatically Designed Deep Networks for Retinal Vessel Segmentation Using a Genetic Algorithm

Jiahong Wei, Zhun Fan

arXiv:2010.15560v4eess.IVcs.CV

TL;DR

Retinal vessel segmentation remains difficult in complex fundus images, and manually designed CNNs can be parameter-heavy and time-consuming to develop. Genetic U-Net searches a compact, flexible U-shaped architecture space with an improved genetic algorithm. The discovered models outperform state-of-the-art models on several public datasets with less than 1% of the original U-Net parameters.

  • Problem

    Complex fundus images challenge retinal vessel segmentation, while manual CNN design is time-consuming and competitive models tend to use many parameters.

    Source: §I · pp. 1–2

  • Method

    Genetic U-Net uses an improved genetic algorithm to search a condensed but flexible U-shaped architecture space with restricted architecture-based parameters.

    Source: §I · p. 2

  • Results

    With less than 1% of original U-Net parameters, the discovered models outperformed state-of-the-art models on several public datasets.

    Source: §I · p. 2

  • Takeaways & Limitations

    Analysis of the discovered architectures identified operations and network patterns reported to improve retinal vessel segmentation.

    Source: §I · p. 2

Abstract

from arXiv · show

Recently, many methods based on hand-designed convolutional neural networks (CNNs) have achieved promising results in automatic retinal vessel segmentation. However, these CNNs remain constrained in capturing retinal vessels in complex fundus images. To improve their segmentation performance, these CNNs tend to have many parameters, which may lead to overfitting and high computational complexity. Moreover, the manual design of competitive CNNs is time-consuming and requires extensive empirical knowledge. Herein, a novel automated design method, called Genetic U-Net, is proposed to generate a U-shaped CNN that can achieve better retinal vessel segmentation but with fewer architecture-based parameters, thereby addressing the above issues. First, we devised a condensed but flexible search space based on a U-shaped encoder-decoder. Then, we used an improved genetic algorithm to identify better-performing architectures in the search space and investigated the possibility of finding a superior network architecture with fewer parameters. The experimental results show that the architecture obtained using the proposed method offered a superior performance with less than 1% of the number of the original U-Net parameters in particular and with significantly fewer parameters than other state-of-the-art models. Furthermore, through in-depth investigation of the experimental results, several effective operations and patterns of networks to generate superior retinal vessel segmentations were identified.

I. INTRODUCTION

Retinal vessel segmentation is challenging, while manually designed U-Net variants and architecture search approaches leave design and parameter-efficiency gaps. Genetic U-Net uses an improved genetic algorithm to search a compact, flexible U-shaped architecture space, and the discovered models outperform state-of-the-art models with far fewer parameters.

I. INTRODUCTION

  • Complex fundus images challenge vessel segmentation through subtle vessel-background contrast, intricate thin and cross-connected vessels, lesions, and uneven illumination.Manual inspection is also subjective, time-consuming, and laborious.Source: §I · p. 1
  • Manual architecture design requires domain knowledge and time, while existing medical-image NAS approaches often constrain topology or repeat identical blocks and retain many parameters.The authors identify these limitations as especially relevant where labeled fundus data are scarce.Source: §I · p. 2
  • Genetic U-Net combines a condensed but flexible U-shaped search space with an improved genetic algorithm to discover architectures tailored to retinal vessel segmentation.The search diversifies and optimizes different U-Net blocks individually while restricting architecture-based parameters.Source: §I · p. 2
  • With less than 1% of original U-Net parameters, discovered models outperformed state-of-the-art models on several public datasets.The reported comparison also describes the found models as having the least parameters.Source: §I · p. 2

A. Retinal Vessel Segmentation

  • Retinal vessel methods progressed from traditional image processing and handcrafted features to deep networks, with U-Net variants becoming mainstream but often complex and manually designed.Some existing models also use pretraining on external datasets.Source: A. Retinal Vessel Segmentation · pp. 2–3

B. Neural Architecture Search

  • Prior medical-image NAS work optimized layer operations or repeated one or two block types, whereas this work allows each block’s topology and operations to be optimized flexibly.The paper situates its approach among reinforcement-learning, evolutionary, and differentiable NAS methods.Source: B. Neural Architecture Search · p. 3

C. Genetic Algorithms

The method applies genetic search to a U-shaped encoder-decoder and encodes both block topology and operations. Its search space allows different blocks to vary while limiting architecture parameters.

C. Genetic Algorithms

  • To the authors’ knowledge, earlier genetic algorithms had not been used to optimize CNN architectures for retinal vessel segmentation.Prior GA applications cited include medical image segmentation, registration, disease detection, and denoising.Source: C. Genetic Algorithms · p. 3

III. THE PROPOSED METHOD

  • The proposed method defines an architecture search space, encodes each architecture as a binary string, and uses genetic operations including crossover, mutation, and selection.The method section presents these as the stages for searching competitive architectures.Source: §III · p. 3

1) Backbone of the Search Space:

  • The backbone has four stages and seven encoder-decoder blocks; decoder features are fused by element-wise addition to avoid concatenation’s larger feature maps.Skip connections supply encoder features to decoder stages, except at the last stage.Source: 1) Backbone of the Search Space · p. 3, Figure 1 · p. 4

2) The Building Blocks and Their Encoding:

  • Each block is encoded as a directed acyclic graph, with operation choices and connections represented in its gene; seven block genes form an architecture genotype.Sixteen operational sequences are available, and blocks can have diverse structures and operations.Source: 2) The Building Blocks and Their… · p. 4, Figure 3 · p. 5

3) Number of Architecture-based Parameters:

The search space constrains architecture size while retaining flexibility, and the genetic algorithm iteratively evolves and evaluates candidate architectures.

3) Number of Architecture-based Parameters:

  • Most search-space architectures have fewer than 0.4 million parameters, compared with normal retinal-segmentation architectures having several or dozens of millions.The search space caps intermediate nodes at five per block and convolution channels at 20.Source: 3) Number of Architecture-based… · p. 5

B. Evolutionary Algorithm

  • Genetic U-Net starts from a random population and evolves it through crossover, mutation, and selection over T generations.Each population individual represents an architecture, and its fitness depends on performance in the application.Source: B. Evolutionary Algorithm · p. 5
  • New individuals are evaluated by training their encoded architectures from scratch on the provided dataset.Source: B. Evolutionary Algorithm · p. 5

1) Crossover Operation:

The genetic operators use difference-guided multi-point crossover and bitwise mutation to produce and vary candidate architectures.

1) Crossover Operation:

  • Multi-point crossover exchanges information between individuals, and the method selects relatively different parents using a normalized Hamming-distance threshold.Parents are chosen by binary tournament; after ten unsuccessful reselections, the last pair is used.Source: 1) Crossover Operation · p. 5
  • Difference-guided crossover reselects parent pairs until their normalized Hamming distance exceeds threshold μ or ten reselections have occurred.Source: 1) Crossover Operation · p. 5

2) Mutation:

  • Offspring undergo mutation with probability p_m, while each bit flips independently with probability p_b, which is relatively small, such as 0.05.The stated purpose is to promote population diversity and prevent trapping in a local optimum, while limiting how much mutation alters an individual.Source: 2) Mutation · p. 5

3) Environmental Selection:

Environmental selection combines preservation of top-performing individuals with tournament selection to maintain population diversity and size.

3) Environmental Selection:

  • Selecting only the top N individuals risks premature convergence through loss of population diversity, while tournament or roulette selection may miss the best individual.The authors therefore combine elitist and non-elitist selection to improve convergence while maintaining diversity.Source: 3) Environmental Selection · p. 6
  • The five best individuals from the current population and offspring are placed directly into the next population.Source: 3) Environmental Selection · p. 6
  • The remaining population slots are filled by binary tournament selection, keeping the next population the same size as the current one.Source: 3) Environmental Selection · p. 6

4) Fitness Evaluation:

Each architecture is scored by its best validation F1 during a training and validation procedure that runs for up to 130 epochs.

4) Fitness Evaluation:

  • An individual's fitness is the validation F1 of the architecture it represents.The paper uses F1 as a comprehensive metric for retinal vessel segmentation that helps address imbalanced samples.Source: 4) Fitness Evaluation · p. 7
  • Before training, architecture weights receive He initialization, then training uses Lookahead with Adam as its base optimizer.Source: 4) Fitness Evaluation · p. 7
  • After 80 training epochs, validation occurs after each epoch through the 130th, and the best observed F1 becomes the individual's fitness.Source: 4) Fitness Evaluation · p. 7

IV. MATERIALS FOR EXPERIMENTS

The experiments use focal loss to address class imbalance, evaluate four public datasets, and assess segmentation with five metrics, generally within field-of-view masks.

A. Loss Function

  • Focal loss is used to address sample imbalance in fundus images, where vessel pixels make up less than 0.1 of pixels.The loss balances positive and negative samples and simple and hard samples.Source: A. Loss Function · p. 7

B. Datasets

  • Experiments use DRIVE, STARE, CHASE_DB1, and HRF, with dataset-specific training and testing splits and expert annotations as ground truth.Only the first expert’s annotations are used where multiple annotations are available; HRF has one expert’s annotations.Source: B. Datasets · p. 7, Table II · p. 7

C. Evaluation Metrics

  • Segmentation is evaluated as pixelwise vessel-versus-non-vessel classification using five metrics, generally calculated only inside field-of-view masks.The model produces a probability map, thresholded at 0.5 for evaluation.Source: C. Evaluation Metrics · p. 7, Table III · p. 7

V. EXPERIMENTS

Architectures searched on DRIVE were evaluated across four public datasets and against existing methods and U-shaped baselines. The discovered network led on F1 and AUROC while using fewer parameters and computational resources than the compared baselines.

V. EXPERIMENTS

  • The experiments first searched for architectures with a genetic algorithm and then trained the selected architectures from scratch to evaluate their segmentation performance.The search used a population of 20 over 50 generations, with crossover probability 0.9 and mutation probability 0.7.Source: §V · p. 8, A. Experimental Setup · p. 8

A. Experimental Setup

  • Architecture search used DRIVE, reserving five of its 20 training images for validation and 15 for training, then tested searched architectures on three other datasets.The second-stage training ran for 900 epochs; HRF images were randomly cropped to 1000 × 1000 for training and evaluated at full size.Source: A. Experimental Setup · p. 8
  • Search-stage training used flipping and random rotation, normalized images, and full-image inputs, with one image per iteration.The optimization used Lookahead and Adam with a learning rate initialized at 0.001.Source: A. Experimental Setup · p. 8

1) Comparison with Existing Methods:

  • The discovered architecture leads compared methods on F1 and AUROC across all four datasets, with 0.27 M parameters and successful transfer from DRIVE to the other datasets.The authors also report stronger sensitivity and competitive accuracy, without post-processing or special preprocessing.Source: Table IV · p. 8, Table V · p. 8, 1) Comparison with Existing Methods · p. 8

2) Comparison with the Baseline Models:

  • The discovered architecture outperforms original U-Net and FC-DenseNet on all four datasets under matched training settings.The comparison uses the original U-Net and FC-DenseNet as U-shaped baselines.Source: Table VIII · p. 9, 2) Comparison with the Baseline Models · p. 9
  • The discovered model has 0.27 million parameters, 41 billion MACs per forward pass, and a 1.2 MB model size, each below the reported U-Net and FC-DenseNet values.The reported reductions are 115×/34× for parameters, 3.2×/2.0× for MACs, and approximately 100×/32× for model size, respectively.Source: Table IX · p. 9, 2) Comparison with the Baseline Models · p. 9

C. Experimental Analysis of Architecture Search

The genetic search’s best fitness converged near generation 50, and inspection of top architectures identified recurring structures and operations associated with improved segmentation.

C. Experimental Analysis of Architecture Search

  • The best individual’s fitness converges at approximately generation 50, so the search stops there and selects the best individual from the final population.The selected individual is decoded into the discovered architecture.Source: C. Experimental Analysis of… · p. 9

1) Observations and Findings:

  • Top architectures commonly use blocks with the maximum allowed nodes, complex internal structure, skip connections, and two or three parallel branches.The parallel branches resemble InceptionNet blocks.Source: 1) Observations and Findings · p. 9
  • Instance normalization and pre-activation improve U-Net performance somewhat, their combination has a more notable effect, and pre-activation with Mish is slightly more effective than with ReLU.Changing only the activation to Mish does not improve U-Net.Source: 1) Observations and Findings · pp. 10–11
  • Operation sequence ID 11 occurs most frequently and, when substituted for U-Net’s basic convolutional layer, significantly improves DRIVE segmentation with little change in parameters and MACs.The substitution also surpasses existing methods listed for DRIVE except the discovered architecture.Source: 1) Observations and Findings · pp. 9–10, Figure 7 · p. 11, Table X · p. 11
  • The authors report that evolutionary results yield multiple competitive architectures and may provide principles for future retinal-vessel network design.Their analysis is presented as a potential knowledge base for further work.Source: 1) Observations and Findings · p. 11

D. Ablation Study

The experiments report stronger segmentation on high-resolution and challenging images, parameter-efficient performance, and greater stability with reduced training data; ablations favor difference-guided crossover and diversity-aware selection.

D. Ablation Study

  • Difference-guided crossover improved search performance, while the proposed selection scheme outperformed top N and elitist selection; top N selection led to premature convergence.The selection scheme combines elitism of size 5 with diversity; Fig. 8 shows trajectories across the compared settings.Source: D. Ablation Study · p. 11, Figure 8 · p. 12

A. Performance on Challenging Cases

  • On challenging images, the discovered architecture produced fewer lesion-area false positives and fewer missed cross-connected or tiny vessels than the competing models.Its vascular trees best matched the ground truth among the methods compared.Source: A. Performance on Challenging Cases · pp. 11–12

B. Performance on High-Resolution Fundus Images

C. Adjusting the Number of Architecture-based Parameters

  • At c=5, MACs and Params fell approximately 94%, while DRIVE F1 fell approximately 0.20% and AUROC approximately 0.13%.The adjusted model had about 0.06%/0.19% of the original U-Net/FC-DenseNet parameters and remained competitive with those models and other listed methods.Source: C. Adjusting the Number of… · p. 12, Table XI · p. 13

D. Performance using Reduced Training Data

E. Generalization Ability

The architecture searched on DRIVE was evaluated on cell-boundary segmentation using a 20-image training set and 10-image test set. It outperformed the compared models on five metrics, though the authors note that very challenging vessel cases may still fail.

E. Generalization Ability

  • On cell-boundary segmentation, the discovered architecture outperformed the other models on ACC, SE, SP, F1, and AUROC, with qualitative gains on irregular, tiny, and ambiguous boundaries.The EM dataset had 30 images; 20 were used for training and 10 for testing because test-set ground truth was not public.Source: E. Generalization Ability · p. 13, Table XIII · p. 13, Figure 11 · p. 14

F. Future work

  • The architecture may fail on very challenging vessel cases, and future work will investigate a better search space and test the method in additional scenarios.Source: F. Future work · pp. 13–14

VII. CONCLUSION

  • The conclusion reports that a condensed, flexible search space constrained parameter counts, while analysis identified effective operations and block patterns for vessel segmentation.The authors state that the resulting architecture reduces parameters and computational cost.Source: §VII · p. 14

VIII. APPENDIX

The appendix presents visualizations of the five highest-ranked discovered architectures.

VIII. APPENDIX

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