# Automatic Segmentation of the Retinal Nerve Fiber Layer by Means of Mathematical Morphology and Deformable Models in 2D Optical Coherence Tomography Imaging

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

- Preprocessing to reduce the speckle noise and undesired artifacts in peripapillary 2D B-scan OCT images. This filtering is mainly performed by morphological operators.
- Peak detection on positive and negative part of the vertical gradient. This column-wise process (1D scenario) provides a rough detection of the layer’s boundaries.
- Reduction of possible discontinuities in previous coarse detection by processing adjacent columns (2D scenario) with a sliding window low-pass filter.
- Refinement of previous result by the imposition of the physical characteristics of biological tissues. The properties of elasticity and rigidity of the solution are incorporated by using a deformable model (in a 2D scenario).

#### 2.1. Materials: OCT Database

#### 2.2. Preprocessing: Mathematical Morphology

#### 2.3. Boundary Segmentation: Active Contours

#### 2.4. RNFL Layer Segmentation Process

#### 2.5. Segmentation of Boundary #1-UB

#### 2.6. Segmentation of Boundary #2-AB

#### 2.7. Segmentation of Boundary #3-LB

#### 2.8. RNFL Thickness Calculation

## 3. Results

## 4. Discussion

#### 4.1. Robustness against Parameter Variations and Speckle Noise

#### 4.2. Analysis of the Performance of the Methods

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## Correction Statement

## References

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**Figure 1.**Peripapillary B-scan OCT centered on the optic disc and its relative axial position with respect to a retinal fundus image. Screenshot taken from the Spectralis OCT device. I, S, N, and T stand for inferior, superior, nasal, and temporal, respectively.

**Figure 2.**Screenshot provided by the Spectralis software version 6.9.4.0. From left to right and top to bottom: Retinal fundus photography centered on the optic disc (the yellow circle indicates the location of the peripapillary B-scan, which is shown on the right with the segmentation of the RNFL); 2D peripapillary B-scan OCT on Cartesian coordinates; estimated mean values for RNFL layer thickness for the temporal (T), temporal superior (TS), nasal superior (NS), nasal (N), nasal inferior (NI), and temporal inferior (TI) sectors, as well as the overall mean (G); rectified outline of the RNFL with estimated thickness and reference values according to the database European Descent (2009).

**Figure 3.**Example of a peripapillary B-scan OCT image with the manual segmentation of the layer of interest RNFL and description of the sectors: T, TS, NS, N, NI, and TI.

**Figure 4.**Layers of the retina from top to bottom. RNFL: retinal nerve fiber layer; GCL: ganglion cell layer; IPL: inner plexiform layer; INL: inner nuclear layer; OPL: outer plexiform layer; and ONL: outer nuclear layer. Boundary delineation in the segmentation process. #1-UB: upper boundary of the RNFL; #2-AB: auxiliary boundary corresponding to the lower boundary of the ONL; #3-LB, lower boundary of the RNFL. The dashed boxes exemplify some of the artifacts of the layers.

**Figure 5.**Retinal fundus imaging of the eye under analysis. The green circumference represents the OCT analysis circumference centered on the optic nerve, marked with a

**+**. The numbers represent the vessels crossing this analysis circumference.

**Figure 6.**Intensity inhomogeneities and boundary artifacts caused by shadows cast by blood vessels. The numbers identify each of the vessels crossing the circular ray tracing depicted in Figure 5.

**Figure 9.**Selection of the #2-AB vertical position. On the left, the positive vertical gradient image ${I}_{9}^{\#2}$. On the right, 1D profile of the dashed column of ${I}_{9}^{\#2}$.

**Figure 11.**Representation of the filter used in the first stage of blood vessel suppression: (

**a**) space domain representation of the filter or point spread function (PSF), and (

**b**) frequency domain representation or transfer function.

**Figure 13.**Selection of the #3-LB vertical position. On the left, the negative vertical gradient image ${I}_{9}^{\#3}$. On the right, 1D profile of the dashed column of ${I}_{9}^{\#3}$.

**Figure 14.**RNFL thickness measurements for each sector of the peripapillary circumference. On the left, diagram detailing the value of the average thickness of the RNFL in each sector of the eye. On the right side, representation of the borders #1-UB and #3-LB, and the average RNFL thickness in these sectors.

**Figure 15.**Segmentation results for the right eye of (

**a**–

**d**) patient 2, (

**e**–

**h**) patient 20, and (

**i**–

**l**) patient 69.

**Figure 16.**Results of changing the radius of the structuring element from ${\u25ef}_{7}$ to ${\u25ef}_{5}$ and ${\u25ef}_{9}$, used in the steps illustrated in Figure 7b–d for the delineation of #1-UB.

**Figure 17.**Results of changing the radius of the structuring element from ${\u25ef}_{3}$ to ${\u25ef}_{1}$ and ${\u25ef}_{7}$, used in the steps illustrated in Figure 8h–k for the delineation of #2-AB.

**Figure 18.**Results of testing the robustness against synthetically incorporated speckle noise from ${\sigma}^{2}=0.001$ to ${\sigma}^{2}=0.1$ ($\sigma =0.031$ to $\sigma =0.316$). The NOLSE estimation [71] of the speckle noise for the raw image is ${\sigma}^{2}=0.0000381$ ($\sigma =0.0062$).

Eye | Healthy | Suspicious | Unhealthy |
---|---|---|---|

Left | 88 | 31 | 43 |

Right | 97 | 32 | 38 |

Sector | Polar (Degrees) | Cartesian (Pixels) | ||
---|---|---|---|---|

Min | Max | Min | Max | |

Temporal (T) | 0° | 45° | 1 | 96 |

Temporal Superior (TS) | 45° | 90° | 97 | 192 |

Nasal Superior (NS) | 90° | 135° | 193 | 288 |

Nasal (N) | 135° | 225° | 289 | 480 |

Nasal Inferior (NI) | 225° | 270° | 481 | 576 |

Temporal Inferior (TI) | 270° | 315° | 577 | 672 |

Temporal (T) | 315° | 360° | 673 | 768 |

**Table 3.**Dice similarity coefficient calculated comparing the manual segmentation of the expert with results of the proposed method and H-DLpNet method for each sector of the eye and for the whole layer, G, for the right eye of patients 2, 20, and 69.

Dice Similarity Coefficient | ||||||
---|---|---|---|---|---|---|

Patient 2 | Patient 20 | Patient 69 | ||||

Sectors | Proposed | H-DLpNet | Proposed | H-DLpNet | Proposed | H-DLpNet |

Method | Method | Method | ||||

TS | $0.974$ | $0.951$ | $0.943$ | $0.927$ | $0.899$ | $0.832$ |

T | $0.959$ | $0.927$ | $0.929$ | $0.857$ | $0.927$ | $0.887$ |

TI | $0.955$ | $0.954$ | $0.941$ | $0.926$ | $0.947$ | $0.950$ |

NS | $0.959$ | $0.912$ | $0.818$ | $0.873$ | $0.851$ | $0.820$ |

N | $0.934$ | $0.902$ | $0.896$ | $0.893$ | $0.895$ | $0.850$ |

NI | $0.965$ | $0.914$ | $0.943$ | $0.926$ | $0.924$ | $0.886$ |

G | $0.956$ | $0.927$ | $0.916$ | $0.901$ | $0.908$ | $0.874$ |

**Table 4.**RNFL thickness (mean and standard deviation in µm) provided by the proposed method, the H-DLpNet method and Spectralis for each sector of the eye (TS, T, TI, NS, N, and NI) as well as for the whole layer (G).

Sectors | RNFL Thickness Measurement (µm) | |||
---|---|---|---|---|

Proposed | H-DLpNet | Spectralis | ||

Left eye | TS | 122.8 ± 23.6 | 128.5 ± 27.4 | 121.7 ± 30.5 |

T | 79.0 ± 11.6 | 70.7 ± 13.9 | 67.3 ± 13.3 | |

TI | 136.2 ± 30.2 | 132.7 ± 31.8 | 127.4 ± 34.8 | |

NS | 116.0 ± 21.4 | 111.4 ± 28.1 | 105.5 ± 30.2 | |

N | 86.5 ± 15.7 | 74.7 ± 16.4 | 68.7 ± 19.1 | |

NI | 114.2 ± 23.6 | 109.1 ± 27.1 | 102.2 ± 28.0 | |

G | 102.5 ± 13.2 | 96.6 ± 17.0 | 90.9 ± 17.8 | |

Right eye | TS | 126.5 ± 24.9 | 129.8 ± 25.5 | 125.2 ± 29.5 |

T | 80.9 ± 14.0 | 72.7 ± 15.6 | 68.6 ± 15.6 | |

TI | 133.4 ± 26.0 | 131.9 ± 29.9 | 126.0 ± 34.3 | |

NS | 112.0 ± 23.5 | 106.0 ± 27.6 | 98.6 ± 27.4 | |

N | 90.9 ± 14.9 | 79.6 ± 16.3 | 72.8 ± 17.9 | |

NI | 113.4 ± 23.5 | 105.9 ± 25.8 | 102.6 ± 27.3 | |

G | 103.6 ± 13.6 | 97.3 ± 16.7 | 92.0 ± 17.8 |

**Table 5.**Absolute thickness error (mean and standard deviation in µm) calculated as the difference of the RNFL thickness provided by the proposed approach to both H-DLpNet and Spectralis methods. Relative error (mean and standard deviation) computed for each sector as the absolute error divided by the thickness value determined by the proposed method. These values are calculated for each sector of the eye (TS, T, TI, NS, N, and NI) as well as for the whole layer (G).

Sectors | Absolute Thickness Errors (µm) | Relative Thickness Errors | |||
---|---|---|---|---|---|

H-DLpNet | Spectralis | H-DLpNet | Spectralis | ||

Left eye | TS | 13.1 ± 11.8 | 14.5 ± 12.9 | 0.12 ± 0.11 | 0.13 ± 0.12 |

T | 8.3 ± 6.1 | 11.8 ± 7.8 | 0.11 ± 0.09 | 0.15 ± 0.10 | |

TI | 10.0 ± 18.1 | 11.9 ± 10.0 | 0.08 ± 0.08 | 0.10 ± 0.11 | |

NS | 12.3 ± 10.9 | 14.9 ± 12.6 | 0.11 ± 0.10 | 0.14 ± 0.12 | |

N | 11.7 ± 11.0 | 17.6 ± 13.3 | 0.13 ± 0.12 | 0.20 ± 0.14 | |

NI | 10.3 ± 9.2 | 13.5 ± 11.4 | 0.10 ± 0.09 | 0.13 ± 0.11 | |

G | 6.9 ± 6.1 | 10.8 ± 8.0 | 0.07 ± 0.07 | 0.11 ± 0.09 | |

Right eye | TS | 12.1 ± 10.4 | 12.8 ± 11.2 | 0.10 ± 0.10 | 0.11 ± 0.10 |

T | 8.3 ± 6.0 | 12.1 ± 7.9 | 0.11 ± 0.08 | 0.15 ± 0.10 | |

TI | 12.8 ± 11.0 | 15.2 ± 12.4 | 0.11 ± 0.10 | 0.13 ± 0.12 | |

NS | 10.1 ± 9.5 | 15.2 ± 13.5 | 0.10 ± 0.09 | 0.14 ± 0.12 | |

N | 11.3 ± 9.3 | 17.3 ± 12.9 | 0.13 ± 0.10 | 0.19 ± 0.14 | |

NI | 10.9 ± 9.6 | 13.0 ± 10.5 | 0.10 ± 0.09 | 0.12 ± 0.10 | |

G | 7.4 ± 6.4 | 10.4 ± 7.3 | 0.08 ± 0.07 | 0.11 ± 0.08 |

**Table 6.**Dice similarity coefficient (mean and standard deviation) calculated comparing the results of the proposed method and the H-DLpNet method for each sector of the eye and for the whole layer.

Sectors | Dice Similarity Coefficient | |
---|---|---|

H-DLpNet | ||

Left eye | TS | 0.895 ± 0.082 |

T | 0.918 ± 0.071 | |

TI | 0.921 ± 0.057 | |

NS | 0.898 ± 0.059 | |

N | 0.893 ± 0.078 | |

NI | 0.917 ± 0.057 | |

G | 0.908 ± 0.047 | |

Right eye | TS | 0.906 ± 0.059 |

T | 0.919 ± 0.053 | |

TI | 0.914 ± 0.074 | |

NS | 0.907 ± 0.054 | |

N | 0.902 ± 0.063 | |

NI | 0.917 ± 0.062 | |

G | 0.911 ± 0.047 |

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Berenguer-Vidal, R.; Verdú-Monedero, R.; Morales-Sánchez, J.; Sellés-Navarro, I.; del Amor, R.; García, G.; Naranjo, V.
Automatic Segmentation of the Retinal Nerve Fiber Layer by Means of Mathematical Morphology and Deformable Models in 2D Optical Coherence Tomography Imaging. *Sensors* **2021**, *21*, 8027.
https://doi.org/10.3390/s21238027

**AMA Style**

Berenguer-Vidal R, Verdú-Monedero R, Morales-Sánchez J, Sellés-Navarro I, del Amor R, García G, Naranjo V.
Automatic Segmentation of the Retinal Nerve Fiber Layer by Means of Mathematical Morphology and Deformable Models in 2D Optical Coherence Tomography Imaging. *Sensors*. 2021; 21(23):8027.
https://doi.org/10.3390/s21238027

**Chicago/Turabian Style**

Berenguer-Vidal, Rafael, Rafael Verdú-Monedero, Juan Morales-Sánchez, Inmaculada Sellés-Navarro, Rocío del Amor, Gabriel García, and Valery Naranjo.
2021. "Automatic Segmentation of the Retinal Nerve Fiber Layer by Means of Mathematical Morphology and Deformable Models in 2D Optical Coherence Tomography Imaging" *Sensors* 21, no. 23: 8027.
https://doi.org/10.3390/s21238027