Topological Similarity Index and Loss Function for Blood Vessel Segmentation

Blood vessel segmentation is one of the most studied topics in computer vision, due to its relevance in daily clinical practice. Despite the evolution the field has been facing, especially after the dawn of deep learning, important challenges are still not solved. One of them concerns the consistency of the topological properties of the vascular trees, given that the best performing methodologies do not directly penalize mistakes such as broken segments and end up producing predictions with disconnected trees. This is particularly relevant in graph-like structures, such as blood vessel trees, given that it puts at risk the characterization steps that follow the segmentation task. In this paper, we propose a similarity index which captures the topological consistency of the predicted segmentations having as reference the ground truth. We also design a novel loss function based on the morphological closing operator and show how it allows to learn deep neural network models which produce more topologically coherent masks. Our experiments target well known retinal benchmarks and a coronary angiogram database.