Regularizer based on Euler characteristic for retinal blood vessel segmentation

Segmentation of retinal blood vessels is important for the analysis of diabetic retinopathy (DR). Existing methods do not prioritize the small and disconnected vessels for DR. With the aim of paying attention to the small and disconnected vessel regions, this study introduced Euler characteristics (EC) from topology to calculate the number of isolated objects on segmented vessel regions, which is the key contribution of this study. In addition, we utilized the number of isolated objects in a U-Net-like deep convolutional neural network (CNN) architecture as a regularizer to train the network for improving the connectivity between the pixels of the vessel regions. The proposed network performance of the regularizer based on EC in reconstructing vessel regions is compared over the network without our regularizer. Furthermore, the capacity of the proposed regularizer approach in enhancing the smoothness and pixel connectivity of the vessels is compared with graph-based smoothing (GS) and combined GS with isolated objects (GISO) regularizers for delineating blood vessel regions. The proposed approach achieved the area under the curve value of 0.982, which is much higher than the state-of-the-arts, and thus it is suggested that the proposed system could support accuracy and reliability in decision-making for DR detection.