# Improving Glaucoma Diagnosis Assembling Deep Networks and Voting Schemes

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Convolutional Neural Networks

**h**that is finally classified by a set of fully-connected layers. The vectorial space of vectors

**h**is called latent space. Figure 2 shows the architecture of a CNN network.

- makes the input representations smaller and more manageable;
- reduces the number of parameters and computations in the network, therefore, controlling overfitting;
- increases the field of view of higher layers thus allowing more general features of the input image to be obtained;
- makes the network invariant to small transformations, distortions and translations in the input image: a small distortion in the input will not change the output of pooling, since we take the maximum/average value in a local neighborhood.

- helps us to obtain an object recognition method that is almost invariant under translation, which supposes a very powerful feature since we can detect objects in an image no matter where they are located.

- CNN lack of ability to be invariant to large transformations, distortions and translations in the input image. Although CNN solves this problem slightly by using max pooling and convolution, these are simply a bad approach to the solution;
- max pooling loses valuable information;
- the internal representation of a CNN does not take into account the spatial relationships between objects, nor the existing hierarchy between simple objects and the composite objects of which they are a part.

#### 2.2. CapsNets

**h**where an MLP network will try to solve the problem.

#### 2.3. Convolutional Autoencoders

**h**dimension use to be chosen lower than

**x**dimension and

**x**is perturbed by an additive noise obtaining the so-called Denoising AE (DAE), which can be stacked to build a deep network that provides multiple representation levels of the data (output of the hidden layers) where data can be easily classified. This is the Stacked DAE (SDAE) [9].

#### 2.4. Ensemble with K-NN Voting

**h**in latent spaces are classified by means of an MLP network. The output $\mathbf{y}$ of the MLP is a C-dimensional vector, being C the number of classes of the problem. In this way, the prediction of the ensemble for the i-th input sample is given by

**w**vectors can be considered as probabilities because the sum of theirs components is one, so vector $\mathbf{y}$ can also be easily normalized in such a way that its components represent probabilities too.

## 3. Results and Discussion

#### 3.1. Fundus Images Datasets

#### 3.1.1. JOINT Dataset

#### 3.1.2. PAPILA Dataset

#### 3.2. Networks Architecture and Training

#### 3.2.1. CNN

#### 3.2.2. CapsNet

#### 3.2.3. CDAE

**h**was connected to a MLP with a hidden layer of 1024 neurons and an output layer with softmax activations. This joint network was then trained with Adam optimizer to minimize the Cross Entropy loss function for classification purposes.

#### 3.3. Experiments

#### 3.3.1. JOINT Dataset

#### 3.3.2. PAPILA Dataset

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

CNN | convolutional neural network |

CapsNet | Capsule Network |

CDR | Cup-to-Disk Ratio |

ML | Machine Learning |

DL | Deep Learning |

DNN | Deep Neural Network |

SDAE | Stacked Denoising Autoencoder |

MLP | Multilayer Perceptrons |

AE | Autoencoder |

CAE | Convolutional Autoencoder |

MSE | Mean Squared Errors |

CDAE | Convolutional Denoising Autoencoder |

ReLU | Rectified Linear Unit |

ROI | Region of Interest |

AWGN | Additive White Gaussian Noise |

AUC | Area Under the Curve |

ROC | Receiver Operating Characteristic |

CV | Cross Validation |

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**Figure 2.**CNN architecture showing the sequential convolutional and max pooling layers and the final MLP classification after a flatten operation.

**Figure 3.**CapsNet architecture showing the convolutional section (encoder), the latent space and MLP classifier.

**Figure 4.**Representation over an ocular fundus image of the tikckness measurement of neuroretinal rim in the four directions: Inferior (I), Superior (S), Nasal (N) and Temporal (T).

**Figure 5.**CAE architecture showing the convolutional encoder layers, the latent space and the deconvolutional decoder layers.

**Figure 6.**10-fold averaged ROC for positive class (Glaucoma) and each model working over JOINT dataset. (

**A**) is the Convolutional Neural Network, (

**B**) the Capsule Network, (

**C**) the Convolutional Denoising Autoencoder and (

**D**) the Ensemble with 10-NN Voting.

**Figure 7.**10-fold averaged ROC for each class and each model working over PAPILA dataset. Averaged ROC among classes for each model is also showed. (

**A**) is the Convolutional Neural Network, (

**B**) the Capsule Network, (

**C**) the Convolutional Denoising Autoencoder and (

**D**) the Ensemble with 10-NN Voting.

**Table 1.**Contents of JOINT dataset, that was built from fundus image ROIs taken from the proposal of Díaz-Pinto et al. [20]. The original source and number of retinal ROIs are also showed.

Source Dataset | Glaucoma | Normal | Total |
---|---|---|---|

Drishti-GS1 [21] | 70 | 31 | 101 |

RIM-ONE [22] | 194 | 261 | 455 |

sjchoi86-HRF [23] | 101 | 300 | 401 |

HRF [24] | 27 | 18 | 45 |

ACRIMA [25] | 396 | 309 | 705 |

JOINT dataset | 788 | 919 | 1707 |

**Table 2.**Models performance (mean ± standard deviation over a 10-fold CV) obtained with the JOINT dataset in the Glaucoma class. For each model, the best result is shown in bold.

AUC | Sensitivity | Specificity | |
---|---|---|---|

CNN | 0.97 ± 0.01 | 0.92 ± 0.02 | 0.96 ± 0.02 |

CapsNet | 0.97 ± 0.01 | 0.93 ± 0.02 | 0.95 ± 0.02 |

CDAE | 0.96 ± 0.01 | 0.89 ± 0.04 | 0.96 ± 0.02 |

Ensemble ($K=10$) | 0.98
± 0.01 | 0.94 ± 0.02 | 0.97 ± 0.02 |

**Table 3.**Models averaged performance (mean ± standard deviation over a 10-fold CV) obtained with the PAPILA dataset. For each model, the best result is shown in bold.

AUC | Sensitivity | Specificity | |
---|---|---|---|

CNN | 0.77 ± 0.11 | 0.77 ± 0.12 | 0.73 ± 0.10 |

CapsNet | 0.73 ± 0.13 | 0.74 ± 0.16 | 0.74 ± 0.14 |

CDAE | 0.77 ± 0.11 | 0.79 ± 0.15 | 0.73 ± 0.12 |

Ensemble ($K=10$) | 0.78 ± 0.11 | 0.81 ± 0.15 | 0.74 ± 0.09 |

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**MDPI and ACS Style**

Sánchez-Morales, A.; Morales-Sánchez, J.; Kovalyk, O.; Verdú-Monedero, R.; Sancho-Gómez, J.-L.
Improving Glaucoma Diagnosis Assembling Deep Networks and Voting Schemes. *Diagnostics* **2022**, *12*, 1382.
https://doi.org/10.3390/diagnostics12061382

**AMA Style**

Sánchez-Morales A, Morales-Sánchez J, Kovalyk O, Verdú-Monedero R, Sancho-Gómez J-L.
Improving Glaucoma Diagnosis Assembling Deep Networks and Voting Schemes. *Diagnostics*. 2022; 12(6):1382.
https://doi.org/10.3390/diagnostics12061382

**Chicago/Turabian Style**

Sánchez-Morales, Adrián, Juan Morales-Sánchez, Oleksandr Kovalyk, Rafael Verdú-Monedero, and José-Luis Sancho-Gómez.
2022. "Improving Glaucoma Diagnosis Assembling Deep Networks and Voting Schemes" *Diagnostics* 12, no. 6: 1382.
https://doi.org/10.3390/diagnostics12061382