**2. Materials and Methods**

The current SOTA formulates the JSCAV task as a single multi-class semantic segmentation problem. However, this approach leads to incomplete segmentation maps for veins and arteries, and does not directly provide vasculature segmentation maps.

**Citation:** Morano, J.; Hervella, A.S.; Novo, J.; Rouco, J. Deep Multi-Segmentation Approach for the Joint Classification and Segmentation of the Retinal Arterial and Venous Trees in Color Fundus Images. *Eng. Proc.* **2021**, *7*, 22. https://doi.org/10.3390/ engproc2021007022


Academic Editors: Joaquim de Moura, Marco A. González, Javier Pereira and Manuel G. Penedo

Published: 12 October 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

As an alternative, we present an approach that decomposes the joint task into three segmentation subtasks [7]. Each of these subtasks addresses the segmentation of one of three classes of interest: arteries, veins and the whole vascular tree. To implement this multi-segmentation (MS) approach, a deep neural network is trained end-to-end using a novel loss function: BCE3. This loss function computes the loss as the sum of the individual segmentation losses of the aforementioned classes. Each individual loss is computed as the binary cross-entropy (BCE) between the predicted probability map and the manually annotated segmentation map. This setting allows for the intuitive handling of vessel crossings, and directly provides precise and complete segmentation maps of the various vascular trees. It also allows for the direct detection of vessel crossings through the element-wise product of the predicted artery and vein maps.

To train and evaluate the networks in the JSCAV task, we employed the publicly available RITE dataset [8], which is composed of 40 color fundus images and their corresponding arteries, veins and vasculature segmentation masks. To facilitate training of the networks, we used the image preprocessing technique specified in [3], as well as online data augmentation. To validate our method, a U-Net network [9] was trained, using both the traditional and the MS approaches.

#### **3. Results and Conclusions**

Figure 1 shows an example of an RITE retinography and its arteries, veins, vessels and crossings segmentation maps predicted by a model trained using the MS approach. Figure 2 shows the details of the arteries, veins and vessels segmentation maps of the same retinography predicted by a model trained using the MS and the traditional approaches.

**Figure 1.** Example segmentation maps predicted by a model trained using the MS approach. From left to right: arteries, veins, vessels and crossings.

**Figure 2.** Examples of arteries, veins and vessels probability maps (in RGB) predicted by the models trained using the MS and the traditional approaches.

The ablation study performed in the RITE dataset shows that our method provides an adequate performance, especially in the segmentation of the different structures. Notably, the MS approach achieves a mean accuracy of 89.24 ± 0.73 in the classification of arteries and veins, and an AUC-ROC of 98.33 ± 0.04 in the segmentation of vessels; for its part, the traditional approach achieves 88.78 ± 0.53 and 98.07 ± 0.04, respectively.

In addition, the comparison with the SOTA works in the same dataset, depicted in Figure 3, clearly demonstrates that the presented method achieves competitive results in the discrimination of arteries and veins, while significantly enhancing the vascular segmentation.

**Figure 3.** ROC curves in the RITE dataset for the MS approach along with the point representations of the SOTA approaches for artery/vein classification (**left**) and vascular segmentation (**right**).

Therefore, the presented deep multi-segmentation method allows for the detection of more vessels and to better segment the different structures, while achieving competitive classification results. Furthermore, unlike previous approaches, the method allowsfor the straightforward detection of vessel crossings, as well as preserving the continuity of the arterial and venous vascular trees at these locations (see Figure 2).

**Author Contributions:** Conceptualization, Á.S.H., J.N. and J.R.; methodology, Á.S.H. and J.M.; software, Á.S.H. and J.M.; validation, Á.S.H. and J.M.; formal analysis, Á.S.H. and J.M.; investigation, J.M.; resources, J.N. and J.R.; data curation, Á.S.H. and J.M.; writing—original draft preparation, J.M.; writing—review and editing, J.M. and J.N.; visualization, J.M.; supervision, J.N. and J.R.; project administration, J.N. and J.R.; funding acquisition, J.N. and J.R. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was funded by Instituto de Salud Carlos III, Government of Spain, and the European Regional Development Fund (ERDF) of the European Union (EU) through the DTS18/00136 research project; Ministerio de Ciencia e Innovación, Government of Spain, through the RTI2018- 095894-B-I00 and PID2019-108435RB-I00 research projects; Axencia Galega de Innovación (GAIN), Xunta de Galicia, ref. IN845D 2020/38; Xunta de Galicia and European Social Fund (ESF) of the EU through the predoctoral grant contracts ED481A-2017/328 and ED481A 2021/140; Consellería de Cultura, Educación e Universidade, Xunta de Galicia, through Grupos de Referencia Competitiva, grant ref. ED431C 2020/24; CITIC, Centro de Investigación de Galicia ref. ED431G 2019/01, is funded by Consellería de Educación, Universidade e Formación Profesional, Xunta de Galicia, through the ERDF (80%) and Secretaría Xeral de Universidades (20%).

**Conflicts of Interest:** The authors declare no conflict of interest.

