# Multilevel and Multiscale Deep Neural Network for Retinal Blood Vessel Segmentation

^{*}

## Abstract

**:**

## 1. Introduction

- A better pre-processing approach that highlights the blood vessels;
- Incorporation of multilevel and multiscale deep supervision (DS) networks that can dive deep into the final layers of the four convolutional layers with two different scale initializations i.e., 0.001 and 0.0002;
- Furthermore, the receptive field of this multilevel and multiscale deep supervision (DS) network is increased to refine and localize the blood vessels. Therefore, the probability map obtained consists clearly of blood vessels with fewer false predictions.

## 2. Materials and Methods

#### 2.1. Proposed Preprocessing

#### 2.2. Proposed Multilevel/Multiscale Deep Neural Network (DNN)

#### 2.2.1. Base Network

#### 2.2.2. Deep Supervision (DS_1) Layer

#### 2.2.3. Deep Supervision DS_2 Layer

^{3}) and DS_2 output activation is set to 16 (2

^{4}). Also after experimenting with other combinations in powers of 2, it is found that this (8, 16) combination of deeply supervised activation outputs is efficient (with minimal output size, lesser computation, and fewer learning features).

- DS_1 layer parameters = (3 × 3 × 32 + 1) × 32 = 9248
- DS_2 layer parameters = (3 × 3 × 64 + 1) × 64 = 36,928

#### 2.2.4. Increase in the Receptive Field of View of DS Layers

_{1}and sp

_{2}having a similar size as the input image. The dimensions of these two single plane outputs are symmetric after the receptive field is increased for multilevel/multiscale deep supervision layers. These symmetrical planes consist of refined blood vessel features. Finally, the proposed multilevel/multiscale DNN model outcome is obtained by concatenating both the single plane outputs and performing a 1 × 1 convolution on the concatenated feature maps. The output vessel probability map has improved blood vessel segmentation.

#### 2.3. Input Image Augmentation

- Preprocessing the image using the method described in Section 2.1;
- Rotation of the image to 15 different angles;
- Flipping every rotated image;
- Cropping the region of interest in the rotated and flipped images;
- Scaling the rotated and flipped input image to 0.5 and 1.5, respectively.

#### 2.4. Loss Function and Optimization

_{n}is the input dataset with an image of size 562 × 562. Q

_{n}is the corresponding binary ground truth label of the input. Q

_{n}is given in Equation (3). N refers to the total number of input training images i.e., 2880 images.

_{obj}(W

_{p}). It is expressed in Equation (4).

_{p}) is the loss function. Class balancing cross entropy loss function is chosen for training the proposed network. This loss is chosen since more than 80% of pixels are the background while the remaining are the vessel pixels. Let W

_{p}denote the weights of all the regular network layer parameters that are used for backpropagation. After dropping the subscript n in P

_{n}and Q

_{n}, the loss function L(W

_{p}) is calculated for all pixels in the training image and the segmented vessel ground truth. The loss function L(W

_{p}) is expressed in Equation (5).

_{+}| and |Q

_{−}| denotes the foreground and background ground truth label sets respectively. Pr(·) in Equation (5) is obtained by applying a sigmoid function to the activations of the final 1 × 1 convolution layer. The SGD solver is adopted to minimize the objective function. SGD iteratively updates the weight parameters toward the direction of the gradient of the loss function until the minimum is reached. It helps to obtain a robust vessel probability map.

## 3. Results

#### 3.1. Training

^{−8}, weight decay is set as 0.0002 and momentum as 0.9 with an iteration count of 18,000. The proposed DNN model is trained and tested using Quadro M4000 GPU. SGD solver is used to optimize the weights in the network. CAFFE accumulates gradients over iteration size × batch size. To complete one epoch, this network takes 180 iterations (i.e., total no. of images/(iteration size × batch size)).

#### 3.2. Testing

#### 3.3. Qualitative Analysis

#### 3.4. Quantitative Analysis

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**The argument of maxima of output activations for the eight vessel-specific feature maps from the four convolution layers.

**Figure 5.**The argument of maxima of output activations for the 16 vessel-specific feature maps from the four convolution layers.

**Figure 6.**A pictorial view of the increase in receptive field size with 3 × 3 filters and no padding on a 9 × 9 input.

**Figure 7.**Blood vessel segmentation results obtained using the proposed DNN model in the Digital Retinal Images for Vessel Extraction (DRIVE) dataset.

**Figure 8.**Blood vessel segmentation results obtained using the proposed DNN model in the STructured Analysis of the Retina (STARE) dataset.

**Figure 9.**Blood vessel segmentation results obtained using the proposed DNN model in the High-Resolution Fundus (HRF) dataset.

**Figure 10.**First row depicts the real-world retinal images and the second row shows the corresponding blood vessel probability maps obtained using the proposed DNN model.

**Figure 11.**Qualitative analysis of the blood vessel segmented results in DRIVE, STARE and HRF datasets.

**Figure 12.**Plot of receiver operating characteristic (ROC) for the retinal DRIVE, STARE and HRF datasets.

**Figure 14.**(

**a**–

**d**) Vessel probability map for mean value subtracted images and the proposed preprocessed input images before and after the increase in the receptive field at the 18,000

^{th}iteration, (

**e**) ground truth image.

Formation of DS_1 Layer | Size [Width, Height, Depth] | Formation of DS_2 Layer | Size [Width, Height, Depth] |
---|---|---|---|

$\begin{array}{l}\langle {[Conv1\_2]}_{8}\rangle \\ \langle {[Conv2\_2]}_{8}\&{[DeConv2\_2]}_{8}\rangle \\ \langle {[Conv3\_3]}_{8}\&{[DeConv3\_3]}_{8}\rangle \\ \langle {[Conv4\_3]}_{8}\&{[DeConv4\_3]}_{8}\rangle \end{array}$ | $\begin{array}{l}\langle \left[562\text{\hspace{0.17em}}562\text{\hspace{0.17em}}8\right]\rangle \\ \langle \left[564\text{\hspace{0.17em}}564\text{\hspace{0.17em}}8\right]\rangle \\ \langle \left[568\text{\hspace{0.17em}}568\text{\hspace{0.17em}}8\right]\rangle \\ \langle \left[576\text{\hspace{0.17em}}576\text{\hspace{0.17em}}8\right]\rangle \end{array}$ | $\begin{array}{l}\langle {[Conv1\_2]}_{16}\rangle \\ \langle {[Conv2\_2]}_{16}\&{[DeConv2\_2]}_{16}\rangle \\ \langle {[Conv3\_3]}_{16}\&{[DeConv3\_3]}_{16}\rangle \\ \langle {[Conv4\_3]}_{16}\&{[DeConv4\_3]}_{16}\rangle \end{array}$ | $\begin{array}{l}\langle \left[562\text{\hspace{0.17em}}562\text{\hspace{0.17em}}16\right]\rangle \\ \langle \left[564\text{\hspace{0.17em}}564\text{\hspace{0.17em}}16\right]\rangle \\ \langle \left[568\text{\hspace{0.17em}}568\text{\hspace{0.17em}}16\right]\rangle \\ \langle \left[576\text{\hspace{0.17em}}576\text{\hspace{0.17em}}16\right]\rangle \end{array}$ |

Crop | $\begin{array}{l}\langle \left[562\text{\hspace{0.17em}}562\text{\hspace{0.17em}}8\right]\rangle \\ \langle \left[562\text{\hspace{0.17em}}562\text{\hspace{0.17em}}8\right]\rangle \\ \langle \left[562\text{\hspace{0.17em}}562\text{\hspace{0.17em}}8\right]\rangle \\ \langle \left[562\text{\hspace{0.17em}}562\text{\hspace{0.17em}}8\right]\rangle \end{array}$ | Crop | $\begin{array}{l}\langle \left[562\text{\hspace{0.17em}}562\text{\hspace{0.17em}}16\right]\rangle \\ \langle \left[562\text{\hspace{0.17em}}562\text{\hspace{0.17em}}16\right]\rangle \\ \langle \left[562\text{\hspace{0.17em}}562\text{\hspace{0.17em}}16\right]\rangle \\ \langle \left[562\text{\hspace{0.17em}}562\text{\hspace{0.17em}}16\right]\rangle \end{array}$ |

Concatenate (DS_1) | $\left[562\text{\hspace{0.17em}}562\text{\hspace{0.17em}}32\right]$ | Concatenate (DS_2) | $\left[562\text{\hspace{0.17em}}562\text{\hspace{0.17em}}64\right]$ |

**Table 2.**Layers in the proposed DNN with their respective sizes, number of activation maps and weights.

Layers in the Proposed DNN | Output Size [Width, Height, Depth] | Activation Maps | Parameters (Weights) |
---|---|---|---|

Input image | [562 562 3] | 3 planes | |

Conv 1_1 | [562 562 64] | 64 | (3 × 3 × 3 + 1) × 64 = 1792 |

Conv 1_2 | [562 562 64] | 64 | (3 × 3 × 64 + 1) × 64 = 36,928 |

Max pooling | [281 281 64] | 64 | 0 |

Conv 2_1 | [281 281 128] | 128 | (3 × 3 × 64 + 1) × 128 = 73,856 |

Conv 2_2 | [281 281 128] | 128 | (3 × 3 × 128 + 1) × 128 = 147,584 |

Max pooling | [141 141 128] | 128 | 0 |

Conv 3_1 | [141 141 256] | 256 | (3 × 3 × 128 + 1) × 256 = 295,168 |

Conv 3_2 | [141 141 256] | 256 | (3 × 3 × 256 + 1) × 256 = 590,080 |

Conv 3_3 | [141 141 256] | 256 | (3 × 3 × 256 + 1) × 256 = 590,080 |

Max pooling | [71 71 256] | 256 | 0 |

Conv 4_1 | [71 71 512] | 512 | (3 × 3 × 256 + 1) × 512 = 1,180,160 |

Conv 4_2 | [71 71 512] | 512 | (3 × 3 × 512 + 1) × 512 = 2,359,808 |

Conv 4_3 | [71 71 512] | 512 | (3 × 3 × 512 + 1) × 512 = 2,359,808 |

DS_1 layer | [562 562 32] | (8 × 4 = 32) | [(3 × 3 × 64 + 1) × 8 + (3 × 3 × 128 + 1) × 8 + (3 × 3 × 256 + 1) × 8 + (3 × 3 × 512 + 1) × 8] = 69,152 |

DS_2 layer | [562 562 64] | (16 × 4 = 64) | [(3 × 3 × 64 + 1) × 16 + (3 × 3 × 128 + 1) × 16 + (3 × 3 × 256 + 1) × 16 + (3 × 3 × 512 + 1) × 16] = 138,304 |

Conv1_DS_8/16 layer | [562 562 32/64] | 32/64 | (3 × 3 × 32 + 1) × 32 = 9248/3 × 3× 32 + 1) × 64 = 18,496 |

Conv2_DS_8/16 layer | [562 562 32/64] | 32/64 | (3 × 3 × 32 + 1) × 32 = 9248/3 × 3 × 32 + 1) × 64 = 18,496 |

sp_{1}/sp_{2} | [562 562 1/1] | 1/1 | (1 × 1 × 32 + 1) × 1 = 33/(1 × 1 × 64 + 1) × 1 = 65 |

Final 1 × 1 conv output | [562 562 1] | 1 | (1 × 1 × 2 + 1) × 1 = 3 |

Method | Author/Year/Ref. | Metrics Obtained from DRIVE Dataset | Metrics Obtained from STARE Dataset | ||||||
---|---|---|---|---|---|---|---|---|---|

SN | SP | Acc | AUC | SN | SP | Acc | AUC | ||

Ophthalmologist | 0.7763 | 0.9723 | 0.947 | - | 0.8951 | 0.9384 | 0.9348 | - | |

Matched filter | Chakraborti et al. (2014) [17] | 0.7205 | 0.9579 | 0.9370 | 0.9419 | 0.6786 | 0.9586 | 0.9379 | - |

Singh, Srivatsava (2016) [18] | 0.7594 | 0.9708 | 0.9522 | 0.9287 | 0.7939 | 0.9376 | 0.9270 | 0.9140 | |

Multi-scale approach | Saffarzadeh et al. (2014) [22] | - | - | 0.9387 | 0.9303 | - | - | 0.9483 | 0.9431 |

Zhang, Fisher, et al. (2015) [23] | 0.7812 | 0.9668 | 0.9504 | - | - | - | - | - | |

Region growing method | Lazar and Hajdu (2015) [25] | 0.7646 | 0.9723 | 0.9458 | - | 0.7248 | 0.9751 | 0.9492 | - |

Roychowdhury et al. (2015) [26] | 0.739 | 0.978 | 0.949 | 0.967 | 0.732 | 0.984 | 0.956 | 0.967 | |

Active contour model | Zhao, Rada, et al. (2015) [28] | 0.742 | 0.982 | 0.954 | 0.862 | 0.780 | 0.978 | 0.956 | 0.874 |

Zhao, Zhao, et al. (2017) [29] | 0.782 | 0.979 | 0.957 | 0.886 | 0.789 | 0.978 | 0.956 | 0.885 | |

Unsupervised method | Kande et al. (2010) [30] | - | - | 0.8911 | 0.9518 | - | - | 0.8976 | 0.9298 |

Allen et al. (2011) [31] | - | - | 0.9342 | - | - | - | - | ||

Supervised method | Aslani and Sarnel (2016) [35] | 0.7545 | 0.9801 | 0.9513 | 0.9682 | 0.7556 | 0.9837 | 0.9605 | 0.9789 |

Zhang, Chen, et al. (2017) [36] | 0.7861 | 0.9712 | 0.9466 | 0.9703 | 0.7882 | 0.9729 | 0.9547 | 0.9740 | |

Deep learning method | Li et al. (2016) [38] | 0.7569 | 0.9816 | 0.9527 | 0.9738 | 0.7726 | 0.9844 | 0.9628 | 0.9879 |

Liskowski and Krawiec (2016) [39] | 0.7520 | 0.9806 | 0.9515 | 0.9710 | 0.8145 | 0.9866 | 0.9696 | 0.9880 | |

Fu et al. (2016) [42] | 0.7294 | - | 0.947 | - | 0.714 | - | 0.9545 | - | |

Maninis et al. (2016) [43] | 0.9497 | 0.9377 | 0.9386 | 0.9862 | 0.9403 | 0.9552 | 0.9543 | 0.9748 | |

Mo and Zhang (2017) [44] | 0.7779 | 0.9780 | 0.9521 | 0.9782 | 0.8147 | 0.9844 | 0.9674 | 0.9885 | |

Zhou et al. (2017) [45] | 0.8078 | 0.9674 | 0.9469 | - | 0.8065 | 0.9761 | 0.9585 | - | |

Chen (2017) [46] | 0.7426 | 0.9735 | 0.9453 | 0.9516 | 0.7295 | 0.9696 | 0.9449 | 0.9557 | |

Yan et al. (2018) [47] | 0.7631 | 0.9820 | 0.9538 | 0.9750 | 0.7735 | 0.9857 | 0.9638 | 0.9833 | |

Proposed method | 0.8282 | 0.9738 | 0.9609 | 0.9786 | 0.8979 | 0.9701 | 0.9646 | 0.9892 |

DNN Framework | Preprocessed with Mean Value Subtraction | Preprocessed with the Proposed Preprocessing | ||||
---|---|---|---|---|---|---|

SN | SP | Acc | SN | SP | Acc | |

Front end: 4 stages of VGG-16Fine-tuning phase: DS_1 and DS_2 layers with a conv1_DS_8/16 layer | 0.8474 | 0.9652 | 0.9547 | 0.8428 | 0.9677 | 0.9560 |

Front end: 4 stages of VGG-16Fine-tuning phase: DS_1 and DS_2 layers with conv1_DS_8/16 & conv2_DS_8/16 layers (our model) | 0.9058 | 0.9514 | 0.9472 | 0.8282 | 0.9738 | 0.9609 |

DNN Framework | Preprocessed with Mean Value Subtraction | Preprocessed with the Proposed Preprocessing | ||||
---|---|---|---|---|---|---|

SN | SP | Acc | SN | SP | Acc | |

Front end: 4 stages of VGG-16Fine-tuning phase: DS_1 and DS_2 layers with a conv1_DS_ 8/16 layer | 0.6581 | 0.9581 | 0.9379 | 0.9199 | 0.9630 | 0.9599 |

Front end: 4 stages of VGG-16Fine-tuning phase: DS_1 and DS_2 layers with conv1_DS_8/16 and conv2_DS_8/16 layers (our model) | 0.4184 | 0.9875 | 0.9461 | 0.8979 | 0.9701 | 0.9645 |

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## Share and Cite

**MDPI and ACS Style**

Samuel, P.M.; Veeramalai, T.
Multilevel and Multiscale Deep Neural Network for Retinal Blood Vessel Segmentation. *Symmetry* **2019**, *11*, 946.
https://doi.org/10.3390/sym11070946

**AMA Style**

Samuel PM, Veeramalai T.
Multilevel and Multiscale Deep Neural Network for Retinal Blood Vessel Segmentation. *Symmetry*. 2019; 11(7):946.
https://doi.org/10.3390/sym11070946

**Chicago/Turabian Style**

Samuel, Pearl Mary, and Thanikaiselvan Veeramalai.
2019. "Multilevel and Multiscale Deep Neural Network for Retinal Blood Vessel Segmentation" *Symmetry* 11, no. 7: 946.
https://doi.org/10.3390/sym11070946